Category Archives: Fusion Science

the science behind fusion energy

Nuclear Fusion

UCSD Physics Dept Tom Murphy

Ah, fusion. Long promised, both on Do the Math and in real life, fusion is regarded as the ultimate power source—the holy grail—the “arrival” of the human species. Talk of fusion conjures visions of green fields and rainbows and bunny rabbits…and a unicorn too, I hear. But I strike too harsh a tone in my jest. Fusion is indeed a stunningly potent source of energy that falls firmly on the reality side of the science fiction divide—unlike unicorns. Indeed, fusion has been achieved (sub break-even) in the lab, and in the deadliest of bombs. On the flip side, fusion has been actively pursued as the heir-apparent of nuclear fission for over 60 years. We are still decades away from realizing the dream, causing many to wonder exactly what kind of “dream” this is.

Our so-far dashed expectations seem incompatible with our sense of progress. Someone born in 1890 would have seen horses give way to cars, airplanes take to the skies, the invention of radio, television, and computers, development of nuclear fission, and even humans walking on the Moon by the age of 79. Anyone can extrapolate a trajectory, and this trajectory intoned that fusion would arrive any day—along with colonies on Mars. Yet we can no longer buy a ticket to cross the Atlantic at supersonic speeds, and the U.S. does not have a human space launch capability any more. Even so, fusion remains “just around the corner” in many minds.

I am sympathetic to delayed predictions, and the fact that fusion has failed to deliver on the promise that it’s “just around the corner” for decades does not mean that it will never arrive. I can compare this to Malthus’ insight that exponential population growth was on a collision course with finite agricultural capability, or to various warnings about collapse along the way. Just because the predictions have not yet been satisfied does not mean that they will not be someday. In fact, the two divergent predictions become related. If we can manage to hold it together this century and maintain a high-tech civilization during our forced transition off of fossil fuels, it becomes far more likely that we will get to the point of employing fusion. If, on the other hand, we overshoot and collapse, we may descend too far to viably pursue fusion this century.

Fusion by the Numbers

What’s fusion all about, anyhow? Let’s come at it with numbers. We saw in the post on nuclear fission that allowing a heavy nucleus like uranium to split into two comparable pieces resulted in the sum of the resultant masses being less than the initial mass. The missing mass emerges as (kinetic) energy according to E = ?mc², where ?m is the change in mass, and c ˜ 3×108 m/s is the speed of light. In essence, some of the nuclear binding energy invested the heavy nucleus—which actually reduces the net mass of the nucleus—has been liberated.

To understand this better, consider the fact that a single neutron has a mass of 1.08665 atomic mass units (amu: 1.66×10-27 kg), and a neutral hydrogen atom (one proton plus one electron, minus a trivial amount of electromagnetic binding energy: just 14 parts per billion) has a mass of 1.007825 amu. To make 235U, we take 92 hydrogen atoms, add 143 neutrons, and stir. Without considering nuclear binding energy, the sum would be 236.96 amu. Yet the neutral 235U atom has a mass of 235.044 amu. The “missing” 1.92 amu is the nuclear energy that would be released by building (fusing) this ensemble.

Think of it this way: when a nucleus grabs hold of a passing neutron, the deathly-strong nuclear grip slams the neutron into the nucleus, momentarily giving it kinetic energy. Initially, the nucleus jiggles like jello in an excited state, before releasing this energy (via gamma ray, or fast electron in beta decay, etc.) back to the world. In releasing this energy, its mass must decrement in deference to Einstein’s most famous relation. In this way, every nucleon added (proton or neutron) contributes its direct mass to the nucleus, but then subtracts about 0.008 amu of binding energy, on average—in effect weighing in at only 0.992 amu-a-pop.

Of fundamental importance in appreciating the energy gains inherent in fusion and fission processes is the chart of binding energy per nucleon. The graph below plots the binding energy per nucleon in units of MeV, where 1 MeV = 1.6×10-13 J and is equivalent to 0.00107 amu via E = mc². Or, roughly speaking, 1 MeV is one-thousandth the mass of a single nucleon. The horizontal axis of the plot is the total number of nucleons—protons plus neutrons—in the nucleus.

Higher binding energy translates to smaller net mass, compared to the dumb sum of constituent masses. So the higher on the curve, the more energy can be given up in building that nucleus. Iron sits at the top (with plenty of company in neighbors like nickel). On the left side, adding pieces together constitutes a net energy gain (fusion), while on the right, one must tear nuclei apart (fission) to climb up the hill. Thus it is said that fusion yields net energy for atoms smaller than iron, and that fission yields energy for atoms heavier than iron.

But let’s refine that point. If I tried to split 86Kr, for instance, at 8.71 MeV/nuc into two 43Ca atoms at 8.60 MeV/nuc, I have not climbed up the binding energy hill. In practice, one must have mass number above about 100 before fission into two equal pieces will release net energy. But the point is almost meaningless, given that the only three nuclei susceptible to slow-neutron fission have 233, 235, and 239 nuclei—well above the threshold for energy gain.

You may have noticed by now that if climbing the hill is the goal for energy gain, we have a lot more climb available on the left (fusion) side than on the right (fission) side. In particular, notice 4He sitting pretty atop a local spike. 4He is such a tightly-bound nucleus that heavy nuclei undergoing radioactive decay often eject one of these hard nuggets like a boxer spitting out a tooth, called alpha decay. 238U, for instance, will typically spit out 8 “teeth” and 6 electrons (beta) in its journey to become 206Pb. In any case, 4He is unique among nuclei, and bears the special name of alpha particle.

For example, building a 4He nucleus out of four protons—as our Sun is so talented at doing—we gain 28.3 MeV (7.07 MeV/nuc times four nucleons). Second-best would be starting with two deuterium (2H, or D) nuclei to build 4He. In this case, we go from two nuclei bound at 1.112 MeV/nuc (times two nucleons each; then times two deuterons for 4.45 MeV total) to 28.3 MeV for a total climb of 23.85 MeV. Still pretty darned good: not much penalty starting with D. Another relevant starting point is combining D with tritium (3H, or T), popping out the unwanted neutron. In this case, we start at 7.88 MeV total, for a net climb of 20.4 MeV.

Compared to fission, where each split releases about 200 MeV of energy, it might appear that this fusion stuff is comparatively wimpy—seeming out of kilter when we look at the steeper slope for fusion on the binding energy plot. The discrepancy is the number of nucleons involved. Mirroring the example in the nuclear fission post, 235U, at 7.6 MeV/nuc splits into 97Rb and 137Cs at about 8.4 MeV/nuc each. Although the slope is meager (a mere 0.8 MeV/nuc step), multiplying by the nucleon number yields a binding energy gain of 97×8.4 + 137×8.4 – 235×7.6 = 180 MeV.

On a per mass, or per nucleon basis, fusion wins hands-down: one gram of deuterium results in 1012 J of energy, or 275 million kcal. Fission gives a comparatively small 20 million kcal per gram of 235U. So fusion is over ten times as potent. Keep in mind that chemical energy like that in fossil fuels is capped around 10 kcal/g. Note the conspicuous absence of the word million. On the energy scale, then, nuclear in either form is outrageously more potent than chemical energy.

Fusion Fuel Options

The two fusion schemes for which we can produce the requisite fuel are D-D and D-T, involving deuterium and/or tritium. Deuterium comprises 0.0115% of natural hydrogen, and is thus abundant in anything containing hydrogen—e.g., water. Tritium, on the other hand, is virtually non-existent in the natural world because it is unstable and decays with a half-life of 12.3 years. But as it happens, the requirements on D-T fusion are less impossible than for D-D, so all current efforts are focused on a technique for which there is no natural resource available.

Okay, so the pointy-heads aren’t that stupid. There is a way to create 3H by smacking lithium (either 6Li or 7Li) with a neutron and knocking out a tooth—er, 4He—leaving either 3H or 4H (in the latter case promptly dripping a neutron to become tritium).

I find it helpful to consult a chart of the nuclides when considering such shenanigans. Here is the bottom-end of the chart, which is basically the physicist’s version of a periodic table.

The number of neutrons increases from left to right, and the number of protons increases vertically. Thus all helium nuclei will be on the same row, for instance. Gray shading indicates a stable nucleus (stable well beyond the age of the Universe), light blue is semi-stable, and yellow less so. Each block contains the name of the nucleus/isotope, the fractional abundance (if stable), the half life (if unstable), the mass of the neutral atom in atomic mass units, and the decay path (arrows). Decays can be beta-minus (blue, transition to upper left), beta-plus (magenta to lower right), alpha (long yellow arrow to lower left), neutron drip (green arrow to left), or proton drip (red arrow down) These are the chess-board rules. Incidentally, it is possible to reconstruct binding energies from the mass numbers in each block.

We can use the chart to follow the two reaction types:

D + D ? 4He

The D-D reaction is pretty straightforward. Marrying two nuclei together, each with one proton and one neutron, the result has two protons and two neutrons. No extra neutrons are generated in the bargain.

For D-T, we must first create the tritium from either flavor of lithium:

6Li + n ? 4He + T, or

7Li + n ? 4He + 4H ? 4He + T + n

In either case, the “decay” chain is not the natural one, but is jarred out of the nucleus in the impact. Nominally, adding a neutron to 6Li just yields the stable 7Li, and adding a neutron to 7Li makes 8Li, which beta-decays in about a second to 8Be and then instantly splits into two alpha particles (4He). But in smackdown mode, one can conjure tritium, possibly yielding an extra neutron, depending on the isotope of lithium used. Then we have:

D + T ? 5He ? 4He + n

Note the extra neutron. This is handy, since we need neutrons to convert lithium to tritium. But note also that using 7Li generates two neutrons per D-T reaction, while 6Li only generates the one. Neutrons will be lost to other parasitic causes, so it’s handy to have extras around. On the other hand, neutron capture by the containment vessel makes it radioactive and will also damage its structural integrity, so we want to be careful about how many extra neutrons there are. Unfortunately, natural lithium is 92.4% 7Li, so tuning the 6Li/7Li mix to give the critical number of neutrons implies some sort of lithium enrichment on the front-end.

We aren’t exactly swimming in lithium, so did we make a bad trade in picking this horse? Each lithium atom converted to tritium will end up yielding about 20 MeV of thermal energy, so that we need 1.3×1032 Li atoms annually to produce our world consumption of 4×1020 J. That’s about 1500 metric tons of lithium annually, or about 5% of current lithium production. Proven world reserves give us 9000 years, and estimated resources give us 22,000, according to the U.S.G.S. Mineral Commodities Summaries.

For fun, let’s look at how much water each person needs to supply each year to provide enough deuterium. The average American demands 10,000 W of continuous power, or 3×1011 J of energy per year. At 20 MeV per whack, each person needs 1023 reactions per year. In the D-D case (requiring twice the deuterium as D-T), this means we need 2×1023 deuterium atoms—coming from 2×1027 hydrogen atoms at a fractional abundance of 0.01%. Sounds like a lot, but it’s 3,300 moles—amounting to 60 kg of ordinary water. 60 liters is similar to the amount of water used in a typical American shower. It’s hard to emphasize enough the extent to which deuterium availability poses no problem: there is enough deuterium in the ocean to provide our current energy demand for billions of years.

I think now you’re seeing a big part of the reason why fusion makes our eyes sparkle. Even given lithium limitations, I place D-D and D-T fusion in the “abundant” box.

What Makes Fusion Hard

A simple obstacle stands between us and fusion. It’s called the Coulomb barrier. Protons hate to get near each other, on account of their mutual positive charge and concomitant electrostatic repulsion. And they must get very close—about 10-15 m—before the strong nuclear force overpowers Coulomb’s vote. Even on a perfect collision course, two protons would have to have a closing velocity of 20 million meters per second (7% the speed of light) to get within 10-15 m of each other, corresponding to a temperature around 5 billion degrees! Even if the velocity is sufficient, the slightest misalignment will cause the repulsive duo to veer off course, not even flirting with contact. Quantum tunneling can take a bit of the edge off, requiring maybe a factor of two less energy/closeness, but all the same, it’s frickin’ hard to get protons together.

Yet our Sun manages to do it, at a mere 16 million degrees in its core. How does it manage to make a profit? Volume. The protons in the Sun are racing around at a variety of velocities according to the temperature. While the typical velocity is far too small to defeat the Coulomb barrier, some speed demons on the tail of the velocity distribution curve do have the requisite energy. And there are enough of them in the vast volume of the Sun’s core to occasionally hit head on and latch together. One of the protons must promptly beta-plus decay into a neutron and presto-mundo, we have a deuteron! Deuterons can then collide to make helium (other paths to helium are also followed). A quick and crude calculation suggests that we need about 1038 “sticky” collisions per second to keep the Sun going, while within the core we get about 1064 bumps/interactions per second, implying only one in 1026 collisions needs to be a successful fusion event.

Deuterons have an easier time bumping into each other than do lone protons, mainly because their physical size is larger. In fact, a deuteron’s relatively weak binding makes them even puffier than the more tightly bound tritium nucleus (go tritons!). At a given temperature, deterons will move more slowly than protons, and tritons more slowly than deuterons. All flavors contain a single proton—and so exert the same repulsive force on each other—but the increased inertia from extra neutrons exactly counters the slower speed, so that each has the same likelihood of trucking through the Coulomb barrier. Then we’re left with size. Deuterons are bigger than tritons, so D-D bumps will be more common than D-T bumps.

But there’s a catch. As soon as D and T touch, they stick together. Conversely, when D touches D, a photon (light) must be emitted in order for them to stick, which doesn’t usually happen. It is therefore said that D-T has a greater cross section for fusion than D-D. Estimates for the critical temperature required to achieve fusion come in at 400 million Kelvin for D-D fusion, and 45 million K for the D-T variety. But these temperature thresholds depend on the density of the plasma involved, so should not be taken as hard-and-fast. Still, we need our fusion reactors to be hotter than the center of the Sun because we do not have the luxury of volume and density that the solar core enjoys. Does this fact give you pause?


Overcoming the Coulomb barrier requires enormous kinetic energies of the particles, translating into enormous temperatures—well beyond any container’s ability to hold. No material resists melting above a mere 5000 K. 50 million degrees is not even funny.

At these temperatures/energies, electrons are not able to hold onto their rides, so we get a completely ionized plasma zipping this way and that. At 100 million degrees, for instance, deuterium nuclei have an average velocity of about one million meters per second. Left alone, the plasma would explode to the size of a football field in 0.1 milliseconds. Recall that we can’t get fusion to happen without these ridiculous velocities, so we’re stuck having to herd these hyper-fast particles without the help of Ritalin. It has been found that plasmas at the requisite temperature suffer instabilities from turbulence that we have been unable to tame. It becomes like a game of whack-a-mole, according to my colleague George Fuller: clamp down on one pesky behavior, and another one pops up.

The main scheme being pursued in the world today is magnetic confinement in a plasma containment vessel called a tokamak. Charged particles follow curved arcs in a magnetic field, so that strong fields confine the particle paths to tight curls. The radius of the path is proportional to the particle velocity, which spans a large range of values in a thermal plasma. One must produce a magnetic field strong enough to contain the fast tail of the velocity distribution, else the plasma has a leak at the high-velocity end and depletes itself rather quickly. Every particle collision resets velocities, so a leaking fast tail is constantly re-populated. At a field strength of 10 Tesla (near the upper end achievable), the mean-velocity deuteron at 50 million K has a 2 mm path radius. ITER, the International Thermonuclear Experimental Reactor, is a tokamak design being built in France under international support. The current timeline calls for achievement of a 480 second burst of 500 MW power in the year 2026, although there is no plan to capture the generated heat for the production of electricity (note the “Experimental” in the project name).

The other primary scheme gives up on trying to confine the plasma in some steady state, instead following a path similar to the philosophy behind fusion bombs: force an implosion of the fuel to extraordinarily high densities and temperatures, and let the cursed thing explode. This scheme goes under the name inertial confinement, since one relies on the inertia of the implosion to bring nuclei close together. In the U.S., the National Ignition Facility (NIF) focuses 192 high-power laser beams onto a small pellet to initiate a symmetric crunch. The idea for a power plant would be that pellets are loaded one after the other, detonated, and the effluent heat collected to make steam. As far as I know, there is no current plan to harness any heat generated at the NIF—being experimental, like ITER.

Flies in the Ointment

The ITER experiment, if it adheres to its schedule and projected budget, will cost something like $20 billion to build and produce pops of unharnessed thermal power by 2026. I should note that most large experimental projects have slipping schedules, and it would be a fantastic irony if a fusion experiment violated this trend! In any case, we could imagine another several decades before commercial fusion tentatively steps onto the scene, putting us at mid-century. The projects will undoubtedly be very expensive, require intimate involvement of the highest level of expertise, and will likely not catch on in a big way until investors see a track record of profitability—if that ever comes to pass. So that’s fly number one: we’re looking at very long term.

Fly number two is that D-T fusion necessarily involves neutrons, which do not respond to magnetic or electrostatic confinement and therefore hurtle off to the walls of the containment vessel. In doing so, they knock into the atoms comprising the vessel, dislocating them within the lattice and causing structural damage. The integrity of the containment vessel will degrade like plastic in sunlight. The neutron flux from a D-T reactor is substantially higher than for a conventional fission reactor.

Fly number three is also related to neutrons: after doing their damage in the containment walls, the neutrons will marry a nice, plump nucleus and settle down. But the marriage is often radioactive, so that the container becomes radioactively “hot.” In fission, we get two radioactive daughters for each 200 MeV produced. For D-T fusion, if we are able to utilize most of the neutrons for conversion of lithium into tritium (and use enriched 6Li), we might be able to lose less than 0.2 neutrons per 20 MeV reaction (pure, uninformed guess on my part), which comes out to the same number of radioactive products per unit of energy. But at least materials choices for the container walls offers some control over the menagerie of radioactive products—unlike the randomness of fission. All told, the radioactive toll from a D-T fusion reactor may be comparable to that of a fission reactor, though with shorter half-life.

Then there is the extremely finicky nature of achieving fusion. Getting something to work in the lab is much different from having it operate reliably for years on end. Any significant departure from optimal conditions will see the fusion yield diminish. ITER aims for a thermal output ten times that of the input energy. In an eventual self-running mode, siphoning 10% of the output power in electrical form requires pulling out about 30% of the thermal power to run the heat-engine generator. This makes for a 3:1 net energy gain, which could quickly transition to a net energy drain if things are not maintained in tip-top condition through the years.

Another possible fly is that the superconducting magnets used to generate the extreme magnetic fields for confinement could lose cryogenic cooling, “go normal,” and explode. An explosion that damaged the tokamak could result in a radioactive release to the environment. Even though the probability is small, we routinely go to great expense to mitigate low-probability catastrophic events, and so a massive, expensive containment building would likely be required.

Each fly translates into cost. In the end, it is unclear whether a fusion plant—even after the physics is tamed—would be economically viable, and attractive enough for investors to take on endeavors of this scale, complexity, and risk.

A Solar Perspective

A few days after watching a television show on fusion, I had an epiphany while walking to the bus. Why are we enamored with fusion? Because the fuel supply is virtually unlimited; the energetics represent the epitome of what physics has to offer; the primary emission is useful helium; the radioactive waste is shorter-lived than for fission (damning with faint praise?); fusion plants could presumably be sited anywhere; surely it’s one step closer to warp drive. But then I realized that the Sun (being its own fusion reactor) also provides billions of years of energy, well in excess of our current demand. And my refrigerator and other appliances already are run by this source in a modest PV/battery installation at my home. I personally can’t ignore the asymmetry between the promise of future technology and technology that sits on my roof! If we removed the storage barrier for solar, would fusion still be viewed as the holy grail?

This prompts two questions. First, what is the relative funding expenditure for fusion research and for battery/storage research? Second, what are the appeals offered by fusion that could leave solar in the shade?

A cursory investigation reveals that the U.S. spends approximately $450M per year on the NIF, and chips in about $32M per year to ITER (though expected to escalate to about $350M/year during the construction phase from 2014–2016). Meanwhile, the U.S. Department of Energy Hub for Batteries and Energy Storage plans to operate at $24M per year, with a similar expenditure in Fuels from Sunlight. It’s about as I thought.

I can only muse about the appeals of fusion over solar. I think area is one: fusion plants could be comparatively compact. I think location-dependence is another. Most people don’t realize that the worst site in the continental U.S. (Olympic peninsula) delivers fully half as much annual solar energy as the Mojave desert. Given a good storage solution, solar becomes useful almost anywhere. I think in part, we are driven by the sense of progress/conquest. Cracking the fusion problem matches our precious narrative. But I am left wondering if these reasons are compelling enough to keep us reaching for the gold that may continue to disappoint when we have other options whose viability may be closer at hand.

Naturally, it’s not an all-or-nothing proposition. I support research whatever the direction. But I want to make sure we aren’t falling victim to irrational hangups and expectations. We at least need to evaluate this notion: to know ourselves. One may object that I’ve simply replaced one holy grail (fusion) for another (storage). Which one is voted more likely to succeed?

Fusion Prospects

No one can truly say whether we will achieve fusion in a way that is commercially practical. If teams of PhDs have spent over 60 years wailing on the problem while spending tens of billions of dollars, I think it’s safe to use our fusion quest as the definition of hard. It’s a much larger challenge than sending men to the Moon. We have no historical precedent for an arduous technological problem on this scale that ultimately succeeded to become a ho-hum commercial reality. But for that matter, I don’t think we have any precedent for something on this scale that has failed. In short, we’re out of our depths and can’t be cocky about predictions in either direction.

I am hopeful that fusion can one day become a practical reality. I certainly understand it to be feasible in principle. My misgivings mainly lie in the extreme complexity of the challenge. It may take a year of intense study to become an expert on a coal-fired plant, to the point of being a go-to resource for troubleshooting and maintenance. A nuclear fission plant may take five years to master—it took about that long to get the first break-even performance after discovery of fission. But after a century of development (by the time any commercial fusion reactor sees the light of day), how long must one study plasma physics in order to have a firm handle on operation of a fusion plant? The NIF uses two lasers occupying a floorspace the size of a Wal-mart store (no exaggeration). How many PhDs will it take to keep a state-of-the-art laser of this magnitude operating? I know that the 2 W laser I use in my research causes this PhD enough trouble!

I became interested in energy because I sensed that we are approaching a phase change in society as the age of fossil fuels begins to ebb. So much of what we have become can be attributed to cheap and abundant surplus energy. Our energy future is highly uncertain. Commercial fusion may come along decades down the road—mid-century at the earliest—but even then it is yet another source of heat that we can use to make electricity. Another step (mobile storage) must accompany fusion development to replace petroleum functions, and even then at significant disadvantage in energy density using current technologies. So yeah—I hope it helps us out one day. But I’m not sure we can wait that long.

I thank Bob Hirsch for his review and comments.

Labs Conducting Fusion Science Projects

Princeton Plasma Physics Laboratory
Princeton, NJ 08543-0451
GPS: 100 Stellarator Road
Princeton, NJ 08540 U.S.A.
+1-609 243-2000

Lawrence Livermore National Labs
National Ignition Facility (NIF)
Lawrence Livermore National Laboratory
7000 East Avenue • Livermore, CA 94550
Los Alamos National Laboratory
Take from Company Index

Sandia National Laboratories
Z Pulsed Power Facility

Plasma Science and Fusion Center
77 Massachusetts Avenue, NW16
Cambridge, MA 02139

Laboratory for Laser Energetics
University of Rochester
250 East River Road
Rochester, New York 14623-1209

Fusion Energy Sciences
U. S. Department of Energy
List of U.S. (Government Funded) Fusion Program Participants
SC-24/Germantown Building
1000 Independence Ave., SWWashington, DC 20585P
+1-301 903-4941

Fission vs. Fusion – What’s the Difference?

Duke Energy Nuclear Information Center

Inside the sun, fusion reactions take place at very high temperatures and enormous gravitational pressures

The foundation of nuclear energy is harnessing the power of atoms. Both fission and fusion are nuclear processes by which atoms are altered to create energy, but what is the difference between the two? Simply put, fission is the division of one atom into two, and fusion is the combination of two lighter atoms into a larger one. They are opposing processes, and therefore very different.

The word fission means “a splitting or breaking up into parts” (Merriam-Webster Online, Nuclear fission releases heat energy by splitting atoms. The surprising discovery that it was possible to make a nucleus divide was based on Albert Einstein’s prediction that mass could be changed into energy. In 1939, scientist began experiments, and one year later Enrico Fermi built the first nuclear reactor.

Nuclear fission takes place when a large, somewhat unstable isotope (atoms with the same number of protons but different number of neutrons) is bombarded by high-speed particles, usually neutrons. These neutrons are accelerated and then slammed into the unstable isotope, causing it to fission, or break into smaller particles. During the process, a neutron is accelerated and strikes the target nucleus, which in the majority of nuclear power reactors today is Uranium-235. This splits the target nucleus and breaks it down into two smaller isotopes (the fission products), three high-speed neutrons, and a large amount of energy.

This resulting energy is then used to heat water in nuclear reactors and ultimately produces electricity. The high-speed electrons that are ejected become projectiles that initiate other fission reactions, or chain reactions.

The word fusion means “a merging of separate elements into a unified whole”. Nuclear fusion refers to the “union of atomic nuclei to form heavier nuclei resulting in the release of enormous amounts of energy” (Merriam-Webster Online, Fusion takes place when two low-mass isotopes, typically isotopes of hydrogen, unite under conditions of extreme pressure and temperature.

Fusion is what powers the sun. Atoms of Tritium and Deuterium (isotopes of hydrogen, Hydrogen-3 and Hydrogen-2, respectively) unite under extreme pressure and temperature to produce a neutron and a helium isotope. Along with this, an enormous amount of energy is released, which is several times the amount produced from fission.

Scientists continue to work on controlling nuclear fusion in an effort to make a fusion reactor to produce electricity. Some scientists believe there are opportunities with such a power source since fusion creates less radioactive material than fission and has a nearly unlimited fuel supply. However, progress is slow due to challenges with understanding how to control the reaction in a contained space.

Both fission and fusion are nuclear reactions that produce energy, but the applications are not the same. Fission is the splitting of a heavy, unstable nucleus into two lighter nuclei, and fusion is the process where two light nuclei combine together releasing vast amounts of energy. Fission is used in nuclear power reactors since it can be controlled, while fusion is not utilized to produce power since the reaction is not easily controlled and is expensive to create the needed conditions for a fusion reaction. Research continues into ways to better harness the power of fusion, but research is in experimental stages. While different, the two processes have an important role in the past, present and future of energy creation.

Private Fusion Companies

Fusion Start-up Companies

First Light Fusion
First Light Fusion Ltd
Unit 10 Oxford Industrial Park,
Mead Road,Yarnton,Oxfordshire,OX5 1QU
Telephone +44(0)1865 807670

Energy Matter Conversion Corporation (EMC2)
9155 Brown Deer Road Suite 4
San Diego, CA 92121-2260
Jaeyoung Park, Ph.D., Chief Scientists
Company Information & Scientific Papers at “Inertial Electrostatic Confinement

Tri Alpha Energy
19631 Pauling
Foothill Ranch, CA 92610
Company Information & Scientific Papers at “Z Pinch

Fusion Energy – Space Propulsion
8551 154th Ave NE
Redmond, WA 98052

Helion Energy
Redmond, WA
Company Information & Scientific Papers at “Fusion Engine: Magneto-inertial fusion via non-destructive magnetic compression of a field-reversed configuration target (Helion)

General Fusion
108-3680 Bonneville Place
Burnaby, BC V3N4T5
Company Information & Scientific Papers at “Inertial Shock Magnetized Target

Tokamak Energy Ltd
Small Spherical Tokamaks
120A Olympic Avenue
Milton Park, Oxfordshire OX14 4SA
+44 (0)1865 408303

LPP Fusion
Focus Fusion

128 Lincoln Blvd.
Middlesex, NJ 08846-1022
Eric Lerner, Principal
Company Information & Media at Lawrence Plasma Physics

Magneto-Inertial Fusion Technologies, Inc. (MIFTI)
2600 Walnut Ave
Tustin, CA 92780
ph: (714) 329-3990
Company information

Commonwealth Fusion Systems, LLC
Cambridge, Massachusetts
Company organized as a DE LLC 2017

Mature companies engaged in fusion research

General Atomics
3550 General Atomics Court
San Diego, CA 92121-1122
(858) 455-3000
Main website:
Fusion Education at:

Lockheed Martin
6801 Rockledge Drive
Bethesda MD 20817-1877
Thomas McGuire Project Manager
Company Information & Scientific Papers at “Thermal Magnetic Confinement Axisymmetric Magnetic Cusp hybrid (Lockheed Martin)

National Laboratory projects in need of private funding/partners

Los Alamos National Labs
Plasma Jet Magneto Inertial Fusion (PJMIF)
P. O. Box 1663
Los Alamos, New Mexico 87545
Scott Hsu, Ph.D. Principal Investigator/Project Leader
Project Information & Scientific Papers at “Plasma Jet Magneto Inertial Fusion (PJMIF)
Los Alamos among new DOE projects to create new technology pathways for low-cost fusion energy development

Nuclear Fusion – The Theory

By Barrie Lawson, UK

The Holy Grail of nuclear energy, nuclear fusion is the process by which the Sun generates its prodigious energy providing us with the warmth and light we receive. It is the process by which the nuclei two light atoms combine to form a single, bigger nucleus of a new atom releasing large amounts of energy as a consequence. In 1939 Hans Bethe explained that this process occurs in the stars all over the universe but up to now we have not been able to successfully duplicate this process on earth despite over 70 years of trying, but at last we are coming close.

The great attractions of nuclear fusion as an energy source are that the fuel, mostly isotopes of hydrogen, is plentiful and easy to obtain, and the elements produced as a result of the fusion are usually light and stable atoms rather than the heavy radioactive products which result from nuclear fission. Furthermore, the potential release of energy per unit mass of the fuel is much higher in the case of fusion than in fission since reactions allowing greater increases in binding energy are possible with fusion reactions. See the graph of binding energy above.

The Coulomb Barrier

Unfortunately, although bringing about fusion is theoretically possible, achieving it in practice is fraught with major difficulties.
Coulomb Barrier

For fusion between two positively charged nuclei to take place, they must get close enough to eachother to undergo a nuclear reaction. For this to occur the nuclei must overcome the energy barrier due to the "repulsive" electrostatic Coulomb force, known as the Coulomb barrier, between the nuclei, to force them close enough to each other to come within the influence of, and be captured by, the "attractive" Strong nuclear force which holds the nucleons in each nucleus together.

The magnitude of the Coulomb barrier corresponds to the work done or energy needed for the two nuclei overcome the Coulomb force to come together. This is equal to the potential energy between the particles and is given by the Coulomb force between two nuclei multiplied by the distance between them integrated over the distance over which the force is effective. Thus for fusion to occur, the nuclei must have at least enough kinetic energy to exceed the Coulomb repulsion and this is proportional to the mass of the nuclei and the square of their velocity. The magnitude of the this kinetic energy is also directly proportional to the temperature of the nuclei.

All fusion reactions require the fusing nuclei to have extremely high kinetic energies in order to overcome the Coulomb barrier and get close enough to each other to fuse. Their temperature must therefore be extremely high, 100 Million°C or more, so that the nuclei collide with each other at great speed.

A Note About Temperatures:
The temperature and energy of a moving gas or plasma particle are directly proportional to its velocity squared.

In nuclear physics, temperature is typically used to express the "average" energy of the particles in a fuel sample. Conversely, it is also common to express very high temperatures in terms of energy units (Joules or electronVolts).

The energy in Joules is given by multiplying the temperature in degrees Kelvin by Boltzmann’s constant of 1.38 X 10-23 Joules/degree Kelvin (J/K)


1 Joule (J) ≡ 6.24 x 1012 Million electronVolts (MeV)


1000 electronVolts (KeV) ≡1.16 X 107 °K

Fusion temperatures are so high that °Kelvin and °Celsius are almost the same and are often used interchangeably

As a point of reference, the temperature at the core of the Sun is around 1.5 X 107 °K. This does not mean that all the atomic particles are at that temperature. This temperature represents the average energy of the atomic particles in the core. In thermal equilibrium, the atoms have a range of velocities (energies) described by the Maxwell-Boltzmann distribution which represents the number of particles at each energy level in the sample.

Maxwell-Boltzmann Temperature Distribution
The energy distribution shows a very high percentage of particles with energy levels around the average level and relatively low percentage of very low and very high energy particles at the lower and upper tails of the distribution. In absolute terms however, because of the extremely high particle density at the centre of the Sun, there will be a very large number of particles in the longer, upper tail with energies or temperatures many times higher than the mean

The Coulomb barrier between two protons in free space is 3.43 MeV and this corresponds to a temperature of 4 × 1010 °K. This is over 1000 times the temperature of 1.3 KeV (1.5 X 107 °K) at the core of the Sun. How then can proton fusion occur on the Sun with such low particle energy levels? There are two explanations for this apparent anomaly.

  • The calculation of the Coulomb barrier determines the "average" energy per proton needed for fusion, however these energies are distributed according to the bell shaped Maxwell-Boltzmann distribution. Within its long tail there is a sufficiently large number of particles whose energy is much larger than the average and thus enough to initiate fusion.
  • It is not necessary for the incident protons to have sufficient energy to overcome the Coulomb barrier entirely. Due to the wave-particle duality and the statistical probabilities of the properties of very small particles, as explained by quantum mechanics, the protons can also pass through the barrier by a phenomenon known as quantum tunnelling, provided the barrier height is not too high above the kinetic energy of the incoming particle.
Fuel Density

For significant fusion to take place, the particle density of the fuel must also be very high to provide sufficient opportunities for collisions between the particles to occur.

In a star, the high temperatures are provided by the self sustaining nature of the nuclear reaction itself and the density of the fuel is maintained by the star’s massive gravity. On earth, attempts have been made to create these extreme conditions in a plasma of ionised gases but containment is a serious problem since no known materials for containing the fuels can withstand such high temperatures. An alternative is to capture the energy from a series of tiny, controlled thermonuclear explosions which has so far been more successful. See Nuclear Fusion Reactors

The story so far

Fusion Fuels
Fusing two light nuclei can liberate more than the fission of Uranium-235 or Plutonium-239. Ideal fuels are the lightest elements since they experience the lowest repulsive force, or Coulomb barrier, between their nuclei, so that the energy needed to bring about fusion is reduced. The most common fuels used in fusion attempts are Deuterium and Tritium, gaseous isotopes of hydrogen, in the so called D-T reaction.

  • Deuterium
    Deuterium (2H) also known as heavy Hydrogen is a naturally occurring, stable isotope of Hydrogen found in the earth’s oceans where it accounts for approximately 0.015% of the Hydrogen atoms, or 0.030% of the weight of Hydrogen. Deuterium is extracted from the water by a variety of separation methods which exploit the small differences in physical and chemical properties between Deuterium and Hydrogen.

    The Deuterium in one gallon of sea water has the energy content of 300 gallons of gasoline and the oceans contain enough energy to supply the world’s energy needs for thousands of years..

  • Tritium
    Tritium (3H) is also an isotope of Hydrogen. It is radioactive with a half-life of 12.3 years decaying at the rate of 5.5% per year by beta decay into Helium-3 with the release of an electron and of 18.6  keV of energy. Because of its short half-life, only tiny quantities are found naturally as the result of the reactions of cosmic rays with atmospheric gases. Supplies of Tritium are produced as a by-product of other nuclear reactions, notably those involving Lithium and much of it is reserved for nuclear weapons. It is consequently both rare and very expensive.

    Due to their low energy, the emitted electrons can not penetrate the skin and so Tritium is not considered an external radiation hazard though it could cause damage if inhaled or ingested. Tritium is however often used as a biological tracer in medical research because of its short half-life and low radiation.

The fusion of Hydrogen nuclei (protons) in a proton-proton reaction is not practical since it would require too much energy or too high a temperature to start. The fusion of Deuterium with Tritium needs a temperature of 100 million to 150 million degrees Centigrade. All other fusion reactions need even higher temperatures.

Fusion Energy Release

The D-T fusion reaction between Deuterium and Tritium is shown below:

Nuclear Fusion

2H1    +    3H1    ⇒    4He2    +   1 n0    +    @ 17.6 MeV

The diagram above shows that the fusion of one atom of Deuterium with one atom of Tritium to form one atom of Helium (also called an alpha particle) releases about 17.6 MeV of energy.

Note that this reaction results in the release of a troublesome surplus neutron which can cause problems in practical fusion reactors, such as the Tokamak. Since they carry no electric charge, neutrons are not constrained in the the plasma by the magnetic field and can migrate to the walls of the reactor where they can react with parts of the reactor construction materials which may consequently become radioactive.

This unavoidable side effect can however be turned to an advantage. By using a Lithium metal blanket to capture the surplus neutrons in the reactor, two useful fission reactions are possible, both of which result in the release of alpha particles (Helium nuclei) and, more importantly, the production of Tritium, the scarce, radioactive, isotope of Hydrogen, which is one of the basic fuels for the fusion reaction.
The first reaction is exothermic and uses the isotope Lithium-6 to capture slow neutrons producing Tritium while releasing an alpha particle and 4.8 MeV of energy as follows:

6Li3 + 1 n04He2 + 3T1+ @ 4.8 MeV

The second reaction is endothermic using the isotope Lithium-7 to capture fast neutrons, also producing Tritium and releasing an alpha particle while leaving a free neutron and absorbing 2.5 MeV of energy.

7Li3 + 1 n04He2 + 3T1+1 n0 – @ 2.5 MeV

Natural Lithium is relatively abundant in the earth’s crust and is typically composed of 92.6% of the isotope Lithium-7 and 6.4% of Lithium-6.

The energy released at the atomic level by the fusion of Deuterium and Tritium can be calculated from the binding energies of the parent and daughter atoms as shown in the following table:

The table shows that the combined binding energy of the Deuterium and Tritium atoms of 10.7 MeV increases to 28.3 MeV when the atoms fuse into Helium releasing energy of 17.6 MeV, equivalent to 2.8 X 10-12 Joules.

Note that 80% of the released energy is carried by the neutron with the Helium alpha particle accounting for only 20%

The energy released from practical amounts of fuel can be calculated as follows:

The atomic mass of the Deuterium nuclide is 2 amu = 3.34 X 10-27Kg
1 Kg of Deuterium therefore contains 1Kg/2 amu = 2.99 X 1026 atoms.

The atomic mass of the Tritium nuclide is 3 amu and hence 1.5 Kg of Tritium also contains 2.99 X 1026 atoms.

The energy released by fusion of 1 atom of Deuterium with 1 atom of Tritium is 17.6 Mev = 2.82 X 10-12 Joules.

The energy liberated by the fusion of 1 Kg of Deuterium with 1.5 Kg of Tritium is therefore 2.82 X 10-12 X 2.99 X 1026 = 8.43 X 1014 Joules = (8.43 X 1014) / (3.6 X 1012) GWHours = 234 GWHours.

This energy appears in the form of heat. If it was used to generate electricity in a conventional steam turbine power plant with an efficiency of 38%, it would provide 88,900 MWH of electricity which is near enough equivalent to one year’s operation with a constant output power of 10 MWatts.

Fission – Fusion Energy Comparison

Note that the 234 GWH (8.43 X 1014 Joules) released by the fusion of 2.5 Kg of the fuel in the D-T (40-60 proportion) reaction above is equivalent to 93.6 GWH (3.37 X 1014 Joules) per Kg. This is over four times the 22.5 GWHours (8.1 X 1013 Joules) of energy released by the fission of 1 Kg of Uranium – 235. The fusion reaction also uses safer fuels which are inexpensive, more plentiful, and easier to manage, leaving behind much more benign waste products resulting from the process.

To put these values into perspective, 1 Kg of petrol (gasoline) has an energy content of about 4.7 X 107 Joules or (4.7 X 107) / (3.6 X 106) kWH = 13 kWH, less than one millionth of the energy from either nuclear fission or fusion. See also Energy Content Comparison Table

Other Fusion Fuels

There are actually four possible fusion reactions which could take place in a reactor fueled by Deuterium only.

2H1    +      2H1    ⇒    3He2    +   1 n0     +    @ 3.3 MeV
2H1    +      2H1    ⇒    3H1      +    1 H1    +    @ 4.0 MeV
   2H1    +      3H1    ⇒    4He2    +    1 n0    +    @ 17.6 MeV
2H1    +     3He2   ⇒    4He2    +   1 H1    +    @ 18.3 MeV

The results of these four reactions can be summarised as follows:

62H1   ⇒    21H1   +   24He2   +   21 n0    +    @ 43.2 MeV

The first two of the above reactions using only Deuterium as the fuel, known as D-D reactions are equally probable. This fuel combination has the advantage that the Deuterium fuel does not have the mildly radioactive properties of Tritium, but the energy release is relatively low.

  • The first reaction produces the He3 isotope of Helium and an energetic neutron.
  • The second reaction produces Hydrogen and Tritium which is mildly radioactive.
  • The third and fourth reactions involve the Deuterium fuel reacting with the fusion products of the first two reactions producing a much higher energy release.
  • The third reaction is the well known D-T reaction between Deuterium and Tritium which produces a Helium atom (alpha particle) and a high energy neutron.
  • The fourth reaction between Deuterium and the Helium isotope He3 produces a Helium nucleus (alpha particle) and 2 energetic neutrons and is known as the D-He3 reaction.

Other promising fusion fuel candidates are the Hydrogen-1 (proton) with / Boron reaction, which releases Helium (alpha particles).

Solar Fusion Chain

Solar fusion is initiated by the fusion of two Hydrogen nuclei (protons) in the following reaction in which the two protons fuse to form a Deuterium atom as one proton is transformed into a neutron, with the release of a positron and a neutrino and 0.42 MeV of energy.

1H1    +     1H1    ⇒    2H1    +    e+    +    ν     @ 0.42 MeV

At the same time, the positron emitted by the beta decay of the proton is almost immediately annihilated with an electron, and their combined mass energy, as well as their kinetic energy, is carried off by two gamma ray photons.

e+    +    e    ⇒    2 γ   @1.02 MeV

Proton – Proton (p-p) Chain Reaction
After the initial reaction, solar fusion continues with more protons reacting with the Deuterium produced in the first reaction to form a light isotope of Helium releasing more energy in the following reaction and initiating a chain of reactions.

2H1    +     1H1    ⇒    3He2    +    ν     @ 5.49 MeV

In turn, the products of this second reaction fuse with even more particles to form ever more complex, heavier nuclei releasing more energy in further reactions such as the Deuterium D – D reactions above.

Power from Nuclear Fusion

Unfortunately immense amounts of energy are needed to create the conditions for self-sustaining fusion to take place and in practice there are serious technical problems to overcome in order to achieve a net energy gain. These are considered in the section on Nuclear Fusion Reactors

About the author, Barrie Lawson:

Barrie graduated from Birmingham University with a degree in Electrical and Electronic Engineering in 1964. Since then he as has worked at Director level in many branches of the electronics industry including military electronics, telecommunications, computers, automotive and consumer electronics. During the last 10 years he has been involved in the battery business, originally as Chairman of MPower Batteries, a custom battery pack making company in Scotland which he helped to found and later in China where he set up a similar business. He is currently Chairman of CHE EVC, another battery startup company pioneering some interesting new technologies. In his spare time he writes and maintains the Electropaedia web site, a comprehensive knowledge base about batteries and energy sources.

Nuclear Fusion Reactors

By Barrie Lawson, UK

Solar Fusion

The Sun’s immense energy is due to ongoing nuclear fusion occurring in its core where the temperature is around 15 Million degrees Celsius. It’s not a simple reaction, but a series reactions starting with the fusion of the two simplest atomic nuclei, the Hydrogen nuclei (protons), followed by fusion of the products of the initial reactions to create ever more complex atomic nuclei in a chain of reactions known as the p-p chain described on the Nuclear Theory page.

Earthly Fusion

Over the last 50 years, the promise of reaping unlimited energy from safe, low cost fuels has launched numerous attempts to mimic the thermonuclear action of the Sun and the stars in order to harness the potential energy of nuclear fusion. However, it is difficult to recreate the environment of the Sun here on Earth and the only successful project so far has been the Hydrogen Bomb. Up to now, none of the attempts to produce sustained, controlled nuclear fusion has been able to produce energy on a commercial scale, although small scale demonstration units have delivered enough power to verify that the principle works and to show that power generation by nuclear fusion should be feasible.

Attempts at achieving controlled thermonuclear fusion have followed two basic methods, magnetic confinement as pioneered by the Tokamak (Russian acronym for: "torus-shaped magnetic chamber") developed in Russia and inertial confinement as exemplified by the National Ignition Facility (NIF) reactor in the USA. Both of these methods employ gigantic, expensive machines whose principles are described here and development times are measured in decades rather than years.

The Tokamak was first on the scene, conducting the first ever controlled fusion reaction in 1968. Since then the concept has been used by pursued by several research institutions throughout the world but though they have demonstrated that the technology works, none of these reactors have have achieved breakeven performance to deliver more power than was consumed in initiating the fusion. The best that has been achieved so far in a Tokamak type reactor was achieved in 1997 by the Joint European Torus (JET) reactor at Culham in the UK which produced a fusion power output of 16 MWatts from an input power of 24 MWatts giving a conversion gain Q of 0.65.

The NIF Laser Fusion reactor at the Lawrence Livermore National Laboratory (LLNL) in the USA first went live in June 2009 and up to now it is the only reactor to have exceeded breakeven performance. In 2013 it achieved a conversion gain of 1.4 but the technology but its output power is much lower than the Tokamak’s and is still a long way from producing commercial power.

The quest for commercially viable fusion power continues.

Fusion Fuels

The most promising fuels for achieving practical fusion energy release on Earth are the two isotopes of Hydrogen, Deuterium and Tritium, which may be fused together to produce a positively charged Helium nucleus, also called an alpha particle, and a surplus neutron in a so called D-T reaction. The energy released by the fusion is shared between the alpha particle which carries 20% of the total energy released and the neutron which carries 80%. Hydrogen nuclides carry the lowest charge of all atoms since they have the fewest protons. They therefore have the lowest Coulomb barrier to fusion and so offer the potential to achieve fusion with the minimum amount of applied energy.

The D-T reaction yields 17.6 MeV of energy from the fusion of just two atoms, but to give them enough energy to overcome the Coulomb barrier and initiate the fusion requires the energy of each of the Deuterium and Tritium atoms to be raised to between 10 KeV and 20 Kev. This corresponds to a temperature of 100 to 200 Million °C which is over six times hotter than the 15 Million °C temperature at the center of the Sun. At these high temperatures all matter is in the plasma state, the fourth state of matter, in which the kinetic energy of the particles strips the electrons from the atomic nuclei leaving positively charged ions producing an ionised plasma.

Deuterium is naturally abundant constituting 0.015%, or one in every 6,700 atoms, of seawater from which it is easily extracted. The Earth’s oceans contain enough Deuterium to supply the World’s energy needs for millions of years.

Tritium on the other hand is an unstable isotope of hydrogen in the form of a radioactive gas with a half life of 12.3 years and is not found naturally but would have to be manufactured. Tritium is actually produced by the fusion plant itself as an essential part of the neutron capture system which extracts the heat generated by the fusion reaction. The bombardment of Lithium with neutrons splits the Lithium into Helium and Tritium and since neutrons are produced in abundance by the D-T fusion reaction, the reactor can provide its own Tritium source. Tritium is also produced by similar processes commercially.

Lithium is a fairly common metal, also found in seawater as well as many of the world’s salt flats. Thus there is sufficient available fusion fuel to supply the world’s power for millions of years.

Other possible fusion fuels include the following combinations, Deuterium-Deuterium used in the D-D reaction and Deuterium with the isotope Helium-3 in the D-He3 reaction but up to now almost all reactors have been based on the D-T reaction which requires the lowest fusion temperature. See the list of other fusion reactions which also shows the corresponding energy release of each reaction.

Fusion Energy Release

Theoretically, the fusion of one atom of Deuterium with one atom of Tritium releases 17.6 Million electronVolts of energy in the following reaction.

2H1    +    3H1    ⇒    4He2    +   1 n0    +    @ 17.6 MeV

Scaling this up, the fusion of 1 kilogram of D-T fuel will thus release enough energy to provide a constant 10 MegaWatts of heating power, which can be converted into electricity, for a full year. Similarly the fusion of just 1 milligram (0.000035 ounces) releases 337 MJoules of energy which is equivalent to 80.7 kg of the explosive TNT, enough to blow a fusion reactor apart. See Fusion Energy Release and the table of Energy Content of Fuels.

Fusion Power

The potential energy available from nuclear fusion is unlimited, but in reality, delivering this energy is proving to be an elusive goal. The actual energy delivered by fusion from the various experimental reactors rarely approaches the amount of energy used to create the fusion reaction with the very best reactors just breaking even.

Fusion or Burning
Fusion is the combination of the two fusion fuel elements, as the result of externally supplied energy, to produce a new element with a consequent release of energy. This is often called the burning of the fuel.

Ignition Point
As the temperature of the burning fuel rises, the fusion reaction rate increases so that the fusion eventually becomes self-sustaining. Ignition is defined as the state in which the energy released by the fusion reactions is sufficient to produce self-sustaining fusion of new fuel nuclei without the need for an external energy supply. Note that ignition is not a necessary condition for a practical reactor since burning alone can release more energy than the energy supplied from external sources.

There is no critical mass for sustained fusion explosion. The fuel mass can be as small as desired.

Conversion Gain
The fusion conversion gain factor, or quality factor, Q is defined as the ratio of the energy released by the fusion or "burning" process and the energy used to create and sustain the fusion in a steady state. Sometimes the ratio is defined in terms of power rather than energy.

The condition of Q = 1 is referred to as breakeven. Unless Q > 1 there will be no surplus usable energy.

Note: The conversion gain refers to the input and output of the fusion reaction only. It does not include the energy consumed in generating the driver power used to initiate the fusion, nor does it include the efficiency loss associated with capturing and converting the energy output of the reactor to usable electricity if that is its purpose. Since the surplus energy usually appears in the form of heat there will be a further conversion loss involved in generating electricity from the heat. This means that only 35% to 45% of this surplus energy can be extracted as electricity after taking into account the conversion efficiency of steam turbine generating plants. The economic generation of electricity by means of nuclear fusion requires a fusion reactor with a conversion factor of at least Q>10.

See how the measuring point influences the fusion system efficiency calculation.

Break-even Point
The breakeven point is the point at which the fusion power generated is equal to the power needed to maintain plasma temperature so that Q=1. However, this is not sufficient for ignition since energy still has to be supplied to overcome losses, due to radiation, conduction and the energy carried away from the fusion mass by dispersion of the neutrons, in order to maintain the plasma temperature.

For ignition the input energy is zero and Q is infinite.

System Dimensioning and the Lawson Criterion

In order to obtain more energy from a fusion reaction than is required for heating the fuel, three conditions must apply simultaneously. These conditions are usually stated in terms of the "triple product" of ion density, confinement time and temperature, known as the Lawson criterion after the British scientist John D. Lawson who first outlined it. For D-T fusion these conditions are:

Plasma Ignition Temperature: (T) The fuel temperature must be high enough so that the particles (ions) have sufficient energy to enable them to overcome the Coulomb barrier (the critical ignition temperature) and fuse with each other. For Deuterium-Tritium fuel, this is 100 to 200 Million °C or 10 to 20 KeV.

Ion Density at the center of the fuel: (n) The particle (ion) density of the fuel is specified as the number of particles / m3 or the number of fuel ions /m3 (not mass / m3) and must be very high to provide as many opportunities as possible for collisions between the Deuterium and Tritium ions to increase the probability of fusion occurring.

For D-T plasma fuel the particle density is around 1020 particles / m3. For solid D-T fuel, it is 1030 particles / m3 after compression.

Energy Confinement Time: (τE) For sustainable fusion to take place, the rate of rate of energy supplied to the fuel must be greater than the rate of energy loss to the environment from the burning fuel. The confinement time is an indirect measure of the rate of this energy loss and is defined as the total amount of energy in the burning fuel divided by the rate at which energy is lost. It corresponds to the time constant of the rate of energy loss from the reaction. A short time constant means very rapid energy loss. It is often incorrectly interpreted as the necessary time duration for which the temperature of the fuel must be maintained for fusion to take place. The confinement time depends on the physical nature of the fuel.

For fusion of the D-T fuel supplied in gaseous form, with magnetic confinement of the heated plasma, the confinement time is around 3-6 seconds. For the fusion of solid D-T fuel using inertial confinement, the confinement time is less than 1 nanosecond (10-9 seconds).

The Lawson Triple Product
The triple product n T τE is an empirical measure of the conditions necessary for sustained fusion to take place. It is often used as a useful figure of merit to characterize or compare fusion reactions. It depends on factors such as the type of fuel, the method of fusion, the type and method of energy supply and the particle sizes and densities and is valid only for fusion temperatures between 10 KeV and 20 KeV.

In practical terms this means that for the reaction to be sustainable, the temperature, or energy, of the fusion fuel has to be very high. The particle density of the fuel must also be very high for reactions to occur reasonably often. At the same time the energy lost from the system per unit time must be relatively small (slow loss rate) which means that the τE confinement time (time constant) equivalent will be relatively long.

For ignition to occur, the energy input rate must be equal to or greater than the energy loss rate 1/τE.

Since the units of Temperature X Density are equivalent to a Pressure (From the Gas Laws PV=nRT) the units of the Triple Product are often stated as Atmospheres*Seconds

The following graph shows the value of the "triple product" necessary for sustained fusion to occur over a range of fuel temperatures for three different fuel combinations.

It shows that, as the temperature is increased the corresponding triple product necessary for fusion decreases. This is due to an increase in the fusion reaction rate which occurs as the temperature rises. However the fusion rate eventually reaches a maximum or "sweet spot"around 100 to 200 Million °K after which it gradually begins to fall. This sweet spot corresponds to the lowest triple product value at which sustained fusion can occur. For the D-T reaction this optimum condition occurs at a temperature of just over 10 keV. This is six times the temperature at the core of the Sun. See why Solar fusion seems to be possible at a lower temperature.

Note that to initiate fusion, both the D-D and the D-He3 fusion reactions require a greater triple product, or greater energy, than for D-T fusion.

Lawson Criteria for Nuclear Fusion

The engineering challenge is to find practical fusion methods which satisfy the Lawson technical conditions.

Fusion Methods

To initiate fusion, the amount of energy in the form of heat and pressure from external sources applied to the fuels must be sufficient to raise the energy levels of the fuel nuclei to a sufficient level to overcome the Coulomb barrier between the nuclei. For significant fusion reactions to take place, these high energy levels of the fuel elements must be maintained for a period long enough for a sufficient number of collisions between the atoms of fuel to occur. Such conditions prevail at the center of a star where the massive gravitational forces compress the matter, mostly Hydrogen, in its core to extremely high densities and temperatures causing fusion to take place.

To produce self-sustaining fusion, the rate at which energy is released by the fusion reaction itself must be greater than the rate of energy loss to the environment from the burning fuel. In the Sun or a star, the gravitational field balances the enormous thermal expansion forces resulting from the fusion, holding the fuel in place and maintaining the thermonuclear reactions in a controlled and steady rate. This stellar process of keeping the fuel in place is called gravitational confinement.


Various methods have been tried for generating and controlling the high temperatures and huge energy flows involved in keeping the fuel dense enough and hot enough for long enough to undergo sustained fusion in practical reactors. Two of the most successful reactor technologies are described here. Known as magnetic confinement and inertial confinement, they are optimized for the physical nature of the fuel.

The Earth does not have the immense gravitational pressure of the Sun to contain the fuel and compress it to a very high density. For fusion to take place on Earth, to compensate for the lower densities of the available fuels, the fuel or plasma must be be heated to temperatures six or more times higher than those in the Sun in order to achieve a sufficient number of fusion reactions. This is consistent with meeting the requirements of the Lawson triple product.

Creating the conditions necessary to initiate and maintain D-T and similar fusion reactions places severe requirements on the fusion reactor design. Unfortunately there are no materials for containing the plasma which can withstand the temperatures required of over 100 Million degrees Kelvin. Furthermore the plasma must be prevented from coming into direct contact with any solid material which could lead to contamination of the fuel so that the plasma must be enclosed in a vacuum. Obtaining a high enough particle density of gas molecules confined within a vacuum chamber for fusion is a major problem. Since the high temperatures also imply high pressures, and fusion causes very fast expansion of the plasma, some external force is required to act against this thermal pressure and keep the plasma in place.

In the stars the necessary confinement force is provided by gravitation. On Earth the force can be provided by magnetic fields in magnetic confinement plasma fusion reactors.

Alternatively the fusion reaction may be triggered in solid fuel pellets by a high intensity energy pulse in the very short period before the resulting plasma starts to expand. In this case there is nothing to counteract the expansion of the plasma but its inertia keeps the material together long enough for fusion to occur. The inertial confinement time is simply the time it takes the plasma pressure to overcome the inertia of the particles before they are dispersed, hence the name.

In general, increasing any one of the three factors ( n T τE) of Lawson’s triple product should allow the requirements on the other two factors to be reduced. As an example the fuel used in the magnetic confinement reactor has a very low density because it is a plasma of gas ions and it is contained in a vacuum. It also has a high rate of energy loss. It therefore needs longer confinement times for sufficient particle collisions to take place. Inertial confinement by contrast uses solid fuel which has a much higher density so that it can work with very short confinement times.

Fuel in Plasma Form – Magnetic Confinement Fusion (MCF)

Fusion of the Deuterium and Tritium fuel is designed to take place in a high temperature plasma circulating in a toroidal vacuum chamber such as the Tokamak reactor. Since the plasma consists of moving charged particles, it constitutes an electrical conductor carrying a current, hence it can be affected by magnetic fields. The tendency of the hot plasma to expand can therefore be counteracted by the Lorenz force, arising from its reaction with a magnetic field of appropriate geometry.

The plasma is created by injecting a small puff of the gaseous fuels into the toroidal chamber where they are heated to over 100 Million °C by electrical induction created by a transformer, with its inner poloidal magnetic coils acting as the primary winding and the plasma itself as the secondary winding. See diagram of the MCF magnetic fields below.

Strong magnetic fields around the torus serve two purposes. They are used to increase the plasma density to a level necessary to achieve fusion. At the same time, since they are not affected by heat, these fields act as a container confining the extremely hot conductive plasma to the center of the toroidal chamber so that it does not touch or damage the chamber walls.

After compression the particle density is greater than about 1020/m3 and the corresponding confinement time must be longer than 1 second.

Note that a particle density of 1020 particles (fuel ions)/m3 is very low corresponding to a mass density of around 1 milligram/m3 which is about one millionth of the density of air of 1.225 kg/m3 (at sea level and 15 °C).
The minimum Lawson’s triple product ( n T τE) required for sustained D-T fusion in an MCF reactor is approximately 3.5 X 1028 °K seconds/m3 ≡ 3 X 1021 keV seconds/m3.

See how this is implemented in the Tokamak Reactor

Fuel in Solid Form – Internal Confinement Fusion (ICF)

Before compression in an inertial fusion reactor, the density of the solid fuel used for ICF, at atmospheric pressure, is about 2 X 108 times denser (by mass) than same fuel in the form of a plasma. Solidifying the gaseous Deuterium and Tritium fuel by cooling it to -255 °C, to create small, dense, solid pellets gives the reactor an energy efficient head start in reaching the density required to satisfy the Lawson criteria for fusion.

The fuel pellets are bombarded from all directions, to provide uniform illumination of the target, by simultaneous pulses of high energy such as intense UV laser radiation, X-rays, or ion beams, with a duration of around one nanosecond and sufficient total energy to cause the pellet to implode. This sends a shock wave through the solid fuel pellet compressing it by 30 times or more causing the inner core to reach such a temperature and pressure that it fuses the D-T fuel in a mini thermonuclear explosion. After compression the particle density is around than 1030/m3, which is around 1010 times denser than the plasma used in magnetic confinement fusion. Because the density is so high, and the energy loss rate is relatively low compared with the plasma fuel, the confinement time can be 1010 times less to compensate and still satisfy the Lawson triple product requirement for fusion. This means that the confinement time can be as low as 10-11 seconds or more.

The inertia of the fuel ions within the pellet keeps the pellet together only long enough for fusion to take place under the influence of the high energy pulses before the explosive fusion reaction blows the pellet apart. There is therefore an upper limit of less than a nanosecond (10-9 seconds) to the possible confinement times for inertial confinement reactions because fusion must occur during the very short period before disintegration of the fuel pellet.

The minimum Lawson’s triple product (n T τE) required for sustained D-T fusion in an ICF reactor is approximately 1028 °K s/m3 ≡ 0.9 X 1021 keV seconds/m3.

See how this is implemented in the NIF Reactor

Inertial confinement was first used in the hydrogen bomb where the driver was x-rays created by a fission bomb.

The Tokamak Reactor – Magnetic Confinement

The principles of the Tokamak reactor are described here but it important to note that this is based on experience with small scale experimental units designed to verify the feasibility of key sub-system designs. There is still much work to do to scale up the system to deliver commercial power generation.

Benefits of D-T Fusion and the Tokamak
  • Nuclear fusion has the potential to provide much more energy for a given weight of fuel than any technology currently in use.
  • Secure and inexhaustible supply of low cost fuel.
  • No chemical effluent combustion products
  • Waste is less radioactive and in much lower volume than waste from fission reactors
  • No radiation leaks above normal background levels
  • No possibility of nuclear runaway (Chain reaction)
  • Shutting of the energy or the fuel supply causes the reaction to stop
  • Intrinsically safe system, does not require the elaborate safety systems needed for fission reactors
  • No after-heat problems associated with loss of coolant as in fission reactors
  • No use of, or production of, weapons grade nuclear materials
  • Major technical challenges still to be overcome
  • Tokamak technology (and alternative fusion technologies) still not ready after over 40 years of parallel development programmes by several nations.
  • Needs huge amounts of energy to initiate and control the fusion process
  • The plasma is prone to instabilities. See more about plasmas.
  • Produces radioactive waste though in much smaller amounts than fission reactions
  • Produces pulsed not continuous power.(Using a heat engine (steam turbine) to generate electricity makes this irrelevant.)
  • Requires immense pulsed power to start the reaction. This could affect the grid supply unless local, isolated, short term energy storage is provided.
  • Economic viability not yet proven
  • Tokamak System Principle

    Deuterium and Tritium atoms are heated and fused together in a high temperature plasma circulating in a vacuum chamber where the fusion reaction produces Helium and a surplus neutron. The plasma is maintained in place by powerful magnetic fields. Large amounts of electric power are needed to heat the plasma and to power the electromagnets. See diagram below.


    Surplus neutrons from the fusion reaction are captured by a Lithium blanket where they react with the Lithium producing more Tritium which is one of the two fusion fuels as well as alpha particles (Helium nuclei). The heat energy released by the fusion should be enough to maintain the fusion reaction and to provide a surplus which can be used to generate electricity. The surplus heat from the fusion and the neutron capture by the Lithium is used to raise steam in a heat exchanger and the steam is used to drive a conventional turbine generator.

    Engineering Challenges

    The quest for cheap, renewable energy using nuclear fusion is pushing the limits of technology in several directions simultaneously. Immense technical problems have to be overcome and solutions proposed and progress is painfully slow since it could take several years just to implement and verify a major sub-system change.

    • Containment
      The design of the reactor is dictated by the requirements for containment of the D-T reaction since there are no materials which could possibly withstand the extremely high temperatures necessary for fusion to take place. The solution is to confine the Deuterium and Tritium fuels in a plasma circulating within a toroidal chamber and kept from touching the walls by powerful magnetic fields.

      Note that the confinement time is measured in seconds. This indicates the order of magnitude of the engineering aspirations. A few seconds of fusion is currently regarded as a great success with the best achievement so far measured in minutes, albeit at a low efficiency.

      At higher plasma densities the required confinement time could be shorter but the ability to achieve higher plasma densities is limited by the ability to achieve higher magnetic fields.

      Only the Helium atoms are confined (neutrons, having no charge, escape the magnetic field) and therefore only 20% of the total fusion power is available for plasma heating

    • The Fuel
      The enormous JET Tokamak fusion reactor is designed to deliver megaWatts of power from a plasma of only a few grams of Deuterium and Tritium circulating within the torus.
    • The Plasma
      The temperature of the D-T plasma in the Tokamak is over 100 Million °C. Since the plasma comprises charged particles it becomes conductive and can be controlled by electrical and magnetic fields. These fields confine the plasma to the centre of the torus so that it cannot come into contact with, or damage the chamber walls.

      Instabilities of the plasma are a serious nuisance rather than a major disaster.

    • The Plasma Chamber
      The fusion needs to take place in a vacuum to avoid contamination by other elements. Since the plasma circulates in a toroidal shape, it needs a toroidally shaped vacuum chamber to contain it. Though the amount of fuel is very small, only a few grams, the cross section of the chamber needs to be very large to allow sufficient separation of the extremely hot plasma from the chamber walls . The outer diameter of the chamber ring in the JET Tokamak for example is over 10 metres. The cross section of the toroidal ring through which the plasma flows is "D" shaped with an internal height of over 4 metres. This is a small scale demonstration plant!
      The physical requirements of this huge structure are severe.

      • It must maintain a very high leak free vacuum inside
      • The chamber walls must allow the externally applied magnetic fields to pass through.
      • It must accommodate access for fuel and instrumentation while maintaining the vacuum boundary.
      • It must absorb the thermal radiation coming from the extremely hot plasma allowing for the occasional momentary contact of the plasma with the walls in case of temporary instability.
      • When heated to extremely high temperatures, the chamber walls should not release impurities into the plasma which would contaminate and cool it.
      • More seriously, it must allow the neutron flux resulting from the fusion reaction to pass through chamber walls to the Lithium blanket surrounding the chamber. The neutron flux in a D-T fusion reactor is about 100 times that of fission power reactors and some of these neutrons are unavoidably absorbed by the chamber structure causing it to become radioactive. Once this has occurred, any subsequent activity in the chamber must be done using remote handling equipment.
    The Magnetic Fields

    Magnetic confinement is used to contain the high temperature plasma preventing it from touching the chamber walls.

    Since the plasma comprises charged particles, its location can be fixed by two superimposed external magnetic fields interacting with the magnetic field of the plasma current itself as shown in the diagram below.

    The toroidal chamber carrying the plasma passes through a series of toroidal field coils (shown in green) mounted vertically around the circumference of the chamber. These coils create a toroidal magnetic field along the center line of the plasma chamber. Electrons and ions in this field will tend to follow helical paths along the magnetic field as they circulate around the inside of the chamber. This field provides the primary mechanism of confinement of the plasma particles.

    Toroidal Magnetic Field

    The poloidal coils, also confusingly called vertical coils since they are mounted horizontally parallel to the plane of the toroidal chamber, are located around the perimeter of the chamber. The inner poloidal field coils serve a dual purpose, acting as the multi-turn primary of a transformer whose secondary is the plasma itself which is essentially a single short circuited turn. In this way a large current can be induced in the plasma causing it to flow along the inside of the chamber, winding its way through the torus in a helical path. At the same time the secondary current raises the plasma temperature by Joule (I2R) heating.

    Poloidal Magnetic FieldSource ENS European Nuclear Society (Modified)

    The interaction of the external poloidal and toroidal magnetic fields and the field due to the plasma current serves to locate the plasma within the cross section of the chamber at the same time squeezing it towards the centre line and away from the walls

    TokamaK Magnetic Fields

    Tokamak Magnetic CircuitsSource – European Fusion Development Agreement (EFDA)

    The diagram opposite provides an alternative view showing the iron core of the transformer poloidal magnetic circuit.

    The dependence of the system on the transformer raises other problems since transformers only work with varying currents, whereas DC is required for continuous power generation. This limits the existing Tokamak design to the production of pulsed power. The actual waveform is a sawtooth current ramp.

    Sawtooth Wave

    The main plasma current in the JET reactor (See below) is around 5 Million Amperes.

    Energy consumption in the magnetic field coils is minimized by using superconducting technologies which require very low temperature operation.

    Plasma Heating

    In current Tokamak designs the Joule heating supplied by by the poloidal transformer is insufficient to raise the temperature to the necessary 100 Million °C or to maintain it there. Consequently, the heating must be supplemented from other sources.

    Magnetic Compression
    The gas laws tell us that the temperature of a fixed volume of gas is directly proportional to its pressure. The same compression heating effect can be achieved in the Tokamak by increasing the magnetic field confining the plasma. At the same time this compression increases the plasma density facilitating the fusion reaction.

    Radio frequency (RF) Heating
    RF heating is another technology which is used for plasma heating.

    Plasma Self Heating
    Once fusion starts the fusion products contribute to the overall heating.

    The high speed neutrons produced by the fusion carry 80% of the energy released, but having no charge, they escape from the magnetic field. Because they have high penetrating power, most of the neutrons pass through the chamber wall and are eventually captured by the Lithium blanket to which they give up their energy. A neat way of passing the fusion energy through the chamber walls without heating them up. The neutrons which don’t make it through the chamber wall react with the materials in the wall causing them to become radioactive.

    The positively charged Helium ions (alpha particles) on the other hand carrying 20% of the fusion energy remain trapped by the magnetic field in the plasma where they give up their energy in collisions with the Deuterium and Tritium ions increasing their temperature in the process.

    If the heat energy is sufficient and there are enough D-T ions to accept it and given enough time for collisions to occur then fusion can occur. This is the basis of the Lawson criterion.

    Only the Helium ions are confined (neutrons escape magnetic field and plasma) and therefore only 20% of the total fusion power is available for plasma heating

    Additional heating is needed to raise the temperature of the plasma
    RF heating with radio/micro-wave radiation (~25-55MHz)
    Neutral beam heating: accelerate beam of H or D ions then neutralisation + collision with plasma

    The Lithium Blanket
    The Lithium blanket serves several purposes:

    • It captures the neutrons emitted by the fusion reaction and extracts their energy converting it into heat.
    • It reacts with the neutrons emerging from the plasma to form Tritium, which is fed back into the reactor as fuel.
    • It is an essential part of the heat exchanger in which the heat energy is transferred to a water/steam circuit, raising steam for conventional electricity generation while at the same time cooling the reactor.
    • It contains the radiation from the radioactive structure.

    Alternative designs for of the blanket are still being investigated. Options are pellets of Lithium or pebbles of Lithium alloys which help facilitate the extraction of the Tritium and the purging of the Helium produced in the blanket. This is complicated by the fact that Lithium melts at 180 °C  and boils at 1347 °C. More likely, Lithium will be used in liquid form which simplifies the heat transfer in the heat exchanger.

    Extracting the power

    The first stage is to extract energy from the fusion process. Up to now, no fusion reactors, including Tokamaks have produced significant power with a conversion gain better than unity.

    The Plasma

    The main difficulty is in producing and maintaining a sufficiently high temperature for fusion to occur. So far this has been, and can only be, possible in short pulses with Tokamak designs dependent on transformer heating. The pulse durations achieved, that is the duration of controlled maintenance of the plasma, have been only a few tens of seconds. The confinement time which is the average time that the ions and electrons remain in the plasma (as specified in the Lawson criterion) is generally much shorter than this. Commercial power plants will need pulse lengths of many hours or days.

    The Heat Exchanger

    The heat exchanger is an essential component in the energy conversion chain, designed to take the heat out of the Lithium blanket as explained above. The electricity generating equipment does not see the power pulses coming from the reactor. By converting the energy to heat, the energy pulses are simply smoothed out in the heat exchanger.

    Generating electricity by nuclear fusion or nuclear fission involves three energy conversion stages, each with its own efficiency losses. While direct energy conversion from a nuclear reaction in a single stage may not yet be practical, it seems that the possibility of a two stage energy conversion by combining fusion with MagnetoHydroDynamics (MHD) is still beyond reach. MHD is designed to extract electricity directly from a charged plasma by Faraday induction. The Tokamak already provides the plasma, but it would need to use a different pair of fusion elements which didn’t produce a troublesome neutron. It’s a pity a way has not been found for using it to generate electricity directly by MHD techniques.


    Compared with a fission reactor in which a serious nuclear accident could result if the chain reaction gets out of control, a fusion reactor is intrinsically much safer. The processes involved in a fusion reactor are all set to work at optimum conditions of temperature, pressure and magnetic field. Any deviation from these optimum values, for whatever reason, will immediately cause the fusion energy release to fall and the conditions for maintaining fusion, the Lawson criteria, will rapidly be breached causing the fusion to stop. There is thus no possibility of nuclear runaway and the basic high energy fusion reaction is intrinsically safe.

    • The active plasma is kept in a finely balanced equilibrium position by the applied magnetic fields. Any malfunction in the system or external damage would upset the equilibrium and the plasma would collapse into the walls of the chamber, immediately ending the fusion reaction.
    • The self sustaining fusion action occurs in pulses and energy must be applied to initiate each fusion pulse. In the absence of heating energy pulses there could be no fusion.
    • In the case of a serious accident, the only radioactive product which could be released into the atmosphere is the Tritium fuel. The total amount of Tritium circulating or stored in the plant is only about 1 Kg and this would be diluted to legally acceptable safety limits by the time it reached the plant boundary.
    • The amount of fuel circulating within the reactor at any time is only a few grams. Turning off the fuel supply stops the reaction in seconds.
    • The amount of nuclear waste produced by the Tokamak is much lower than with fission reactors and what waste there is has a much shorter half-life
    Current Experience

    The largest current experiment for controlled nuclear fusion in the world is the Joint European Torus (JET) at Culham in England.

    The JET Tokamak

    Source – European Fusion Development Agreement (EFDA)

    Work on the JET project began in january 1983 and by 1991, it was possible for the first time in the history of fusion research to release considerable energy by controlled nuclear fusion using the JET. For a period of two seconds, the facility generated a fusion power of 1.8 megawatt. In 1997, JET produced a peak of 16.1 MW of fusion power (65% of input power), from an input power of 24 MW sustained for over 0.5 seconds. After a quarter of a century we may know a lot more about fusion and Tokamaks, but we still can not deliver sustained power even on a laboratory scale.

    In June 2005, the construction in France of a much larger Tokamak, the International Thermonuclear Experimental Reactor (ITER), was announced by the European Fusion Development Agreement (EFDA). Designed to produce several times more fusion power than the power put into the plasma over many minutes it dwarfs the JET. Described as “an experimental step between today’s studies of plasma physics and future electricity-producing fusion power plants” it is expected to deliver 500 megawatts of fusion power from an input power of 50 megawatts with a conversion gain Q of 10 and is expected to cost $16 billion while still not delivering commercial power. Full Deuterium-Tritium fusion experiments are not scheduled to start until 2027.

    The Future

    While the demonstration units may verify the technical feasibility of generating electricity by nuclear fusion, the economic viability is yet unproven. Proving out all of the necessary subsystems and scaling up the design from the demonstration systems to commercial generating plants is far from complete and industry experts don’t expect to achieve the goal of commercial exploitation until 2030 or 2040. Meanwhile engineers and physicists have a new set of expensive toys to play with.

    Nice work if you can get it!
    Tokamak History

    Inertial Confinement Reactors

    Inertial confinement fusion (ICF) is loosely based on the principles used in the Hydrogen bomb only on a much, much smaller scale. The fusion fuel is subjected to very high pressure and temperature in order to initiate fusion. In the case of the Hydrogen bomb these necessary operating conditions are created by the nuclear fission explosion of an Atom bomb.

    For controlled ICF, the extreme operating conditions are achieved instead by bombarding a small, solid pellet of fuel with a very high pulse of energy causing its outer layer to be rapidly heated to the necessary 100 million degrees Kelvin and at the same time causing the inner part of the pellet to be compressed very quickly with huge pressure to a density 20 times that of solid lead. The intense heat coupled with the increase in density of the fuel is sufficient for fusion to take place. This all happens in around one to three nanoseconds. The energy pulse could be derived from a variety of sources, known as drivers, including, ultra violet (UV) lasers, X-rays, electron beams and plasma (ion) beams.

    The first fusion reactor ever to successfully achieve a conversion gain greater than unity was the National Ignition Facility (NIF) reactor at the US Lawrence Livermore National Laboratory. The operating principles and challenges of inertial confinement fusion are explained here using the technology of the NIF reactor, and the results of its breakthrough "over unity" fusion demonstration, as an example.

    The NIF Reactor – Inertial Confinement Fusion (ICF)

    In its simplest configuration, a small pellet of frozen Deuterium-Tritium mixture (D-T) held in a plastic shell is irradiated evenly from all sides by intense bursts of energy from very high power laser beams, or X-rays, focused directly on the target, explosively detonating its outer layers and initiating a mini thermonuclear explosion at the core of the pellet. The diagram below illustrates the stages of the process.

    Other inertial fusion drivers include heavy or light ion accelerators.

    Nuclear Fusion Using Laser Energy and Inertial Confinement

    Inertial Confinement Key
    Source: U.S. LANL – Los Alamos National Laboratory (Modified)

    The alpha particles (helium nuclei) produced by the D-T fusion reaction carrying 20% of the released fusion energy deposit this energy within the fuel mass further heating the fuel and increasing the rate of the fusion reactions. The neutrons with 80% of the energy escape from the fuel carrying their energy with them.

    The Confinement Time

    The confinement time of the plasma is mostly determined by the radius of the capsule. The inward shockwave travels approximately at the speed of sound. The inertial confinement time depends on the outward movement of the ions. It is typically only a few nanoseconds and is roughly the time that it takes an ion to travel at its thermal speed across the radius of the fuel pellet. The higher the temperature and density, the more vigorous the reaction and the more difficult it is to contain the plasma.

    The Fuel Target

    The fuel pellet is a 60/40 mixture by weight of Deuterium and Tritium enclosed in a small plastic capsule and frozen to its solid state at -255 °C (18 °K) to keep it solid. The capsule is necessarily small, typically about 2 mm in diameter and only a few milligrams or less in weight, for two reasons. Larger fuel volumes will require larger input energies to bring about ignition and the ignition of larger pellets releases so much energy that it could result in damaging the reactor chamber. For example, the fusion of 1 milligram (0.000035 ounces) of D-T fuel releases 337 MegaJoules (93.6 KWh) of energy, equivalent to 80.7 kg of TNT.

    Typically only a small proportion of the fuel will undergo fusion unless full ignition is achieved since the very short confinement times limit the duration of the fuel burn.

    The Reactor Chamber

    The target must be precisely located at the center of a vacuum chamber where it can be irradiated evenly from all sides by laser beams positioned in apertures in the chamber wall. The NIF chamber is for experimental use only and is 10 meters (33 feet) across with a wall thickness of 10 cm of aluminium and 30 cm (1 foot) of concrete which absorbs neutrons from fusion reactions and contains explosions. The walls in commercial reactors will be designed to incorporate heat exchangers to capture the energy released by the fusion.

    The NIF Laser Driver

    The driver is the mechanism by which energy is delivered to the fuel capsule. The NIF reactor uses a laser for this purpose. With an output of 1.8 MegaJoules (MJ), it is the world’s largest and most energetic laser. To put this energy output into perspective, 1.8 MJ is equivalent to only 500 Watthours or 0.5 "units" of domestic electricity. But the NIF laser can deliver this energy in 3.6 nanoseconds. This means that it can supply a continuous power of 500 TeraWatts (trillion Watts) for 3.6 nanoseconds. This is almost 1000 times more than the 0.535 TeraWatts average instantaneous of electrical power consumption of the entire USA.

    • The Laser
      The process starts with a Neodymium:glass laser which generates pulses of infrared light with precise frequency and pulse shape control. The pulse duration can be varied between 1 and 15 nanoseconds and it is shaped to provide precise timing of the energy flow to optimize the timing of the heating of the plastic ablator surface followed by the implosion of the fuel. Instabilities which cause the uncontrolled break-up of the fuel pellet are suppressed by starting with a low energy intensity followed by a rapid rise to maximum intensity for around 3 nanoseconds during the second half of the pulse.
    • The Splitters and Amplifiers
      After launch, the laser pulse is split into 48 separate beams and passed through 48 preamplifiers each with a gain of 109 times. Each beam is further split into 4 beams to give a total of 192 beams which are passed back and forth several times through 192 main amplifiers consisting of reflective Neodymium doped glass slabs (lasing material) surrounded by Xenon flash lamps powered by a large capacitor bank. The intense flash of light from the lamps pumps the Neodymium atoms up to a higher energy state so that the laser beam gathers more light and energy as it passes through giving a further gain of 106 for an overall gain of 1015.
    • The Frequency Converters
      In the final optical assemblies, the laser’s infrared (IR) light with a wavelength of 1053 nm is converted into ultraviolet (UV) light with a wavelength of 351 nm in Potassium Dihydrogen Phosphate (KDP) crystal frequency converters which merge groups of three of the incoming photons into a new photons with three times the energy and one third of the wavelength. The shorter wavelength beams are absorbed more readily by the fuel targets and cause less uncontrolled preheating of the fuel by electrons.

Laser Beam Alignment
An array of mirrors and optical assemblies positioned around the reactor chamber converge the beams and focus them with great precision on the tiny 2mm target, held on a supporting arm, at the centre of the 10 meter chamber.

National Ignition Facility - Laser Bay, Lawrence Livermore National Laboratory
Source: LLNL – Public domain.
The NIF Laser

The NIF’s 192 laser beams and their amplifiers are housed in two separate laser bays, each the size of a football field and each containing 96 of the beams.

The photograph shows one of the laser bays.
Note the size of the operating personnel.

Direct Drive

With direct drive, the fuel pellets are irradiated directly by the laser beams fired from the chamber walls 5 meters away. To maximise the effect of the incident radiation and ensure controlled fusion, the energy must be precisely concentrated into the centre of the pellet. It is not enough that the beams merely hit the pellet. The 192 beams must enter the 2 mm fuel pellet, at precise angles, at 192 points evenly distributed around its surface. Misalignment will result in insufficent energy being concentrated on the centre of the fuel pellet to initiate fusion and will instead cause breakup of the pellet. In practice, it is very difficult to achieve the necessary uniform illumination of the target simply by focussing the multiple laser beams directly on the pellet.

According to Bruno Van Wonterghem, operations manager for NIF “The precision NIF is designed to achieve is similar to throwing a dime from Livermore to San Francisco [a distance of about 64 kilometers] and landing it perfectly inside the coin slot of a parking meter.”

Indirect Drive

The NIF overcame this alignment problem by using indirect irradiation by means of X-rays derived from the laser beams to initiate fusion instead of the laser beams. Its breakthrough experiment, in which it achieved the first ever over unity conversion gain, used a fuel pellet weighing 0.17 mg, contained in a 2mm diameter plastic capsule held at the center of a, hollow, open ended, cylindrical shaped cavity made of gold called a hohlraum .(German "hollow space"). The 192 laser beams are fired through the holes at each end of the cavity at such an angle that they don’t touch the capsule but instead hit the inside wall of the hohlraum.

The laser pulses heat the gold of the hohlraum to such a high temperature that it in turn radiates a pulse of X-rays which are more dispersed than the laser beams and which spread more uniformly around the capsule, not just focusing on the 192 points. About 15% of the incident energy is lost in this process.

Only about 15% of the resulting X-rays actually impinge on, and are absorbed by, the target capsule but this is enough to initiate the blow off of the plastic ablator and the implosion of the fuel.

Direct and Indirect Fusion Drive
Direct and Indirect Fusion Drives
Source: LLNL
The NIF Hohlraum
Source: LLNL NIF

Measuring about 10 mm long and 5.5 mm in diameter, with a 2.8 mm diameter laser entrance hole at each end, the hohlraum converts the light energy to X-ray energy and provides a much more uniform energy distribution.

NIF Fusion Energy Flow Summary

(The 2013 demonstration)

Approximate energy levels at different process steps of the NIF reactor

Infrared master oscillator (laser) output: 10-9 J

Energy of the infrared light pulse emerging from the Neodymium:glass laser.

Input energy of the laser amplification process: 422 MJ
The energy consumed by the amplifiers and beam splitters in raising the energy in the beams is 422 MJ.
(Efficiency 0.85%)

Laser Infrared output: 3.6 MJ
Energy output from the laser amplifiers applied to the frequency converter.

Laser UV output: 1.8 MJ
Combined output energy after conversion to UV radiation of the 192 beams impinging on the hohlraum target.

Laser energy absorbed by the hohlraum: <1.5 MJ
Theoretical prediction of the energy remaining after the UV radiation is converted to X-rays, about 85%.

Laser energy absorbed by the outer layers of the DT target pellet: <220 kJ
Theoretical prediction of the estimated percentage of the available X-ray energy in the hohlraum which is absorbed by the outer layers of the target, about 15%.

Actual energy absorbed by the DT target pellet: ~10 kJ
Like the X-ray energy in the hohlraum, this is difficult to measure and so is an estimated value which is equivalent to 2.8 Watthours. It is less than 0.6% of the laser energy fired at the hohlraum target.

NIF reactor – Energy out

Energy released by fusion reaction: ~14 kJ
Calculated from the count of neutrons emitted. Neutrons are a product of fusion reactions so they are used as a measure of the energy output. The output energy is equivalent to 3.9 Watthours and is released in the form of heat.

4 Watthours of electrical energy is just enough to power a 60 Watt electric light bulb for 4 minutes.

Conversion Gain and System Efficiency The final fusion energy output of 14 kJ compared with the energy supplied, measured at different points in the conversion chain is as follows:

  • 1.4 times the 10 kJ of energy absorbed directly by the DT fuel – (the fusion gain).
  • 0.8 % of the 1.8 MJ laser energy irradiating the target – (the target efficiency)
  • 3.3×10-5 fraction of the 422 MJ of input energy consumed in amplifying the the output of the master laser – ignoring the small amount of energy used to power the laser. (the system efficiency)
  • Note that the system conversion gain or efficiency just refers to the production of heat from the fusion reaction. It does not include any further system thermodynamic and efficiency losses incurred, typically 35%, if the heat would be used in applications such as generating electricity from the heat of fusion.
  • Sources: The European Fusion Education Network (fusenet), LLNL and others.

    The NIF 2013 Demonstration – Performance Evaluation

    The results of the NIF demonstration are often misinterpreted as having produced net energy. This is plainly not true but the experiment did achieve a most important milestone: The amount of energy released through the fusion reaction exceeded the amount of energy being absorbed by the fuel. The demonstration thus achieved a fusion gain greater than unity which enabled the "burning" of the fuel but this is still a step short of the lab’s goal of “ignition” or self sustained burning. Burning only occurred while the fuel was being irradiated by energy from an external source, in this case, during the pulse of X-rays derived from the laser pulse. See note about Conversion Gain and Breakeven.

    The results indicate that, using the NIF reactor, the overall fusion "system" gain would have to be of the order of 30,000 just to breakeven or 100,000 if the desired system output was the generation of electricity. The biggest factor adversely affecting the system conversion gain however is not the low gain of the fusion reaction, but the poor efficiency of the optical amplification and frequency conversion systems which consume 422 MJ of energy just to provide the 1.8 MJ laser power output, – an efficiency of only 0.4%. Improved laser, or alternative drive, technology could thus make a dramatic improvement in system efficiency.

    Since the results of the 2013 demonstration were published, NIF fusion development has continued. Two months after the first successful shot, modifying the shape and timing of the laser pulse used to detonate the fuel has enabled the conversion gain to be increased by over 20%. Subsequently the efficiency losses in the laser driver chain have been reduced by 25%.

    For comparison, in 1997 the JET Tokamak produced 16.1 MWatts of power for 5 seconds equivalent to 22.4 kWh or 80.5 MJoules.

    Alternative Drivers

    The method of providing the driver energy for detonating the fuel in ICF reactors was pioneered with lasers, but the limited efficiency of these systems and the difficulty of scaling up the technology and modifying it for commercial applications has prompted research into other methods. Both heavy and light ion beam driver systems offer significant advantages over laser drivers. Reactor designs can be greatly simplified and they are capable of higher energy pulses, better driver efficiencies and higher repetition rates.

    Multiple ion beams are accelerated through a series of linear accelerators and made to converge on the target. Heavy ions deposit more energy per ion than lighter species, and therefore a smaller ion current is needed to deposit a given total energy.

    Scaling Up Laser Fusion Systems for Commercial Applications

    While the experimental results are encouraging and demonstrate the feasibility of inertial confinement fusion, there’s still a long way to go to scale up the immense demonstration system into a commercially viable heat source for powering an electricity generating plant. The following are some of the issues which need to be considered.

    • Driver System
      The existing NIF driver system is over complicated and very inefficient. A simpler, more efficient system needs to be developed. Besides producing the required power density, a commercial driver must also have an adequate repetition rate and be efficient and reliable. These requirements are more likely to be satisfied by ion accelerators. There’s lots of scope for improvement here.
    • Capturing the Heat Output
      The demonstration system generates inconsequential amounts of heat energy which is carried away by neutrons which strike the reactor chamber walls. It does not have a method of capturing the heat. Some of the materials in the chamber walls are unfortunately susceptible to radiation damage from the neutrons produced by the fusion, becoming radioactive as well as mechanically weakened. In a commercial reactor where the production of neutrons will be considerably higher than in the experimental reactor, the chamber wall should be able to withstand this neutron bombardment otherwise it would have to be replaced regularly. It must also incorporate a heat exchanger to capture and extract the energy from the neutrons. Such problems have been investigated in depth in the Tokamak reactor whose walls include a Lithium blanket which serves the dual purpose of generating Tritium as well as capturing the neutrons.
    • Continuous Output
      Just as the ICF reactor receives its energy in pulses, so it also delivers its energy in pulses. Currently it is only capable of carrying out one fusion shot per day, each of which delivers only a small amount of energy. For commercial use, continuous energy flow is required so that the fusion repetition rate with an output of 14kJ per shot would need to be increased to at least ten shots per second. This would generate an output 3.36 MWh of heat energy per day. But this is not the net energy gain of the system. The overall inefficiencies prevailing in the 2103 "state of the art" system would have to be taken into account and this would have changed the fusion energy gain to a substantial system energy loss. Progress to eliminate system losses and to improve the fusion gain continues.

      The large number of fuel pellets needed has consequences for fuelling the system.

    • Pellet Production
      To carry out ten shots per second would require production of 864000 pellets and hohlraums per day of the size used in the demonstration unit. A smaller number of larger pellets could be used but the practical maximum pellet size is limited by the potential explosive power of the fusion.
    • Conversion Gain
      Ii is not unreasonable to expect that with further development the fusion energy conversion gain could be increased high enough to cause self sustaining ignition rather than simply burning. This has the dual benefit of improving the overall system gain and while it would still be necessary to have manageable, low fuel weights, the self sustaining reaction would make more efficient use of the fuel by consuming a greater proportion of the pellet mass thus reducing the number of pellets required.
    • Fuel Feed System
      This could be a major problem. The fuel pellets must be refrigerated and fed at high rate into the target holder which will be very hot from previous fusions. The pellets nust also must be placed and aligned very precisely at the convergence point of the laser or ion beams.
      The debris from the fusion must also be collected and removed on a continuous basis.
    • Fuel Costs
      The cost of the gold used in the hohlraums which are destroyed in every shot is not insignificant though much of it could be recovered and recycled. Nevertheless, it will probably be more cost effective to use an alternative driver system.
    • Capital Costs
      The cost of the NIF demonstration system has been over $4 billion. Considering the further development which needs to take place and the complexity of the added technical facilities needed by a commercial reactor, it may turn out that though the system is technically viable, it may be difficult to produce a commercially viable system.
    • Safety
      The ICF system has the same safety issues as the Tokamak, though working at a lower pressure, without the high temperature plasma, it could be considered slightly safer.

    The Way Forward

    We know inertial confinement fusion using lasers works. We also know laser systems have their drawbacks and the technology is still in its infancy. Development work is however continuing at various research institutions throughout the world, across the whole spectrum of fusion technology, to come up with alternative reactor designs with more efficient driver systems, practical heat capture systems and fuel feed systems. There’s a long way to go but we are getting there.

    About the author, Barrie Lawson:

    Barrie graduated from Birmingham University with a degree in Electrical and Electronic Engineering in 1964. Since then he as has worked at Director level in many branches of the electronics industry including military electronics, telecommunications, computers, automotive and consumer electronics. During the last 10 years he has been involved in the battery business, originally as Chairman of MPower Batteries, a custom battery pack making company in Scotland which he helped to found and later in China where he set up a similar business. He is currently Chairman of CHE EVC, another battery startup company pioneering some interesting new technologies. In his spare time he writes and maintains the Electropaedia web site, a comprehensive knowledge base about batteries and energy sources.

Is There a Better Route to Fusion?

Following presentation adapted from T. H. Rider Ph.D. thesis, MIT
Published with permission June 2015
All rights reserved by original author & institution
“Thirty-five years ago I was an expert precious-metal quartz-miner. There was an outcrop in my neighborhood that assayed $600 a ton—gold. But every fleck of gold in it was shut up tight and fast in an intractable and impersuadable base-metal shell. Acting as a Consensus, I delivered the finality verdict that no human ingenuity would ever be able to set free two dollars’ worth of gold out of a ton of that rock. The fact is, I did not foresee the cyanide process… These sorrows have made me suspicious of Consensuses… I sheer warily off and get behind something, saying to myself, ‘It looks innocent and all right, but no matter, ten to one there’s a cyanide process under that thing somewhere.’”
-Mark Twain, “Dr. Loeb’s Incredible Discovery” (1910)

Wish List of Characteristics For the Perfect Nuclear Energy Source

• Little or no radiation and radioactive waste
• Minimal shielding
• Scalable to power everything from computer chips to GW reactors
• High-efficiency direct conversion to electricity
• Utilizes readily available fuel
• Cannot explode, melt down, or frighten Jane Fonda
• Not directly or indirectly useful to terrorists or unfriendly countries

Can we come closer to meeting these goals?

page 9

Fundamental Constraints on Fusion Approaches

Best foreseeable 1 GWe (3 GWt) magnetic fusion reactors:
• D+T: 2.4 GW of 14-MeV neutrons, 1.6 giga-Curies (GCi) of T stockpile/year
• D+D w/o product burnup: 1 GW 2.5-MeV neutrons, 1 GW X-rays, 70 GCi T
• D+D with product burnup: 1.1 GW mainly 14-MeV neutrons, 180 MW X-rays
• D+3He w/o product burnup: 30 MW 2.5-MeV neutrons, 500 MW X-rays, 1.8 GCi T
• D+3He with product burnup: 150 MW mainly 14-MeV neutrons, 500 MW X-rays
• Mainly thermal (Carnot-limited) conversion of fusion energy to electricity

Potential Thesis (or Nobel Prize) Topics

Fusion reactions
• In the table of possible fusion reactions, should additional reactions be green?
(Consider competing side reactions and idealized breakeven against bremsstrahlung.)
• Are there any promising reactions not in the table (due to higher Z or shorter nuclide half-life)?
Can one provide better evidence (especially experimental) for or against spin polarized fusion?
• Benefits of spin-polarized fusion (especially for D+D reaction enhancement or suppression).
• Methods of producing polarized nuclei.
• Mechanisms and rates of depolarization relative to the fusion rate.

Fusion catalyzed by massive negative particles
• Are there more efficient muon production methods?
• Are there practical methods for unsticking muons from alpha particles?
• Are there methods to reduce the muon catalysis cycle time?
• Are there any massive negative particles that are more suitable than muons for catalysis?
• Can the effective electron mass or charge be increased in useful ways?

Other ways to improve the tunneling factor
• Is there a way to keep scattering from hindering shape-polarized fusion?
• Is the resonant tunneling model valid, and does it have useful consequences?
• Is fusion of light elements in liquid metallic states scientifically valid and practical to achieve?
• Are there other ways to improve the tunneling factor?
• Can one prove we have covered the complete phase space of ideas for improving the
tunneling factor?

Other improvements to σfus
• Are there ways to improve the wavefunction cross-sectional area factor in σfus?
• Are there ways to improve the Breit-Wigner compound nucleus energy resonance factor in σfus?
• Are there any other categories of ways to influence σfus?

More Potential Thesis (or Nobel Prize) Topics

Fusion products
• Are there practical ways to influence the reaction channels and products?

Plasma properties
• Are there realistic ways to recirculate power and maintain ions in a monoenergetic or anisotropic state, or two ion species at different temperatures (e.g. hot 3He and cold D or hot p+ and cold 11B?
• Are there practical ways to reduce ion-electron energy transfer or recirculate power from the electrons back to the ions?
• Are there ways to reduce/convert radiation power losses, especially bremsstrahlung?

Confinement of particles and energy
• Are there practical lessons we can learn from stellar fusion and use to improve fusion reactors?
• Are there ways to overcome the main practical difficulties with inertial confinement fusion?
• Which existing magnetic confinement approach is best, or can a better one be created?
• Can the conduction losses be reduced to make acoustic confinement practical?
• Can fusion-fission hybrids be made more attractive?
• How is ball lightning confined, and can fusion reactors employ a similar approach?
• Is there any feasible way to create a small black hole?
• Are there any other confinement approaches worthy of investigation?

Direct conversion
• What are the most efficient/compact thermal-to-electric converters?
• What are the best converters for light nuclei—traveling wave converters, etc.?
• Are there practical ways to directly convert the energies of recoil nuclei or other heavy nuclei emitted by solid materials?
• What are the best converters for electrons?
• How feasible and efficient are the neutron energy conversion methods of Perkins et al.?
• How feasible and efficient are the X-ray and g-ray energy conversion methods of Wood et al.?

Download the original PDF

Development of Practical Fusion Power

T. D. Tamarkin USCL-EnergyCite®
Additional scientific contributors, S. C. Hsu, Ph.D., T. J. Awe, Ph.D., S. Brockington, Ph.D., A. Case, Ph.D., J. T. Cassibry, Ph.D., G. Kagan, Ph.D., S. J. Messer, Ph.D., M. Stanic, X. Tang, Ph.D., D. R. Welch, Ph.D., and F. D. Witherspoon, Ph.D.

Updated December 14, 2014
Energycite ®



Fusion is the ultimate source of energy for human civilization in all sense of the word. Because fusion transforms mass directly to energy according to Einstein’s theory of special relativity (E=MC²,) a very small amount of fusion fuel creates a very large amount of energy. The cost of fusion fuel (Hydrogen-deuterium and Lithium) per mWh of energy is so close to zero that virtually all the cost of electricity generated from fusion arises from the capital cost of the power plant and its amortization of development, operating and maintenance costs. The profit potential of fusion power is immense. Fusion can be used to create synthetic liquid and gas fuels for the transportation industry, thereby replacing petroleum and natural gas, as well as virtually unlimited electricity. Direct fusion propulsion has long been considered by NASA for the next generation of manned spacecraft for long distance space exploration. Fusion power is environmentally clean, emits no greenhouse gases, and produces no appreciable radioactive waste. The planet’s fossil fuel reserves are severely limited. Whereas current nuclear fission fuel resources such as Uranium and Thorium still remain abundant, nuclear power has safety, radioactive waste, and weapon proliferation issues. Fusion power is the only known hope for mankind’s survival on this planet in the foreseeable future.
In this paper, we describe fusion power and its ability to provide all the energy the world can consume for eternity. Next we summarize the status, politics, and legacy of the United States government funded fusion research program and provide a historical perspective of the development of alternate fusion approaches. Then we explain how fusion energy can be developed by private entrepreneurial enterprises using the innovative approach of Plasma Jet Magneto-Inertial Fusion (PJMIF.)

Table of Contents

1. Background
2. The Government Funded Fusion Program
3. The Truth about the Cost of Fusion Development and the Fusion Alternates
4. History and Status of PJMIF R&D
5. The PJMIF Approach to Fusion Energy
6. Reactor Considerations
7. Concluding Remarks
8. References
9. Figures

1. Background

  1.1. What is fusion?
Fusion is the process that powers the Sun and the stars. It is Nature’s way of creating energy and is the opposite of nuclear fission, the process by which nuclear power is produced today. In fusion, the atomic nuclei of two light atoms fuse to form heavier nuclei. In the process, a large amount of energy is produced due to the conversion of mass directly to energy according to Einstein’s principle of special relativity expressed as E=MC². For commercial production of fusion energy, the fusion reactions considered usually involve the two isotopes of Hydrogen, namely 2H or deuterium (D) and 3H or tritium (T). Deuterium exists naturally in sea water which is a plentiful source of the isotope. It is non-radioactive. Tritium is radioactive, but has a very short half-life of approximately 12 years, and thus is very rare in nature. When deuterium and tritium are chosen as the fuel for a fusion power reactor, tritium is produced as part of a carefully designed fuel cycle involving the very common element Lithium, while deuterium is “mined” from the sea. The nucleus of a deuterium atom contains a proton and a neutron, whereas the nucleus of a tritium contains one proton and two neutrons. When a deuterium nucleus fuses with a tritium nucleus, a Helium nucleus is formed with the release of one neutron. Both the Helium nucleus and the neutron carry the energy produced by the fusion reaction. When one gram of deuterium completely fuses with one and a half grams of tritium, 235,852 kilowatt-hours of energy is produced. At a price of 10 cents per kW-hr, this energy is potentially worth $23,585, less reactor costs. Learn more about fusion from this simple video.

 In order to produce fusion reactions, a deuterium-tritium (D-T) mixture is usually heated to a temperature well above 100 million degrees Centigrade in order for the fusion reactions to occur at a significant rate. At such temperatures, the orbiting electrons about the nuclei of the atoms of the D-T mixture are liberated from the electrical attraction of the nuclei which then become positively charged ions, and the mixture of electrons and ions is called a plasma. When a magnetic field is applied to the plasma, the charged particles in the plasma gyrate in circles about the magnetic field lines, preventing their loss from the magnetic field. Thus, in principle, a magnetic field can be used to confine a plasma at very high temperatures keeping them away from any material wall. This is the basic principle of one approach to fusion energy and is called magnetic confinement fusion (MCF). However, in practice, the plasma particles collide and may drift across the field lines and get lost from the magnetic field over a sufficiently long time interval, breaking the magnetic confinement of the plasma.

Tokomak image


Another approach to “confining” a hot plasma is to make use of the fact that no matter how hot a gas is, it takes time for the gas to expand and cool because of its own inertia (mass). This is the basic principle of another approach to fusion energy called inertial confinement fusion (ICF). In this approach, a D-T mixture is compressed by some means such as a blast of high power laser beams, which is called the driver, to fusion temperatures and to a very small volume; usually no larger than 0.1 mm in radius, located at some distance from the chamber wall. The fusion reactions occur in this very tiny but very dense ball of plasma for less than a nanosecond. The plasma ball expands and cools and the fusion reactions cease. The process is then repeated like an internal combustion engine in order to produce a continuous stream of energy pulses equivalent to an average continuous power.

 Indirect-drive  ICF (Lawrence Livermore National Labs NIF)

Indirect-drive ICF (Lawrence Livermore National Labs NIF)

 The difference between nuclear fusion and conventional nuclear fission is that nuclear fission is accompanied by large amounts of radioactive waste products that have long half-lives (tens of thousands of years), whereas fusion proper produces no radioactive waste products. However, it is anticipated that the very early fusion DT reactors will produce some indirect radioactive products with half-lives of only a few years. Thus, commercial fusion power when realized will not give rise to a nuclear waste problem. Furthermore, in order to maintain the fusion reactions in a reactor, input power is required. In the event of an accident causing malfunction, the input power will be lost and the fusion reactions stop in the reactor. In this sense, a commercial fusion power reactor is fail-safe because it does not have a run-away core melt-down problem as might occur in a commercial fission reactor during an accident or reactor malfunction. And, in fact, fusion is an ideal means to destroy 60 years of accumulated radioactive waste created by over 400 fission power plants worldwide.

In summary, fusion is safe, clean, the fuel cost is near zero and there is enough of it to last the human civilization for millions of years. It is Nature’s own way of producing energy in the Sun and in the stars. We know absolutely for a fact that it works because it has been produced by humans in thermonuclear weapons. What remains to be done is to engineer a solution to generate fusion energy in a commercial power plant at a sufficiently low operating cost in order to produce electricity, as well as liquid synthetic fuels for aircraft and the like, at a lower cost than what is available today. In this white paper, we propose a path to commercial fusion power based on a proprietary fusion concept with a corollary project plan to develop and commercialize the technology.
1.2 The need for fusion:
If all peoples of the world are to live comfortable lives and have the ability to prosper, we must increase total worldwide annual energy production by a factor greater than 5 times current production. That is not possible and if it were it would deplete fossil fuel reserves by the 2050-2060 time frame. “Alternative green and renewable” energy sources can supply less than 4% of projected 2050 total energy requirements. There is only one way to produce this amount of energy to support mankind. That is the conversion of mass into energy through the process of controlled fusion. 

The fundamental ingredient required to support mankind is energy. If other nations are to enjoy a decent standard of living, they will require energy resources in amounts approaching those consumed in the United States and west in ratio to their populations. Today the population of the United States is approximately 304,000,000 or 4.4% of the world population, yet the United States consumes 28% of world energy use. Thus, it can be seen that to support our current world population at a standard of living morally acceptable, we would have to increase world energy production by well over 5 times.

Given the fact that energy production from fossil fuels has by most estimates peaked in terms of capacity, and liquid fossil fuels will be depleted within 50 years if developing nations are allowed to become industrialized nations; therefor is only one known and realistic source. That is the direct conversion of mass into energy based on Albert Einstein’s law of special relativity and the equivalency of mass and energy represented by the formula E=MC². This law teaches us that a very small amount of matter, say one gram, has the energy equivalent of a very large amount of energy when converted.

2. The Government Funded Fusion Program and the perception that Fusion Development is necessarily a multi-billion-dollar and multi-decade R&D effort

Fusion research has been funded by the United States Government for over 40 years at a total cost in excess of $23 billion dollars. It must be noted that over half of this has been spent in various military programs most recently managed by the NNSA (National Nuclear Safety Administration) under its nuclear weapons stockpile stewardship mandate. The Government funded fusion research has down-selected to two extreme approaches (tokomak-magnetic confinement and laser inertial confinement fusion) very early on, which have proven to have extremely high R&D costs for each incremental step of progress. The official government position today is that it will take another 50 years and approximately $50B more in funding before either of the two approaches could be commercialized. Legend has it that there are more problems in attaining controlled nuclear fusion than scientists anticipated, and that little progress has been made. “Fusion is still fifty years away, and always has been” has become the common refrain of skeptics. But the reason that we do not have commercially available fusion energy is not what is commonly believed.

 As a legacy of the government funded fusion research, there is a perception within and without the fusion community that fusion R&D is necessarily a multi-tens-of-billion-dollar and multi-decades R&D program and is thus not suitable for development by the private sector at present. It is a perception that is fostered by the establishment fusion research community (tokomak MCF and laser ICF). It is an argument used by the United States Department of Energy Office of Fusion Energy Sciences (OFES) to justify its long-held policy of early down-select and focusing on the tokomak approach as the path for fusion energy[1]. The argument used by OFES is that there will never be enough Federal resources for developing more than one approach to fusion.



There is also the concern that if the U.S. government is exploring alternative approaches to fusion, it might give rise to a public perception that the scientific foundation for the two mainline approaches of magnetic confinement and inertial confinement, is not sufficiently developed, and thus weaken the argument for continuing the commitment to the multi-billion-dollar investment in the two mainline approaches. Furthermore, since the U.S. has been seen by the rest of the world to be a leader in fusion energy sciences, exploring alternative fusion approaches by the U.S. government might send the “wrong signals” to its international partners in the $20B-plus international ITER project. 

Inertial confinement fusion (ICF) research, funded mostly by the National Nuclear Security Administration (NNSA,) has been justified, not for energy application, but for the purpose of scientific nuclear stockpile stewardship in the absence of nuclear weapon testing. Laser ICF is tolerated by the U.S. Department of Energy OFES as a “back-up” (a measure of risk mitigation) to tokomak MCF for fusion energy, because the resources for its development is available from NNSA, and thus the OFES policy of “a focused approach to fusion” (tokomak magnetic confinement) remains whole even though laser ICF is officially pursued by a branch of the U.S. government.  

Another result of the long history of fusion research is the perpetuation of another incomplete truth that the government funded research has practically exhausted all possible alternate fusion approaches and has shown that the alternate approaches do not work. In the next section, we will attempt to put the history of the research in alternative fusion approaches in proper perspective and throw some light on the incomplete truth.

3. The Truth about the Cost of Fusion Development and the Fusion Alternates

Recognizing that the facility cost was a large component of the R&D cost which was the principal impediment to the progress of fusion development at the time, around the mid-1990’s, Drs. Irv Lindemuth, Richard Siemon and Kurt Schoenberg of Los Alamos National Laboratory began to examine the cost of developing various fusion concepts in a fundamental way. The fusion parameter space is spanned by two basic plasma parameters, namely the plasma density and the magnetic field embedded in the plasma, which govern the physics of attaining fusion burn. The tokomak attempts to burn a plasma at a density of 1020 ions per m3 in a magnetic field of several teslas (T), while laser ICF attempts to burn a plasma at a density of 1032 ions per m3. In conventional ICF, no external magnetic field is applied to the target, but laser-plasma interaction can self-generate magnetic fields up to about 100 T. Essentially, these two mainline approaches sit at two extreme isolated spots in the fusion parameter space.

The results of the Lindemuth, et al, analysis were presented in various papers, workshops and conferences, since the mid-1990’s and recently collected and published in their paper of 2009 [3]. The principal results of their analysis are: 

(i) The cost of plasma confinement is proportional to the thermal energy or the fuel mass in the confined plasma, whereas the cost of plasma heating is proportional to the required heating power density. The cost of a breakeven fusion facility is the combined cost of confining the burning plasma at breakeven and the cost of heating the plasma up to ignition.

(ii) For magnetically confined plasma, the amount of plasma energy required to produce fusion ignition is approximately inversely proportional to the square root of the plasma density.

(iii) For fusion approaches that use compression to heat the plasma, the power density of the compression required is proportional to the fuel density and the velocity of implosion.

(iv) The net results of the analysis for the cost of a breakeven fusion facility as a function of the fuel ion density and temperature is shown in Figure 3, which correctly explains the costs of ITER and NIF. ITER corresponds to a point in Figure 3 for a density of 1014 ions per cc and temperature of 104 eV (108 degrees K.) NIF corresponds to a point of 1025 ions per cc and the same temperature.

(v) There appears to be a sweet spot where the burning plasma density is in the range 1019 to 1022 ions per cc. In this sweet spot, the stunning result of their analysis is that fusion approach exists for which breakeven fusion facility might very well cost as low as $51M!  (A typical nuclear fission power plant costs in excess of $5.5 billion 2008 USD.)

The tokomak makes use of a fuel density in the range of 1014 ions per cc. In order to ignite the plasma in the tokomak at this low density, at least 2 to 3 Giga Joules of thermal energy must be confined in the plasma by the applied magnetic field. This explains why ITER should cost at least $10B.
Laser ICF attempts to create a plasma with a density in the range of 1025 ions per cc resulting in a pressure of 1017 Pa at ignition. At the same time, because it does not use a magnetic field to suppress heat conduction in the plasma, it is necessary to implode the fusion fuel at a very high velocity of at least 300 km/s for the heating power to outrun the electron thermal conduction losses from the hot spot. The result is that extremely high heating power density in excess of 1018 W cm-2 is required. Very advanced, short-pulse, high-energy lasers are required. This explains why the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory costs about $4B. The plasma densities in tokomak and laser ICF differs by as much as eleven orders of magnitude and represent the two extremes in the fusion parameter space.
During the early years of research in controlled thermonuclear fusion, energy confinement and the efficient heating of the plasma are identified as the two main technical challenges for the attainment of controlled thermonuclear fusion energy. The research in alternative fusion approaches during the 50’s, 60’s and 70’s thus sought in an ad hoc manner various “clever” ways of improving the energy confinement, and/or the heating of the plasma, and many concepts were explored. Generally the search for better confinement or more efficient methods of heating were not very successful, and led to the conclusion that it was very difficult to achieve better energy confinement and heating efficiency than the tokomak configuration. The remaining alternates in this old era (pre-1995 approx.) sought to overcome the engineering problems of the tokomak approach (e.g., disruption, heat extraction, steady-state operation, linked magnetic coils and non-inductive heating, etc.). All the alternates in this pre-1995 era generally aim for a similar spot in the large fusion parameter space as the tokomak or the laser ICF. The alternates in this old era includes stellarator, tandem mirrors, the Astron system, z-pinch, impact fusion, theta pinch, reversed field pinch, field reversed configuration (FRC), spheromak, Polywell, IEC, dense plasma focus, etc.
Another important facet of the history of fusion R&D is that there was a general aversion towards any pulsed fusion approach in the early days of fusion energy research in favor of steady-state approaches. This is mainly because of the nascent nature of the electromagnetic pulsed power technologies in those days and the concern for the high cost of the fabrication of the targets for each pulse. Thus fusion concepts that made use of electromagnetic pulsed power as the driver were seldom taken seriously by OFES (or its predecessor) and thus were never funded at any significant level.
By the early 1990’s, the state of electromagnetic pulsed power technologies had changed dramatically for the better, thanks to a decade or two of defense and SDI related development of the technology. Low-cost, long-lifetime, repetitive pulsed power storage (capacitors,) switching and transmission technologies became conceivable. A small minority of scientists, mainly from the defense and nuclear weapon establishments, began to see the potential for pulsed power to make a contribution to the quest for practical fusion energy. 

Intellectually, the exploration of alternate fusion approaches experienced a paradigm shift in the 1990’s. The mid-1990’s represent the watershed in the research of alternate fusion concepts.
The fundamental feature that distinguishes the alternates in the modern era (post-1995 approx.) from those in the old era (pre-1995 approx.) is that modern alternates seek to find the “sweet spot” in the fusion parameter space, taking advantage wherever possible of the plasma physics we have learned to-date. The modern alternates include the various embodiments of magneto-inertial fusion (MIF) which aim for the intermediate parameter space between magnetic and inertial fusion, mirror-based gas dynamic trap, centrifugal confinement, flow-stabilized z-pinch, various embodiments of helicity injection, levitated dipoles, etc.

MTF image


It is in this sweet spot of the fusion parameter space that our proposed fusion approach PJMIF sits. Because a lower implosion velocity is planned, a magnetic field is required to suppress the heat loss during the compression. Because it uses a magnetic field as well as plasma implosion, it is essentially a hybrid of MCF and ICF, and is an approach in the class of fusion approaches called magneto-inertial fusion (MIF) or magnetized target fusion (MTF)[4, 5].
Though there were sporadic MIF-related efforts before the 1990’s, significant research effort to develop the scientific knowledge base of MIF or MTF did not begin until the mid and late 1990’s. An issue central to all plasma implosion schemes is the Rayleigh-Taylor (RT) instability. By the early 1990’s, after decades of defense-funded work on the implosion of thin cylindrical metallic shells called solid liners, the science and technology of imploding these thin metallic shells have matured to the point that they are ready for application. The RT instabilities in these liners during the implosion are well characterized and their control is well in hand. Equally mature at the time was the science and technology of producing field reversed configuration (FRC) plasma as the magnetized target plasma to be imploded. The small, fledgling MIF community, led by the Los Alamos National Laboratory group, thus selected the solid-liner technology as the implosion scheme combining with an FRC as the magnetized target to provide the first experimental “existence proof” of MIF[6] (Figure 4). In terms of seeking OFES funding support for the experiment, the choice of FRC has the added political advantage of making connection with the broader magnetic confinement scientific program of OFES. The solid-liner experiment (FRCHX) has been funded by OFES over the last nine years with a cumulative funding total of about $20M.

Tom Tamarkin at Las Alamos national Labs PJMIF experimental laboratory

Tom Tamarkin at Las Alamos national Labs PJMIF experimental laboratory

The implosion of the liner is accomplished by passing megamperes (MA) of current through the liner, which is electrically connected to a set of electrodes and transmission plates. During each shot, a large amount (10s of kg) of electrode and transmission line materials are destroyed as well as the solid liner. Though reactor embodiment of the solid-liner MTF has been suggested in the past, the main criticisms of the approach by critics of the solid-liner MTF are:

a) The relative high-cost of the solid liner to the amount of fusion energy produced;
b) The cost of the recycling of the destroyed hardware after each shot.
c) The clearance of solid material debris from the reactor chamber after each shot.
4. History and Status of PJMIF R&D

The spherically imploding plasma liner concept for MIF was first proposed by Thio et al. [7], [8] in the late 1990’s, inspired by Thio’s extensive work in the area of electromagnetic plasma accelerators, and motivated by the desire to further improve on the favorable attributes of MIF by using a standoff driver that would avoid the practical issues of solid-liner MTF as listed above. Analytic calculations [7] and ideal 3D hydrodynamic simulations [9] were performed to provide the first assessments of the plasma jet parameters required to form a plasma liner and compress magnetized target plasma to fusion conditions. It was realized that electromagnetic plasma accelerators at the time could not achieve the required combination of mass, density, and velocity. Consequently, Thio carried out research [10] that led to a theoretical understanding, supported by numerical modeling[11], of how to improve on existing electromagnetic plasma accelerators to achieve the required jet parameters. The key insights were to use a pre-ionized plasma rather than a neutral gas fill in the accelerator stage, and to prevent blowby instability by shaping the accelerator electrodes which allowed most of the plasma fill mass to get accelerated to high velocity. The findings of these research efforts form the basis for NASA to develop a fusion propulsion concept based on the PJMIF approach for human exploration of the outer planets[12].
In 2004, an experimental research program and HyperV Technologies Corp. were initiated to build and optimize electromagnetic plasma accelerators based on the new insights developed over the prior several years. Since then, HyperV has demonstrated steady advances and set records for the combination of jet mass, density, and velocity[13]. Their initial work focused on the larger coaxial guns with shaped electrodes[14], [15] suggested by Thio’s research. In the past few years, HyperV’s focus has shifted (temporarily) to simpler, more compact parallel plate “mini-railguns” which were originally intended only to ionize and inject the plasma pre-fill into the coaxial guns. However, it was realized that the mini-railguns, much simpler and cheaper than the coaxial guns, could achieve the combination of mass (few mg), density (1017 cm−3), and velocity (50 km/s) required for the first spherical plasma liner formation and implosion experiments to be carried out on the Plasma Liner Experiment (PLX)[12] at Los Alamos National Laboratory (LANL). And thus, for reasons of cost and expediency, the mini-railguns are receiving most of the present research attention, although the coaxial guns will likely be needed for fusion-relevant plasma liner implosions, due to their ability to accelerate large masses to high velocities (> 100 km/s) and their better potential for forming composite jets with D-T fuel in front and a heavy high atomic number pusher species in the rear.
In 2008, a workshop[17] was held at LANL to ponder next steps for developing the plasma liner MIF concept. Several studies, summarized in [17], suggested that this concept has promise both for MIF and for reaching HED conditions, but support for the concept was not unanimous among the attendees[18]. The workshop provided an update on the status of plasma gun development, showing that the gun technology was ready for a plasma liner formation demonstration. Also included in the workshop were several presentations related to a unique code development effort to combine the electromagnetic particle-in-cell (PIC) capability of the LSP code[19] with Prism Computational Sciences’[20] advanced equation-of-state (EOS) and opacity models. Such a modeling capability is required to fully assess the plasma liner MIF concept, especially with respect to modeling plasma jet formation and “gun physics,” as well the significant portions of the liner evolution where radiative and kinetic effects are important. Furthermore, such a code capability would benefit the entire field of high energy density laboratory plasma research. A large subset of the workshop attendees believed that much more research was warranted and needed to fully assess the potential of the concept. A team was assembled to formulate the present PLX research program aimed at exploring and demonstrating the feasibility of forming spherically imploding plasma liners via merging plasma jets to reach 0.1–1 Mbar of peak pressure upon stagnation. With modest investment, PLX promises near term assessment of the feasibility and quality of plasma liner formation via merging plasma jets, while establishing a unique experimental facility capable of forming cm- and μs-scale high energy density plasmas for scientific studies. PLX is also a natural first step toward a longer term plasma liner MIF research and development program.
As of this writing, phase one construction of the PLX facility at LANL is complete. Experimental physics campaigns on single jet propagation and two jet merging are to begin soon, to be followed by 30 jet experiments to form and study converging plasma liners expected to reach 0.1–1 Mbar of peak pressure. Radiation-hydrodynamic simulations[21] using the 1D Lagrangian RAVEN code[22] have explored both PLX- and MIF-relevant liner parameter space and established a physical picture of liner implosion, stagnation, and post-stagnation dynamics. Ideal 3D smooth particle hydrodynamic[23] simulations using the SPHC code[24] are being used to evaluate important issues of 30 jet implosions and peak pressure scaling with initial jet parameters[25]. The LSP code with EOS/opacity modeling capability is being used to generate detailed predictions of jet propagation[26], merging[27], and also synthetic interferometry and spectroscopy data, all of which will guide initial experiments and be compared directly with forthcoming experimental data. Tech-X Corp.’s Nautilus code[28], an Eulerian two-fluid magnetohydrodynamics (MHD) code with EOS modeling, is also being used as an independent comparison with the LSP results.

5. The PJMIF Approach to Fusion Energy

A non-proprietary version of the PJMIF approach available in the public domain is illustrated in sequential steps schematically in Fig. 5. A description of each step is given as follows:
Step (a) Two separate sets of plasma jets of the required species, total mass, density, and velocity are formed and launched in sequence with appropriate timing from electromagnetic plasma accelerators mounted at the surface of a large vacuum chamber (with radius measured in meters). 

Step (b) Each set of plasma jets merge through a merging radius (Rm), forming a spherical shell converging towards the center of the vessel. The spherical shell formed from the first set of plasma jets, which carry a mixture of deuterium and tritium, stagnates when its inner leading edge reaches the center of vessel. The velocity of the first set of jets is selected to produce a plasma ball with the desired ion stagnation temperature of about 1 million degrees (100 eV). Because the equilibration time between electrons and ions are short compared to the stagnating time, the electrons and ions have nearly the same temperature at stagnation. The resultant plasma ball serves as the initial target plasma to be further compressed.

The second set of plasma jets also merge through its own merging radius forming a second spherical shell which we call the imploding liner. The imploding liner carry a heavy pusher element (such as argon, krypton, or xenon, possibly other) in the rear with a leading D-T layer which is thin and dense. The heavy imploding liner is used to compress the target plasma to the density and temperature required to produce thermonuclear reactions. The leading D-T layer is intended to buffer the high-Z liner from the target plasma to prevent the cooling effects of mixing due to Rayleigh-Taylor instability, as well as to supply an additional afterburner layer that would also burn to amplify the energy gain.

The heavy pusher layer is envisioned to fulfill four separate functions: (1) it provides higher mass (of the order of 10 to 30 g) for a given (gun-limited) number density in order to provide the needed initial jet kinetic energy at more modest velocities, (2) the heavier element with both higher mi and lower effective g enhances the jet Mach number M ∼ (mi/γ)1/2 which is a key figure of merit for reaching high liner stagnation pressures ∼ M 3/2 [21], (3) the jet/liner is kept cool and compressible during propagation and convergence due to effective atomic line radiation and cooling associated with having many bound electrons, and (4) upon stagnation and burn, the heavy pusher element helps to trap the radiation from the burning core, thus enhancing the energy confinement time. 

Step (c): Standoff magnetization of the target plasma. The distribution of the second set of jets are chosen such that there are pre-arranged channels in the imploding liner in which the plasma is less dense so that laser beams can penetrate to reach the target plasma. A set of intense laser beams are launched through these pre-arranged channels in the liner to drive currents in the target by plasma beat waves. If “hole boring” is required, a preliminary set of ultra-intense lasers can be used to bore holes through the liner to create the required channels. 

Step (d): The target is compressed adiabatically to the required density and temperature to produce fusion burn.

Launching the jets: Claims[18], [40] that very high initial jet Mach numbers M > 60 are needed were based on the requirement of minimizing density degradation due to jet thermal expansion during jet propagation from the chamber wall to Rm . However, those claims did not take into account that the jet temperature falls and M increases during propagation due to adiabatic expansion and radiative cooling, with the latter expected to be dominant in the case of a high atomic number liner species. Recent research [21], [27], [41] has shown that argon jets with initial temperatures in the 3–10 eV range quickly cool to less than 1 eV well before the jet reaches Rm . This means that it is possible to form and accelerate a highly ionized plasma jet with modest M and then subsequently achieve the desirable situation where M doubles by the time the jet reaches Rm , to a value needed to ultimately reach fusion-relevant liner stagnation pressures. Radiative cooling is not as effective in the D-T fuel layers, although it still enjoys cooling in transit via adiabatic expansion. Experiments and modeling are needed to arrive at optimized composite jet initial parameters and profiles, and for that matter the ability to form the required composite jets in the laboratory. Another requirement is determining the effects of jet density and temperature profiles on jet propagation, merging, peak liner stagnation pressure, and dwell time.

Jet Merging: At the merging radius Rm, the leading edges of the jets meet to form the leading edge of the imploding spherical plasma liner. Since the jets are supersonic, shocks may form even at oblique merging angles θ > 2 arcsin(1/M ), where θ [radians] is the angle between adjacent jets. Shock heating may defeat the beneficial cooling aspects discussed above, and too much shock heating will reduce the jet M and ultimately degrade the peak stagnation pressure. The shocks may also prove troublesome for maintaining the required liner symmetry and uniformity. The analysis is based on a pure fluid treatment of the jet interaction. 

However, the picture is not so straightforward. In reality, the ion collisional mean free path of the merging jets is less than but is not a negligible fraction of the jet radius, and thus some interpenetration of jet ions is expected. Whether a shock would even form is an open question. An accurate treatment of this problem requires two-fluid or hybrid PIC models because, due to the high ion directed velocity (> 50 km/s) and cold electron temperature (< few eV) of the jets, the collisional mean free paths of the jet ions are dominated by the physical mechanism of ions of one jet stopping on electrons of the other jet. 3D two-fluid and/or hybrid PIC codes will be developed and calibrated (validated) against experiments so that they can be used to optimize the jet parameters and the merging process.   Liner Convergence: After the jets merge to form an imploding spherical liner, the liner converges toward the center of the chamber. Both theoretical[18] and numerical modeling[21], [43] have shown that the liner density rises during the quasi-steady-state pre-stagnation phase of convergence as ρ ∼ ρ0 r−2. However, as the liner approaches stagnation, different dynamics take over. A key issue during the convergence phase is the degree of liner non-uniformity (inherited at Rm upon jet merging) and the evolution of this non-uniformity, the reason being that non-uniformity is expected to reduce the achievable peak pressure at stagnation and exacerbate any convergent instabilities that may arise.
The uniformity of the liner during convergence is being examined using 3D SPHC simulations. Initial results are promising in the sense that the relatively substantial non-uniformity present upon jet merging at Rm gets “smeared” by the time the liner reaches stagnation. Fig. 3 of [1] shows 3D SPHC simulation results comparing the evolution of an initially spherically symmetric liner with the evolution of a liner formed by the merging of 30 discrete plasma jets. It is seen that the initial non-uniformity of the discrete jet case gets mostly smeared out during convergence so as to resemble the initially symmetric liner case at stagnation. The peak pressure achieved in both cases is similar. This is a promising initial result suggesting that very stringent requirements on initial liner uniformity may not be required.
Related to the issue of liner non-uniformity is the importance of convergent instabilities (e.g., Rayleigh-Taylor) and associated material mix within an imploding composite liner. Even if the gross liner uniformity is deemed relatively unimportant for achieving a given peak pressure, instabilities and material mix, i.e., trailing colder pusher material mixing and advancing ahead of the leading hotter fuel material, could degrade the peak pressure and temperature of the fuel at liner stagnation and therefore the fusion yield. Ongoing research is addressing these important issues, and definitive answers are not yet available. However, note that unlike ICF or a liner compressing a pre-formed target (as in most MTF schemes) which are both inherently Rayleigh- Taylor unstable during the entire compression phase, the composite plasma liner MIF approach is inherently Rayleigh-Taylor stable for the entire convergence phase because it is imploding on vacuum! There may be a very short duration of Rayleigh-Taylor instability when the central pressure peaks up and the liner has not yet begun to decelerate strongly, and ongoing studies are determining if and how this affects the quality of the implosion.
Target magnetization: Crucial to the plasma liner MIF concept (and all low ρr MIF concepts) is fuel magnetization reducing thermal transport so that the compression of the target plasma ball can be accomplished nearly adiabatically at modest implosion velocities of order 100 km/s or less. The required magnetic field magnitude in the fuel at peak compression is crudely determined by the condition ωci ti » 1 (where ωci and ti are the ion gyro-frequency and collision time respectively) so that particle heat transport is suppressed due to the magnetic field. For a representative compressed D-T fuel density of 1021 cm-3 and temperature of 10 keV, the condition becomes B » 7.1 T. MIF concepts generally compress a more modest “seed” field of order 1 T to order 100 T by virtue of field compression that scales as the compression ratio squared, i.e., Bf = Bi C 2 = Bi (ri /rf )2, where for MTF concepts C ≈ 10. For the plasma liner MIF concept under consideration (no pre-formed magnetized target), the objective is to introduce the required seed magnetic field in the fuel layer of the composite liner prior to peak compression such that the needed field strength is achieved at peak compression. The question of achieving a particular field topology is set aside for now and considered briefly later in this sub-section.

 At present, the favored target magnetization scheme is based on the idea of using beat waves [44], [45] generated by lasers to drive electrical current, which has the substantial advantage of also being a standoff system that would avoid destruction with every shot. This technique relies on resonant acceleration of plasma electrons (and therefore current drive and introduction of magnetic field) by a beat wave generated by two electromagnetic waves separated by a correctly tuned frequency. This has been demonstrated in low density plasmas using microwaves[46]. For the case of plasma liner MIF, it is envisioned that the D-T layer of the liner will have a density of order 1017 –1018 cm-3 when it is about 5–10 cm away from the origin. This sets requirements both on the minimum central frequency of the two electromagnetic waves (for penetrating the plasma) and the difference frequency (so that the beat wave is on the same order as the electron plasma frequency).

A recently initiated research program at U.C., Davis to explore the concept has refurbished two CO2 lasers for exploring the laser generated beat wave current drive technique, with estimated expected efficiency ≈6 x 10-7 A/W and resultant ≈60 A driven currents at 100 MW of laser power[47]. There is also a recently initiated, coordinated PIC numerical modeling effort of the beat wave generation and wave-particle interactions at PLX-relevant densities. The primary objectives of the modeling effort are to help optimize experiments on the beat wave generation and wave- particle coupling processes, and to explore the important issue of current drive efficiency and how it scales up to plasma liner MIF relevant regimes. The simulations examined counter-propagating laser beam injection into a plasma with peak density of 3 x 1016 cm-3. Fig. 8 shows initial 2D LSP simulation results confirming the growth of electrical current density and the presence of the beat wave near the expected 1.07 THz envelope frequency for injected beams at 10.4 and 10.8 μm wavelengths and 1013 W/cm2 intensities (corresponding to available CO2 lasers[47]). The electron acceleration proceeds in the direction of the higher frequency beam. In addition, the electron pressure exhibits strong axial modulation at the 5 μm beat wave wavelength. Ongoing simulations are studying varying angles between the injected laser beams and density gradients with the goal of optimizing current drive with minimal heating. 

The issue of field topology is an important one for plasma liner MIF. For the typically slower implosion MTF concepts, it is generally believed that closed flux surfaces in the pre-formed target are required to provide sufficient thermal insulation. It would be difficult (but not impossible, with some proprietary ideas being considered) to generate closed, mirror-like, or other flux surfaces via laser generated beat wave current drive. However, a recent interesting work[48] suggests that a random field with sufficient connection length might provide sufficient thermal insulation for MIF, and this would open up the possibilities for fuel magnetization methodologies. Ongoing studies are evaluating different possible magnetic field topologies for plasma liner MIF that might be compatible with laser magnetization. 

Another potential liner magnetization scheme, perhaps a natural choice considering the conclusions of [48], would rely on compressing the initial magnetic fields embedded in the plasma jets themselves. However, this would be challenging because the magnitude of the initially embedded magnetic fields are on the order of 0.1–1 Tesla. At jet densities of ∼ 1017 cm-3 and temperatures of ∼ 1 eV, that field decays with an exponential time constant on the order of a few μs and thus would decrease to « 1 T by the time the jets reached Rm . Understanding how the field would evolve and whether it would get amplified during subsequent convergence, and what field topologies and structures are possible in the initial jet, would require further studies.
Stagnation, burn and disassembly. As the target plasma reaches peak compression, an outgoing stagnating shock is formed and propagates outward into the incoming liner. This shock effectively converts the incoming liner kinetic energy into thermal energy of the post-shocked stagnation region. The post-shock region, after spiking to very high pressure, settles to a lower pressure and maintained (within a factor of a few) until the outward propagating shock meets the back end of the incoming liner (see Fig. 3 of [21}), at which time a rarefaction wave propagates inward quickly leading to the disassembly of the high pressure post-shock region. The latter is qualitatively consistent with an analysis based on a self-similar model [49] and was anticipated in [8]. These dynamics are integral in determining the “dwell time” of the stagnated plasma and ultimately the fuel burn-up fraction which is linearly proportional to the dwell time.
Recent theoretical work[50] based on a family of self-similar analytic solutions (so-called spherical quasi-simple waves)[51] to the spherically symmetric ideal hydrodynamic equations has led to the identification of an interesting potential method for optimizing the dwell time via specially chosen initial liner profiles of density and velocity, i.e., “shaped liners.” Such profiles admit an implosion solution where the post-shock high pressure region is maintained at constant pressure and zero velocity, with the region growing in size at a rate determined by the outgoing shock velocity. Physically, the outgoing shock converts the entire kinetic energy of the incoming liner into the thermal energy of the growing stagnated post-shock region. Radiation-hydrodynamic numerical modeling is now proceeding to test these analytic solutions with finite liner thicknesses (the theory is exact only for infinite thickness liners), and eventually realistic effects such as thermal and radiation transport will be included to see if the solutions remain viable in realistic systems. Shaped liners, if they turn out to be viable, may be particularly well-matched to the use of an afterburner D-T fuel layer because the outward shock could bring the afterburner layer up to the same (fusion-relevant) pressure of the inner compressed fuel layer. More studies are needed to investigate the feasibility of this scenario and whether any amplification of energy gain could be realized over the case without an afterburner layer.

6. Reactor Considerations

The plasma liner MIF concept was originally conceived[8] largely with the motivation of making an attractive fusion reactor by introducing a standoff driver embodiment to the otherwise attractive aspects of MIF. Plasma liner MIF is also potentially amenable to other reactor-friendly technologies such as liquid plasma facing and tritium breeding technologies that would avoid a costly and time-consuming radiation resistant materials development program. Power plant studies for MTF have been performed[52], [53], and an initial reactor study of plasma liner MIF is in process[54]. The intention for plasma liner MIF is to aggressively pursue reactor- friendly technologies with less development time and lower development cost.
A key difference between plasma liner MIF and other MTF concepts is that the former, with its standoff driver, can in principle fire at higher repetition rates, e.g., ≈1 Hz rather than ≈0.1 Hz. This would allow for lower energy yield per shot for the same average power, i.e., ≈100 MJ rather than ≈1 GJ per shot for 1 GW average fusion power, which reduces thermal and radiative loading stresses on reactor components. On the other hand, the higher repetition rate places greater demands on pulsed power technology including capacitor, plasma gun, and switch performance. Clearly, much pulsed power research and development is needed to make pulsed power based fusion concepts, including plasma liner MIF, a reality. The plasma guns are deliberately chosen to be “low technology” and low cost in the sense that they can be made of radiation resistant materials that are available today, and that a plasma liner MIF reactor could be configured such that changing out all the guns (even if they number into the hundreds) periodically would require minimal plant down time and keep cost of electricity low. Because the fusion reactor core for plasma liner MIF (i.e., spherical chamber with plasma guns, standoff magnetization lasers, and liquid first wall) is envisioned to be relatively low-cost and low-complexity, plant down time (and repetition rate) could be reduced by operating several imploding plasma liner fusion reactor cores in parallel, sharing the same (more expensive) central tritium processing and electricity generation “balance of plant” systems.
The hydrodynamic efficiency of a plasma liner is expected to be lower than that of a solid liner, and depending on how high of an energy gain is ultimately realizable, it may be necessary to implement technologies to recover part of the energy in the outgoing, post-stagnation liner to keep the engineering gain as high as possible. Examples of potential liner energy recovery techniques were briefly discussed in [49] and would need further assessment for any plasma liner MIF reactor design. Furthermore, additional studies are needed to determine how much energy remains in the outgoing, post-stagnation liner and how much is lost due to radiation.
Many of the reactor technologies envisioned for plasma liner MIF share commonalities with ICF reactors, especially with heavy ion beam driven fusion, which has a substantial body of research, e.g., [55], from which to draw. In particular, flowing molten salts such as a mixture of Lithium Fluoride (LiF) and Beryllium Fluoride (BeF2) as a plasma facing component and tritium breeding medium has been considered extensively for heavy ion fusion. The interesting technique of localized vortex liquid flows[56] on the inside surface of the vacuum chamber appears especially well-suited for plasma liner MIF which requires gun penetrations distributed around the entire spherical chamber. Thus, the guns themselves would be “sacrificial” to neutron and hard x-ray damage, and need periodic replacement, but the spaces between guns would have localized vortex flows of a thick liquid molten salt that would protect the structure from neutrons and x-rays, as well as breed tritium and serve as the coolant for driving the steam cycle to generate electricity. Adapting the vortex surface liquid flow method to plasma liner MIF, and determining required flow rates and re-circulating power will be developed on the program.
The important question of achievable energy gain of plasma liner MIF has been studied using a 1D Lagrangian hydrodynamic code[38]. These initial studies are idealized in that magnetic field effects are not treated self-consistently but are rather approximated by reducing or turning off thermal transport in the code, and α-particle deposition fraction is a specified parameter. In addition, these studies thus far have used only an ideal gas EOS with specifiable adiabatic exponents and have neglected radiation losses. With these caveats in mind, preliminary (and unoptimized) results[38] show energy gains up to 20 with a 30 MJ composite plasma liner, with slightly less than half of the yield coming from the main D-T fuel layer and slightly more than half from a denser D-T “afterburner” layer. Physics and engineering optimizations using proprietary schemes could further improve the gain values, whereas inclusion of more physics in the simulations such as radiation transport and 3D effects could reduce the gain. Therefore more work is needed with a state-of-the-art 3D radiation-magnetohydrodynamics code such as HYDRA [39] to obtain a more realistic, self-consistent, and accurate gain estimate, and to optimize the composite plasma liner initial conditions at Rm .

7. Concluding Remarks

PJMIF is an attractive approach to practical, economic fusion energy for the following reasons:

(a) Plasma guns, made of metallic alloys, are robust.
(b) The plasma guns are energy efficient and theoretically can have efficiency exceeding 50%. They are driven directly by pulsed power, which has lower cost than lasers per unit energy.
(c) Plasma guns and pulsed power supplies, being ‘low-tech’, are inexpensive making the capital cost of the fusion reactor very inexpensive.
(d) The physics of the implosion scheme is robust with respect to practical engineering variability in the fabrication of the targets, etc. The size of the implosion is relatively large. The initial target and liners are about 10 cm in diameter.
(e) The targets and liners are ordinary gases and require no special fabrication. The recycling cost is low. There is no solid debris to be removed from the chamber after each shot.
(f) PJMIF is ‘reactor friendly’. It is compatible with the use of liquid or disposable first-wall to protect the critical components of the system from neutron damage.

Note also that, unlike some MIF approaches, no material debris is generated by the implosion in the PJMIF approach, because it uses plasma jets as drivers launched from standoff distances. And unlike laser ICF, the evacuation of the reactor chamber does not present as challenging an engineering problem as laser ICF, because firstly it is sufficiently economical to operate the reactor at a much lower repetition rate of 1 to 5 Hz, and secondly PJMIF does not requires as high a vacuum as laser ICF in the chamber, as the propagation of dense plasma jets is much more tolerant of residual gases in the chamber as laser light.

The above description of PJMIF is based on PJMIF embodiments and configurations that have been released to the public domain. Proprietary embodiments of PJMIF known to the authors of this paper exist that considerably improve on the overall reactor performance and address the key issues. This forms the basis of proprietary intellectual property (IP; patents and the like) which in combination with scientific expertise and know how, form the competitive “unfair business advantages” enjoyed by a private venture based on the participation of the various authors of this paper.

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[41] C. Thoma, Voss Scientific, Albuquerque, NM 87108, private communication, 2011. [42] J. D. Huba, NRL Plasma Formulary, 2009.
[43] R. Samulyak, P. Parks, and L. Wu, “Spherically symmetric simulation of plasma liner driven magnetoinertial fusion,” Phys. Plasmas, vol. 17, p. 092702, 2010.
[44] M. N. Rosenbluth and C. S. Liu, “Excitation of plasma waves by two laser beams,” Phys. Rev. Lett., vol. 29, p. 701, 1972.
[45] A. N. Kaufman and B. I. Cohen, “Nonlinear interaction of electromagnetic waves in a plasma density gradient,” Phys. Rev. Lett., vol. 30, p. 1306, 1973. 
[46] J. H. Rogers and D. Q. Hwang, “Measurements of beat-wave-accelerated electrons in a toroidal plasma,” Phys. Rev. Lett., vol. 68, p. 3877, 1992.
[47] F. Liu et al., “Laser-driven beat-wave current drive in an unmagnetized plasma,” in Proc. 38th European Physical Society Conference on Plasma Physics, 2011, paper P2.023.
[48] D. D. Ryutov, “Adiabatic compression of a dense plasma “mixed” with random magnetic fields,” Fus. Sci. Tech., vol. 56, p. 1489, 2009.
[49] J. T. Cassibry, R. J. Cortez, S. C. Hsu, and F. D. Witherspoon, “Estimates of confinement time and energy gain for plasma liner driven magnetoinertial fusion using an analytic self-similar converging shock model,” Phys. Plasmas, vol. 16, p. 112707, 2009.
[50] G. Kagan, X. Tang, S. C. Hsu, and T. J. Awe, “Bounce-free spherical hydrodynamic implosion,” submitted to Phys. Rev. Lett., 2011.
[51] R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves. Berlin: Springer, 1976.
[52] R. W. Moses, R. A. Krakowski, and R. L. Miller, “A conceptual design of the fast-liner reactor (FLR) for fusion power,” Los Alamos National Laboratory, NM, Tech. Rep. LA-7686-MS, 1979.
[53] R. L. Miller, “Liner-driven pulsed magnetized target fusion power plant,” Fus. Sci. Tech., vol. 52, p. 427, 2007. [54] R. L. Miller, Decysive Systems, Santa Fe, NM, private communication, 2011.
[55] R. W. Moir, “The high-yield lithium-injection fusion-energy (HYLIFE)-II inertial fusion energy (IFE) power plant concept and implications for IFE,” Phys. Plasmas, vol. 2, p. 2447, 1995.
[56] P. M. Bardet, B. F. Supiot, P. F. Peterson, and O. Savas, “Liquid vortex shielding for fusion energy applications,” Fus. Sci. Tech., vol. 47, p. 1192, 2005.

9. Figures

ITER fusion reactor
Figure 1 ITER – a $20B project scheduled to have first plasma in 2025, with the first DT experiment scheduled for 2034.

Lawrence Livermore fusion reactor
Figure 2. National Ignition Facility at the Lawrence Livermore National Laboratory.

break even graph
Figure 3. Cost of a fusion break-even facility as a function of ion density and temperature of the burning plasma. Cost model consistent with known Tokamak and Laser system costs. Shows that minimum cost occurs between conventional regimes. Assumption of Bohm diffusion is pessimistic.
B= magnetic flux density B=5MG or 500 Teslas Contours 108 – 1012 in US Dollars

Solid-Liner MTF
Figure 4. Solid-Liner MTF

A Schematic of the PJMIF Concept.
Figure 5. A Schematic of the PJMIF Concept. (a) Two sets of jets are launched from the periphery of the chamber. The first set of jets are shown already merged forming the target shell converging towards the center. (b) The second set of jets have just arrived at the merging radius (Rm) and are merging through the merging radius forming the imploding liner. The jets are arranged in such a way that “channels” are provided to allow insertion of laser light in step (c) below. At the leading edge of these jets is a thin, dense layer of DT, serving to buffer the high-Z liner from the target plasma, as well as serving as an afterburner to boost the fusion gain. (c) A set of intense laser beams shine through pre-arranged “channels” in the liner to drive currents in the target by plasma beat waves. (d) The target is compressed adiabatically to the required density and temperature to produce fusion burn.

Surface plots in the x-y plane of plasma liner pressure
Fig. 6. Surface plots in the x-y plane of plasma liner pressure (logarithmic) from 3D ideal hydrodynamic simulations. The top row shows the evolution of an initially spherically symmetric liner, and the bottom row shows the evolution of a liner formed from 30 discrete plasma jets.

Contours of the logarithm of the electron density
Fig. 7. Contours of the logarithm of the electron density (in cm−3 ) as a function of the difference (δλ) and central (λ0) wavelengths of the injected electromagnetic waves of frequency ω1 and ω2 , satisfying the beat-wave resonance condition |ω1 −ω2 | = ωpe .

LSP simulation result for counter-propagating laser beams
Fig. 8. LSP simulation result for counter-propagating laser beams of (left) growing current density versus ti

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Fusion for Children

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Have you ever wondered how the sun keeps burning for such a long time? Why doesn’t the sun just burn out like a campfire? Many years ago, when the author of this book was just in second grade, my teacher told the class about the three things that it takes to make a fire. First she said, “You will need fuel, such as wood or charcoal. Every fire has to have fuel to burn.” After this, she told us the second thing fire needs is enough heat to get things started.


And finally she explained that a fire needs the air around it to combine with the fuel to make a fire. If you take away the air, the fire will just go out. My teacher lit a candle and once it was burning bright, she set a glass over it. The candle flame soon started to get smaller and smaller, then the flame went out. This is because the fire comes from joining together the fuel and the air, but with the glass over the flame, it soon runs out of air. When you light a candle, it is the wax that is the fuel. There may still be plenty of wax left to burn, but with the glass over it, all the air gets used up.

I thought my teacher was so amazing and figured she was the smartest person in the world, except for my dad and mom, of course. So when I got home that day, I sat under our plum tree and began to think about all the things that my teacher had taught us that day.


The sun was shining through the leaves of the plum tree, so I thought about that big fire we call the sun. This seemed like a perfect place to remember the three things that it takes to make a fire. I remembered heat and there was plenty of that since the fire was already going on the sun. Then I remembered fuel. I wondered what was burning on the sun. Was it made out of a super giant piece of charcoal? What about the air; it needed air for the fire. I thought the sun must have a lot of air around it.

Then that big fire ball in the sky, our sun, began to make no sense at all when I remembered the church near us, where after Christmas the people in town would bring their dead Christmas trees. They would pile them into a giant hill that covered the lot next to the church and then they set them on fire. The fire got so hot I could stand back far away and it would still make me too warm. The sun is millions of miles away, so I thought it must be burning a lot of fuel. With the giant pile of Christmas trees, the fire burned so hot and so fast the hillof trees soon turned to a big pile of ashes.

I thought, when is the sun going to burn up all its fuel and become a big pile of ashes? I wondered why it didn’t just burn up all the air on the sun and then go out like the candle? Also, why wasn’t the sun covered with smoke like a giant forest fire? It seemed like the smoke should block out all the light. I began to feel afraid because it seemed from everything our teacher had taught us that the sun just could not last very long. I thought of my grandfather, who seemed very old. I wondered how the sun had lasted so long that he could have had the sun around when he was little.

Suddenly I felt like the sun was surely going to go out any time and the whole world would be dark and cold. Jumping up I hurried into the house. My mother was there, but I ran right past her. I knew that if the world was going to end soon, she would not want to tell me. I found my dad and began to tell him how the sun was going to go out soon and we were all going to die. He listened and then he began to laugh. That made me feel much better. I knew he wouldn’t laugh unless, somehow, I was wrong about the sun going out.


He told me that the sun doesn’t burn like the fires in candles or camp fires. He said the sun burns with something called fusion. He said that campfires burn when the air joins with the fuel, but in fusion the fuel itself is changed into energy. He said that just a tiny bit of fuel turns into a whole lot of energy.

How different is fusion than a regular fire? If we burn one match with the normal kind of fire, we get about 6000 units of energy. That is a good amount of heat energy, enough to burn our fingers. But if we burned the same amount of material that was in the match, using fusion, it would give off around 81,000,000,000 units of energy. Do you see the difference? Just a little bit of material will produce a giant amount of energy using fusion.


That is why it is so important that we learn to use the energy of fusion. We have to burn a great deal of fuel in gasoline, oil and coal every day to give people the energy we need. But with fusion we would only need to burn a little bit of fuel every day, so our fuel will last for millions of years, just like it does on the sun.

Every year the world burns over 10 billion tons of fossil fuels. In 2004 the U.S. used enough crude oil to fill over 10.5 million railroad tank cars, which would stretch between Miami and Seattle (3,300 miles); over 36 times.

That is why we need to do the research and experiments needed to help us learn how to use fusion on Earth. Just as the Sun cannot burn its fuel with a normal fire and last very long, we cannot burn oil and coal using the normal fire and be able to keep it up for very long.

The same amount of energy that is in 21,000 rail cars of coal or 10 million barrels of oil can be replaced with only one small pickup load of fuel using fusion energy.

Also, fusion doesn’t pollute and it is safe. Remember how we said that if the sun was powered by normal fire it would be so full of smoke the light couldn’t get out? Isn’t using the normal kind of fire to power our cars and factories also producing too much smoke and pollution?

This is why we are working so hard to get our country to put money into fusion research, so we don’t have to keep burning large amounts of fuel that pollutes the world. We want to burn a little bit of fuel using fusion so that our energy supply will last for millions of years.

With fusion energy we can feed the world and power machines to turn sea water into fresh drinking water and to irrigate food crops around the world.

Fusion holds the promise for a bright future for us all. There is no other source of energy in the world that can feed the hungry and that holds the promise of a bright future for people to live happy lives without pollution.

Now we will show you just what fusion can bring to the world. Fusion is the energy and light of all the stars in the universe. Fusion is the energy of the light of creation.

Everyone needs to eat, but there are only certain places on Earth that are really good for growing enough food. In many areas only a small amount of crops can be raised. There are different reasons that some parts of the world can’t raise enough food. In some places, the weather is too cold for plants to grow well. In these cold climates, fusion would allow us to heat greenhouses.


We could cover large areas with clear plastic greenhouses to grow food all year round by the warmth of fusion. Where would we get all that clear plastic you might ask. That is what is so amazing about fusion. Since plastic is made from petroleum, such as oil and gas, once fusion is used to power things there will be so much oil left over that it will become very inexpensive. It won’t be used to make gasoline for your car anymore, so billions of gallons will be just sitting there waiting for another use. The companies that make plastic will not have to pay very much to buy all that extra oil and gas, so the cost of making greenhouses will be much lower than it is now with our high oil prices.

In other places around the world the food can’t be grown because there is not enough water to irrigate the farms. Yet, even in these deserts there is usually an ocean of water nearby that could be used to irrigate, if it wasn’t for the salt in the sea water. There are ways to take the salt out of the water, but they require a lot of energy. Fusion energy would be able to power these machines to take out the salt and also power the pumps to carry the fresh water through the pipes to the farms. These pipes would also be made from the low cost plastic, thanks to fusion.

In many places there is starvation and poverty even though the weather is warm and there is enough water to grow crops. This is because of war and terrorism. Many of the wars are fought over oil, since every nation needs energy to keep things moving. Once we have fusion there will not be any more wars over oil. Oil will be used to lubricate machines so they run smooth and to make products such as plastic. There will be so much oil left over once we have fusion that nobody will fight over it. It will become very low in cost since there will not be that much use for it.

The poverty and starvation around the world is wrong. It makes us all sad to see the ads on TV or the signs that ask us to give money to help those less fortunate people. There are wonderful people around the world who spend their lives helping to feed the hungry. They feel the suffering of others and work to bring them food. The problem is this job is getting harder and harder. The deserts around the world are growing larger. The pollution from burning coal and oil and the wars for oil are harming everyone.

So along with those who are trying to bring food to the hungry, there is another group of people who are working to help end hunger around the world in a way that will last for a very long time. It is a way to feed the hungry where everyone will be able to take care of themselves and raise their own food. These people are working to bring fusion to the world. Two of these people are my friends, Pat Boone and Tomer Tamarkin. The picture on the next page shows what they hope to bring to the world. With fusion, most of the wonderful people and organizations that are working to ship food to the hungry will be able to stop. They will be able to close down some of these charitable organizations because the people around the world will have the energy to bring fresh water to their farms and to heat greenhouses so they can grow their own food.

Boone & Tamarikin

Feeding the hungry would be a dream come true for everyone. If fusion helped to do this it would be worth all the work it takes to make it happen. But this is not the end to the fusion story. As we all know, people need food, but there is something else we all need; we need to dream.

Since the beginning of humanity we have been dreamers. We have climbed every mountain, crossed every ocean and built all the things our minds could dream. People used to have to walk wherever they wanted to go. Then they tamed animals and were able to ride horses so they could travel further and faster; exploring new parts of the world. Over the past two hundred year these dreams have grown so fast as we developed trains, cars, powered ships and then airplanes and jets; even rockets to begin letting us explore space. The problem is this takes a lot of energy. Our energy is running out and our dreams will have to be forgotten. What good is a car without energy to make it go? It just sits there in the garage. Right now there is not even enough energy for all the world to have the same dreams we have in America. If everyone had a car there would not be enough gas for everyone.

Fusion is unlimited energy and it will let us have unlimited dreams for everyone around the world. We can explore space in ways we have never done before. The picture on the next page may never happen, but its only chance to have this fun dream come true is with fusion

moon shuttle

We have been given a dream and a hope for the future. Many people don’t even know about fusion and don’t understand the amazing and wonderful things it will do for us all. There are people who scare us with stories about global warming and pollution. They are afraid of the future, but we can go into the future without fear if we just take this great gift of fusion.

We can feed the hungry, power our dreams and go into the future without fear, if only we will. You are young, but you can still help spread the story of fusion, Tell your friends about this book and share it online at

In the next part of this book we will tell you a little more about fusion and how it works. Don’t worry if you only understand a little about what we are teaching here. Take what you do understand and tell people. In time you will begin to understand a lot more.

Part Two

(You might want to wait to read part two so you can think about all you have learned so far.)


The universe has two main ingredients that we can work with. There is matter, which is anything you see around you. The matter around us is mostly made up of tiny little particles called atoms. In fact, you are made of matter. If you look at your floor, the grass, the clouds and the sky and, well, everything around you; it is made of matter. You can touch matter, see it, sometimes you can smell it and hear it.

throw ball

The second ingredient in the universe is energy. Energy is what moves matter around, like when you ride in a car or peddle your bike. When you throw a ball you are putting energy into it. Energy is what speeds things up, it makes things hot and gives us light.

When you throw a ball, you can’t see the energy in the ball. When you put energy into your bike by peddling it really fast, the bike doesn’t feel different than when it was stopped and it certainly doesn’t smell any different. Now, think about going for a ride in a rocket ship. You might get hungry along the way so you bring along a bag of nuts. The rocket ship takes off with so much energy that you and the nuts are now going 25,000 miles per hour; even with all that added energy those fast moving nuts would taste just the same as when they had been sitting on your kitchen counter at home.

So matter and energy seem like very different things, but the really strange truth is that they are the same, because matter can turn into energy and energy can turn back into matter. That’s right, you can have a bit of matter, say a marble, and it can be turned into pure energy, nothing else…no more matter, no more marble. You would not want to be anywhere near this when it happened. But then you can also take a lot of energy and turn it back into matter. What is very surprising is how much energy it takes to make just a little bit of matter. Or looking at it another way, it is surprising how much energy a little bit of matter can turn into. That’s why you would not want to be in the same room if your marble turned into pure energy; in fact you would want to stand about 100 miles away.

Usually when we try to tell a person about something new we think of something that the person already knows about that is like the new thing we are trying to describe. So if you had a friend who had never tasted yogurt, you might say, “It is a little bit like ice cream or pudding.” That is not exactly how yogurt tastes, but it is close enough to give them the idea. Well, turning a little bit of matter into such a large amount of energy is so weird that there is not much else like it, so it is hard to find an example that is close; like yogurt is to ice cream or pudding. But there is one thing you may know about that can help you understand all the energy that comes from a little bit of matter.


It is an Ipad. An Ipad is small, but it can hold so much information that it can have over 100,000 books stored. You can hold an Ipad in one hand with no trouble. But if you printed out all the books in that Ipad, it would fill the shelves of a good sized library with books. So one Ipad equals 100,000 books.


The books would have the same information stored as in the Ipad, but now the information would fill up a building. The Ipad is like matter because it can store a great deal of information in a small place and matter stores a lot of energy in a very small space. Energy is like the library full of books that were printed from the information that was in that tiny Ipad. A lot of books come from one tiny Ipad, a lot of energy comes from a tiny bit of matter.


( A more advanced look at energy for older kids.)


It was a man named Albert Einstein who first realized that matter was really the same as energy. He also figured out just how much energy is in each bit of matter. To figure this out you take the amount of matter you have, say one gram, and multiply that by the speed of light and then multiply that number by the speed of light again. This will tell you how much energy will come from that one gram of matter. The speed of light is a very big number; it is almost 30,000,000,000 centimeters per second. That gram of matter can turn into nearly 900,000,000,000,000,000,000 ergs of energy. You will see this formula everywhere, it is E=mc2.

What is FUSION?

(You may already know some of this, so feel free to look around and jump in wherever you like.)


How Protons and Electrons Behave


Protons, Electrons and Neutrons Make Up Atoms


Protons Make Up the Center of Atoms

The number of protons fused together in the center of the atom tell us what kind of atom it is. 1 proton makes it a hydrogen atom, 2 makes it a helium atom and 3 makes it a lithium atom… all the way to uranium at 92.

Electrons are attracted to the positive charge of the protons. Each electron balances the charge of one proton.

You may be saying,


We were really hoping that you wouldn’t notice;
now we have to do another illustration.

What is holding the protons together?

Before we go into protons sticking together instead of scattering like everyone knows they should, we should take a quick look into forces.

what's holding the protons together?

We are all familiar with three of the forces that shape our world. We have all seen static electicity at work, even if it was just sticking a balloon to a wall. We. have all played with magnets. And, of course, gravity is pretty reliable. I mean, when was the last time you woke up in space because you forgot to pay your gravity bill?

But there is something about these forces you may have never thought about.

How far can they reach?

how far can forces reach?
like electric charges repel
the strong force


has very short arms, but they are very strong.
the strong force and protons

If protons go very fast, when they crash into each other they push right through the electic field that holds them apart. If they are going super fast, they get so close they can grab onto each other with the strong force. The electric force still tries to push them apart, but the stong force is so strong it keeps holding them together. Sure the strong force has stubby little arms, but it keeps the whole universe from blowing up like a giant bomb.

So that’s the story of protons, neutrons and electrons. These three little particles make up every kind of atom. Then all the different kinds of atoms join together in all sorts of ways to make up everything you see around you.

What’s that you say, “I didn’t tell you much about neutrons?”

Well, we can’t go too far in understanding fusion and fission without knowing about neutrons.

The neutron doesn’t have an electic charge of positive or negative, so it doesn’t really get involved with the big electic force tug-of-war going on in the universe.

The neutron stays neutral, but it does have the strong force, just like the proton. This is very important.

The strong force allows the neutron to join with protons in the center of the atom.

hydrogen and helium
Neutrons join with protons in the center of the atom.

Since the neutrons don’t have an electric charge they don’t change the atom very much.

In the drawing above you can see a hydrogen atom with one neutron.
Hydrogen is hydrogen because it has one proton. The number of neutrons it has doesn’t
change it from being hydrogen.
Each kind of atom will have some atoms with one number of neutrons and other atoms will
have a different number of neutrons. For example; some hydrogen atoms have two
neutrons and a very few even have three. Most hydrogen atoms don’t have any neutrons.
Another example is helium, it always has two protons. But if you have a balloon filled with helium, some of the helium atoms in the balloon will have only one neutron and others may have three. Most helium atoms will have two neutrons.

This is one case where it would be better to have more helium atoms with only one neutron because they are lighter and your balloon would fly a little better.


Energy is what moves things. If you pick up a ball and hold it over your head, you are storing energy in the ball. When you drop the ball, the energy that you put in when you lifted it up is now released and the ball falls faster and faster to the ground. The same thing happens when you stretch a rubber band. When you let go of the rubber band, it shoots away using the energy you stored in it when you pulled it back.
The center of the atom is called a nucleus. Just like the stretched rubber band or the ball lifted up high, each nucleus has energy stored inside from all of the protons and neutrons stuck together.
Think about the energy in the atom’s nucleous. What would happen if the strong force suddenly stopped working? All of the protons are charged positive and they would instantly shoot apart from each other.

It would release the stored up energy of each proton as the strong force let go and the atoms would explode.

atom energy
Fission is where we take bie atoms, such as uranium and break apart the nucleus so that it becomes two smaller atoms. The smaller atoms are closer to beine like the iron atom, so this releases a lot of the atom’s stored up energy.
atom energy
Fusion is where we take small atoms, such as hydrogen and collide them together so fast that the protons fuse together to make larger atoms. These new atoms have more protons so they are a little closer to the low energy iron atom. This releases energy.
atom energy

Thanks for taking time to learn about fusion. We hope that you want to help spread this dream to others. If you do want to help, the best place to start is with your family. The next part of this book is for the adults in your family. It is an article by Pat Boone. There are also more articles by Pat Boone and Tomer Tamarkin at our Web site at You can show this Web site to your friends and family. Together we can bring the dream of fusion to the world.

Pat BoonePat Boone is a legendary Hollywood icon in the preforming arts who traces his ancestry to the American pioneer, Daniel Boone. Pat has sold over 45 million albums, had 38 top 40 hits, and starred in more than 12 Hollywood motion pictures. Pat graduated from Columbia University in New York City, magna cum laude in 1958. Pat is well-known for his old-fashioned values, which contributed to his fame and popularity in the early days of the rock & roll era to the present. Today he is still active on television and in the motivational speaking circuit. Pat has spent the last few years writing columns and books and runs his own record label named Lion & Lamb. Pat’s first book, “Twixt Twelve and Twenty,” Prentice Hall, was a number 1 Best Seller in America. Pat lives with his wife of 59 nine years, Shirley, in Beverly Hills, California.

Pat Boone
There Is Hope for the World

I knew a man named John Lennon.

I first met him with his buddies, Paul, George and Ringo, in Las Vegas when they were just fresh, funny and talented young kids from Liverpool.

I and my daughters visited with them backstage between their two shows in the Thomas Mack Arena and found them charming and energetic, relishing their new and sudden stardom.

Like the rest of the world, I watched as their careers blossomed and assumed fantastic proportion. Each record, and then each movie, eclipsed the last … until they had become the greatest singing group in music history. It will never be equaled.

Many years later, I visited with John and producer Phil Spector in a nice health-food restaurant while they working on a new album. As we compared notes and stories about our experiences, I asked John what he thought was the main reason for the Beatles’ incredible success. He thought a minute behind his little round glasses and answered, “Imagination.”

Imagination. As Ted Kennedy quoted his brother, Robert: “He thought of things that never were, and asked ‘why not?’” And young Walt Disney – at a time when the “cartoons” he and a couple others were successfully producing cost an average of $5,000 – told his incredulous brother, Roy, he envisioned a full-length feature film, in total animation, and estimated it would cost $1.5 million! It seemed unthinkable. But it was imaginable, and it became a worldwide sensation: “Snow White and the Seven Dwarfs,” a timeless classic. Imagination. It’s much more powerful than most realize. In fact, hardly anything of value has ever been accomplished without beginning as an idea, which is really imagination. In Genesis 11, a group of mere humans imagined a city and a tower reaching into heaven, and they began to actually build it. The Lord God said, “Indeed the people are one and they all have one language, and this is what they begin to do; now nothing that they propose to do will be withheld from them.” “Come, let us go down and there confuse their language, that they may not understand one another’s speech.” And the Tower of Babel came to a halt. But now the language barrier has been erased and, as Walt Disney said, “If you can dream it, you can do it.” Man can do virtually anything he can imagine.

That’s why I have written five of my recent columns here on nuclear fusion. I’m not a scientist, as I said at the outset, but I have a wonderful imagination. And so do a great number of scientists who have not only envisioned a world empowered by an inexhaustible, eternally available energy source, but have come very close to making it available to humanity.

Guided by physicists and other scientists who’ve been personally involved at various levels, I’ve given asketchy but detailed history of the early experiments and the discoveries that proved the theories of nuclear fusion; described the work and research in a number of American universities, and the funding allocated by our government during the Carter & Reagan administrations, that led to amazing breakthroughs; and I’ve cited the miraculous, almost inconceivable heat levels achieved at Princeton that ached to be used in creating the plasma that would create nuclear fusion as the ultimate energy source.

But I’ve also detailed the unexpected resistance to this amazing progress in various departments of our own government, including the Department of Energy! Who, and why? It shouldn’t be a surprise that various vested interests, powerful lobbying interests who wanted oil and gas and coal and electricity and, yes, even nuclear fission to be utilized first, prevailed.

So the funding, and much of the almost triumphant technology, dwindled and ground nearly to a halt. But we can still imagine, and the goal still can be attained. I want you to imagine with me. Imagine a world where oil is mainly a lubricant and a base for manufactured products, a world where there is plenty of clean, fresh water for drinking, irrigation and sanitation. We already have the technology and tools to desalinate and purify water for every community in the world – but we don’t have the energy source or funding for it.

Fusion can do it.

So the funding, and much of the almost triumphant technology, dwindled and ground nearly to a halt. But we can still imagine, and the goal still can be attained. I want you to imagine with me. Imagine a world where oil is mainly a lubricant and a base for manufactured products, a world where there is plenty of clean, fresh water for drinking, irrigation and sanitation. We already have the technology and tools to desalinate and purify water for every community in the world – but we don’t have the energy source or funding for it.

“Global warming” can be a non-issue when fusion gives us a world where humanity leaves only a small carbon footprint. All the natural sources of energy are frighteningly finite, but fusion is infinite. The physicists with whom I’ve consulted are certain that if we make a very focused, concerted and adequately funded effort, bringing fusion to the world is 100 percent certain. There are others who are more pessimistic and say there may only be a 20 percent chance, at least in the foreseeable future.

But ask yourself: If your family was on the verge of starving and you had evidence that there was a 20 percent chance that unlimited food was just over the next hill, what would you do? Wouldn’t you look at your hungry children and start climbing? You’d climb a mountain, if you had to.This isn’t a pipe dream. There is unlimited food and water, unlimited energy and unlimited opportunity for the human race – just over the next hill.

We’ve got to use our imaginations, millions and millions of us. We’ve got to involve our government through our elected We’ve got to use our imaginations, millions and millions of us. We’ve got to involve our government through our elected representatives, all the way to the president. We’ve got to use the energy we have and vote for the future just over the hill. Please visit the Fusion 4 Freedom website.

Fusion Energy for Our Future

In the months just ahead, scientists will be meeting, organizing, holding workshops with top fusion and plasma leaders, military strategic planners in the model of Admiral Hyman Rickover, who led the development of the nuclear submarine, and major philanthropists. The goal? A clear plan leading to the demonstration of a working fusion test reactor by the end of this decade. This year is the 50th anniversary of John Kennedy’s challenge to America to put a man on the moon and bring him safely home to earth. We did it then. And we can do it now – if we harness the skills and brilliance of American and Israeli scientists. I imagine we can!

Join with us at

Steve Cooper
Steve Cooper is the founder of Diamond Bar Productions. They are now producing their first Web based video series, The Epic Tale of Wyatt C. Mollusk. This is a new method for teaching science within an adventure show. The show has a large cast of strange outer space characters, but also features young Pat Boone and Tomer Tamarkin as they work to bring fusion to the galaxy. Steve met Tomer at a political rally and along with Pat, now helps to make the promise of fusion understandable to the world.

Steve is also the author of Paradigms for Pinocchio and The Christian Guide to Dragon Slaying. He lives with his wife, Liz, on their ranch in the Sierra foothills where they raised their four children.


Mainline Fusion Approaches

Innovative Confinement Concepts

Innovative Confinement Concepts and Alternative Fusion Approaches
Between 1996 and 2000, the Fusion Energy Sciences Advisory Committee (FESAC) recommended a vigorous program in Innovative Confinement Concepts to explore several practical alternative paths to the mainline Magnetic Confinement and Inertial Confinement programs. It was never funded. After the U.S. joined the ITER program as a 9% partner, the ICC program was essentially dropped within the United States Department of Energy Office of Science.
US DOE Fusion Energy Sciences link

Fusion Engine: Magneto-inertial fusion via non-destructive magnetic compression of a field-reversed configuration target (Helion)

Shear flow stabilized Z-pinches