Supersonic Plasma Jet Driven MIF Fundamentals

Y. C. Francis Thio

Office of Fusion Energy Sciences
January 24, 2008
Presented at the LANL Plasma Jet Workshop

Supersonic plasma jets as drivers for MIF

Options for plasma jets

Plasma guns possibilities

Idealized mathematical models

High-Z is needed for the imploding liner

  • Pressure and density amplification by factors of 104 to 105 are required
    – Requires high Mach number flows
  • As the liner implodes, it compresses on itself, heating itself up, losing
    compressibility and compressing power

    – Sound speed goes up, depressing the Mach number
  • By using high-Z species in the liner, ionization and radiation helps to clamp
    the liner temperature

    – Lowers the effective Γ of the liner

Confinement and burn: The strategy

  • Batch burns
  • Not looking for self-propagating burn, target or in the afterburner
  • For this discussion, high gain means G > 30
  • Requires advanced PJMIF schemes
  • Very high density burn the in target and the afterburner
  • Intermediate gain means 5 < G < 30
  • Lower density burn
  • Still makes use of the afterburner
  • The target needs to burn to produce sufficient alphas to heat the afterburner layer to fusion temperatures
  • Low gain means G < 5
  • No afterburner burn

A Framework for Analysing the Performance of the Reactor Concept

  • The overall performance of the reactor scheme is very sensitive to
    the choice of the target parameters: radius, density and magnetic
  • Starting with a bad combination of these parameters often leads to a
    performance envelop that could preclude the attainment of desired
    performance goals
  • The following slides aimed at presenting a framework that would
    avoid the pitfalls of picking the bad combination of design
    parameters from the beginning.
  • It does so by working backwards from the desired performance and
    setting up the physics conditions that need to be satisfied in
    reaching the desired performance goal in a self consistent manner.
  • The framework separates out the physics parameters as critical
    parameters to be attained through further analysis, and thus helps to
    focus on the physics issues for further research


After peak compression, the inner surface of the outer liner will begin to retreat

Because the outer liner is much colder and denser, the retreat of the inner surface is governed by the flow in the outer liner

The inner surface is accelerated by the pressure gradient against the high density in the outer liner

Motion takes time to develop

The characteristic speed = sound speed of the outer liner

Relaxation length?

Burn considerations: Target

The B field in the target needs to satisfy the ignition requirement, and determines the fractional alpha deposition in the target. (Basko, 2000).

Burn considerations: Afterburner

Burn considerations: Total fusion yield and gain

For a given fusion gain G and total fusion yield Ef, the equations can be solved for target radius, target density, afterburner thickness and density during burn

An Example: G=20 (plasma gun eff = 50%), Yield = 2 GJ

  • Assumptions: (1) relaxation length = 1 x target radius; (2) fusion burn
    temperature = 10 keV; (3) Jets-to-target hydro efficiency, ηΗ = 20%
    (Pecheck, Colgate, and Kirkpatrick have estimated efficiencies in the range
    of 20% to 25% in similar situations)
  • Results from solving the system equations (1-4) follow:
  • Jets: Zn, 1 eV, 27 km/s, Mach number = 20
  • With initial jet density > 1024 m-3. maximum stagnation pressure > 143 Mbar
  • Target at peak compression:
    – radius 5.93 mm, density 4.47 x 1027 m-3
    – Target confinement time = 66 ns
    – Burn fraction = 0.17, pressure 143 Mbar
    – Target fusion yield: 914 MJ
    – Target alphas: 182 MJ
    – Prescribe a B field of 2.17 MG (217 T) in the target to be above the ignition threshold (Basko or Kirkpatrick)
    – Results in alpha deposition of 0.3 in the target
    – 128 MJ of alphas escapes, available to heat the afterburner
    – Plasma energy: 20 MJ
    – Total jet energy required = 100 MJ
  • Number of plasma guns required for assembling the outer liner: 300 – 500

An Example: G=20, Yield = 2 GJ

  • Afterburner during burn
    – Thickness 9.68 mm, density 2.5 x1027 m-3
    – Burn time: 33 ns
    – Burn fraction: 0.046
    – Thermal energy: 80 MJ
  • 80% is assumed to be provided by the alpha heating
    – Need to verify this with the hydro consideration
  • 64 MJ needs to be provided by alpha heating, out of 128 MJ
    of alpha energy escaped from the target
  • Alpha fractional deposition required = 0.5
    – Minimum B field in afterburner required = 2.7 MG (270 T)
    – Fusion yield from afterburner: 1.1 GJ
    – Burn amplification of 4.7
  • Total yield = (0.9 + 1.1) GJ = 2 GJ
  • Gain = Yield/jet energy = (2 GJ/100 MJ) = 20

Magnetized compressional heating of the target

Minimum Imploding velocity to overcome all the thermal losses: For adiabatic heating, the imploding velocity needs to be several times larger

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