HIGH ENERGY DENSITY PHYSICS: RECENT DEVELOPMENTS WITH Z PINCHES

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HIGH ENERGY DENSITY PHYSICS RECENT DEVELOPMENTS
WITH Z PINCHES

• N. Rostoker, P. Ney, H. U. Rahman, and F. J.
  Wessel
• Department of Physics and Astronomy
• University of California, Irvine

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ABSTRACT

• High density Z-pinches have been studied for
  many years as intense sources of soft X-rays.
  More recently, there have been investigations of
  possible applications to thermonuclear fusion
  that involve staging. This usually involves
  multiple shells of plasma that collide. For
  example, an outer shell of high-Z material, such
  as Kr, or Xe, is accelerated and collides with an
  inner, coaxial plasma of DT. The result is
  compression and heating, which is of interest if
  stability is maintained for a sufficiently high
  compression ratio. The main problem is control of
  the Rayleigh-Taylor Instability, which has been
  studied theoretically and experimentally with
  substantial success.1 The compression has been
  investigated with a 2-1/2 D, radiation MHD code,
  MACH2, and studies indicated that neutron yields
  close to break-even were possible. Recent
  investigations involve shock waves, which preheat
  the plasma. This new feature facilitates a higher
  compression ratio, so that break-even and beyond
  are predicted for a machine of a scale of the
  Sandia Z-Facility.2

• H. U. Rahman, N. Rostoker, A. Van Drie, and F. J.
  Wessel, Phys. Plasmas 11, p. 18(2004).
• H. U. Rahman, P. Ney, F. J. Wessel, and N.
  Rostoker, 7th Symposium on Current Trends
• in International Fusion Research, March 2007, to
  be published in the proceedings.

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Physics of Z-Pinches at UCI

• Joseph Shiloh (1978), High Density Z-Pinches.
• James Bailey (1983), Effects of Radiation Cooling
  and Plasma Atomic Number on Z-Pinch Dynamics.
• Irving Weinberg (1985), X-Ray Lithography and
  Microscopy using a Small Scale Z-Pinch.
• Edward Ruden (1988), Magnetic Flux Compression
  with a Gas-Puff Z-Pinch.
• Gus Peterson (1994), Effects of Initial
  Conditions on a Gas-Puff Z-Pinch Dynamics.
• Brian Moosman (1997), Diagnostics of Exploding
  Wires.
• Alan Van Drie (2001), Thermonuclear Fusion in a
  Staged Z-Pinch.

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Staged Z-Pinch
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Physical Phenomena Associated with Compression

• Rayleigh-Taylor Instability
• Current transfers from the outside surface of Xe
  to the inside due to
• Multiple ionization of the Xe
• Shock wave propagation
• The outside surface is unstable and its growth
  eventually limits the compression

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INITIAL RADIUS
INITIAL CONFIGURATION
DT
Xe
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Physical Phenomena Associated with Compression
(contd.)

• The pinch energy is
• The initial radius, ri , is important - it should
  not be too large so that the outer surface
  instability grows too much. The perturbation
  grows exponentially and the pinch energy grows
  logarithmically.
• ri should not be too small so that W is
  substantial.
• Shock waves in Xe cause mass to accumulate at the
  outer surface of the DT, into which the current
  transfers. The transmitted shock waves preheat
  the DT plasma up to several hundred eV, prior to
  adiabatic compression.

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Current Amplification in a Staged Z-Pinch
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Current Amplification in a Staged Z Pinch
(contd.)

• Initial fiber current due to prepulse.
• Flux is conserved during the compression.
• For example, (PRL, 74, p.715(1995), I0 200 kA,
  r0 2 cm, a0 10-2 cm, T0 200 eV, Bz0 200
  Gauss, tm 1 msec, then, I 2 MA.

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Numerical Simulation

• Mach2 Code
• Single fluid, 2-1/2 D, time-dependent,
  MHD-coupled radiation, resistive and thermal
  diffusion, electron and ion temperatures
  separate, tabulated equation of state for shock
  waves, including ionization (SESAME), generalized
  Ohms Law, with Hall Effect.
• Machine parameters
• Current 18 MA, Risetime 90 nsec, Energy 2.1 MJ
• Initial load parameters
• Radius 0.5 cm, height 1.5 cm
• Xe shell 0.2-cm thick, density 8.3 x 1020 cm-3
• DT fill 0.3-cm radius, density 8.1 x 1020 cm-3
• Initial plasma temperature 2 eV

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Numerical Simulation (contd.)

• Current transfer to the inside surface of the Xe
  driver causes a separation of a Xe layer that
  collides with the DT and transmits a shock. The
  current continues to rise in the remainder of the
  Xe liner.
• The gap between the Xe/DT surface and the inner
  surface of the Xe leads to current amplification
  as previously described. A detailed description
  of the currents from the calculations is shown in
  the next figure, which begins at 80 ns.
• The pinch radius reaches a minimum of 0.01 cm at
  121 ns. The current is amplified from 18 MA to
  200 MA, with a magnetic field maximum of 600 MG.
  The DT plasma is preheated by the initial shock
  waves to about 100 eV. The adiabatic compression
  and a-particle heating bring the temperature of
  the DT to about 25 keV, after which explosion
  takes place. The fusion energy is 80 MJ, when the
  initial stored energy of the capacitor bank was 2
  MJ.
• Recent calculations for a 100 kJ initial
  capacitor bank energy predict a fusion energy
  yield of about 150 kJ.

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Iso-contour (z-r) profiles of the axial-current
density computed at various times during the
implosion.
time progression right to left, top to bottom
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Line-out (z-r) profiles of the axial-current
density computed at various times during the
implosion.
time progression right to left, top to bottom