HIGH ENERGY DENSITY PHYSICS: RECENT DEVELOPMENTS WITH Z PINCHES

1. 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

2. 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.

3. 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.

4. Staged Z-Pinch

5. 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

6. INITIAL RADIUS INITIAL CONFIGURATION DT Xe

7. 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.

8. Current Amplification in a Staged Z-Pinch

9. 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.

10. 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 Ohm’s 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

11. 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.

12. 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

13. 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