A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
Figure 46. Plot of ρ (kg m −3 ) as a function of (r − r w )(µm) on a log log plot for wire radius
r w = 5 µm (lower curve) and 15 µm (upper curve) for 100 wires and a current of 3 MA. The dashed
lines show ρ ∝ [(r − r w )(µm w )] −1.1 . Reprinted with permission from [338]. Copyright 2007,
American Institute of Physics.
Figure 47. Lineout of T e (eV) (black), radiation temperature T r (red) and T rfit = 2.46Te
0.6 (green),
this being a good fit to the simulations. Reprinted with permission from [338]. Copyright 2007,
American Institute of Physics.
examines what physics is dominant in a given region and compares a simplified analytic model
with simulations. He finds that up to 35 µm from the wire-core surface the inward radiation
energy flux approximately balances the outward enthalpy flux but beyond this Joule heating
is the dominant heating mechanism. This is consistent with earlier modelling by Alexandrov
et al [339]. In [338] rather than use the Lee–More–Desjarlais [340] transport coefficients in
the core, better agreement with experiment is found by reducing the core conductivity by a
factor of 10–100. As in liquid-metal MHD power generation, the effective conductivity is
strongly dependent on whether there are vapour bubbles in connecting liquid or liquid droplets
immersed in vapour. Percolation theory [341] gives a critical density of the mixture as one
third of the liquid density below which it becomes a poor conductor. Figures 46 and 47 show
density and temperature profiles computed away from the wire core radius. Note that ρ is
approximately proportional to (r − r w ) −1.1 from1to35µm from the core surface.
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