A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
Figure 74. Density contours at (a) t = 205 ns and (b) t = 218 ns for a 2D simulation.
The calculation exhibits short wavelength growth which saturates and then develops into longer
wavelengths. Reprinted with permission from [321]. Copyright 1998, American Institute of
Physics.
reconnection, when, prior to this the J r B θ forces in the outgoing m = 0 flares are confining
the flares and preventing coalescence. But of course the axial electric field in the vacuum gaps
will be enhanced by the feeding of magnetic flux into the inward-going bubble, analogous to
current switching in nested arrays. When simulating this there is a problem that the vacuum
regions are usually modelled with a low density plasma of high resistivity, so the results will
depend on this numerical artefact. A second ∫problem is the conversion of magnetic energy
stored in each bubble to ion thermal energy. P dV work is cited in some of these papers,
e.g. [458]. But this is reversible and will heat both species in the ratio of their pressures.
Furthermore LePell in [130] has shown that experimentally the ion temperature continues to
increase whilst the mean pinch radius is increasing. Another point is that within each bubble
B θ falls off as 1/r, and at the outer surface, as shown in figure 73 the current density is reversed
leading to an outward J × B force which will work against buoyancy. Lovberg states that
magnetic ‘flux is detached from the circuit and ingested by the turbulent pinch’. How the
magnetic energy is converted without resistivity is rather vague in LRV. J × B could lead
to local ρ dv/dt ion acceleration and then to viscous dissipation via shocks or steep velocity
gradients. Indeed, insofar as numerical simulations are able to give enhanced radiation, large
amplitude MHD modes with numerical viscosity to provide the dissipation is the probable
energy route. So far no simulations have included the real physical viscosity, let alone the full
stress tensor. Douglas et al [501] found that computationally the growth rate was limited if
fewer than ten mesh points per wavelength were employed. In Peterson et al [321] while there
is evidence for shorter wavelengths growing more quickly and saturating, emphasis is placed
on the evolution of longer wavelength modes, as shown in figures 74 and 75. At stagnation,
density profiles in figure 75(a) indicate that pronounced spikes are dominant while in (b) the
contours of rB θ which may be interpreted as current streamlines show that work can continue
to be done on this outlying material by the Lorentz force. There could be a few current loops
in the plasma indicative of magnetic bubbles, but they do not appear to be dominant. Recently
Lemke [367; see also 392] has shown that 70% of the radiated energy arises from numerical
heating associated with artificial or von Neumann viscosity. He also showed that there was an
optimum ablation rate (in the precursor phase) for maximizing the x-ray power.
In Chittenden et al [324] a 3D MHD simulation with GORGON shows helical m = 1
structures as well as m = 0 hot spots. Agreement on x-ray emission occurs if there is significant
112