A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
Figure 75. Contours of (a) density and (b) rB θ at stagnation, t = 230 ns. Reprinted with permission
from [321]. Copyright 1998, American Institute of Physics.
m = 1 activity in the simulation which itself is dependent on the initial, arbitrary azimuthal
perturbations in the simulation. In ALEGRA simulations in order to obtain energy conservation
when switching from Lagrangian to Eulerian meshes plus the numerical viscosity, Lemke [367]
transfers the excess energy to ion thermal energy. This then appears equivalent in effect to the
ion-viscous heating of Haines [130]. It is interesting that because the choice of k, the wave
number of the fastest growing mode in equation (5.7) with L µ = 2, depends on the value of the
viscosity, the resulting viscous heating is independent of both k and viscosity. Thus, provided
S ≫ R holds, and provided the excess energy is the result of 2D or 3D activity, it is reasonable
in simulations to deposit the excess energy into thermal energy.
Early attempts to account for the extra heating included an arbitrary increase in all
dissipative processes by some assumed turbulence [401]. The 3D modelling introduces an
initial chosen azimuthal perturbation, and together with artificial viscosity and a coarse mesh
leads to an axial magnetic field of the same order as the azimuthal field [443] much earlier than
the experimental observation of any helical structure. This means that there is a generation
∫or injection of helicity to the pinch. Helicity per unit volume, A · B (or some authors use
A · B dV ) where A is the magnetic vector potential is governed by the equation
∂
(A · B) + ∇·(E × A + B) =−2E · B, (7.6)
∂t
where E is −∂A/∂t−∇. The source term, −2E·B is usually negligible in a highly conducting
plasma and so the local change of A · B must be due to a surface flux of (E × A + B) which
in simulations has to be prescribed in effect at the outer boundary. This implies the imposition
of a radial magnetic field or a radial component of E × A at the outer boundary.
7.3. Plasma focus
There are two main configurations of the plasma focus device; the ‘Mather type’ and the
‘Filippov type’, named after their inventors [40, 41] and shown in figure 76. The largest
Mather-type device, the 1 MJ experiment at Frascati, produced 10 12 neutrons when optimized
for 500 kJ stored energy at 5–8 Torr filling pressure [42]. The neutron yield has a I 4 scaling, as
does the x-ray yield, and there are many mechanisms proposed, [241, 243, 246, 503], most of
which are designed to account for the anisotropy of the neutron production through the onset
of an intense ion beam followed by beam–plasma nuclear reactions. As pointed out in [243]
and in section 3.14 ideal and resistive MHD cannot produce a uni-directional flow of ions
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