A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
a copper conductor buried in the insulator leads to almost equal behaviour of both polarities.
In contrast an unshielded insulator with a central cathode leads to two orders of magnitude
reduction in the neutron yield. Only with a central anode can there be electron charging on
the insulator surface. The employment of a high dielectric insulator is also important. But this
result is perhaps consistent with the Hall effect model, since both models depend on the angle
between the current and electric field.
In the breakdown process and early heating of the plasma sheath, radial spokes or filaments
can occur. This could be due to the current-driven electrothermal instability [158], discussed
in section 3.12. Bostick et al [508] claimed that the filaments came as pairs of plasma vortices.
But Mather and Williams [509] were not convinced that there was a paired effect. Nardi [510]
constructed a theory for the production of filaments, which he envisages are bundles of helical
field lines, in the regions of high plasma vorticity behind a shock wave. Bykovskii and
Lagoda [511] investigated the occurrence of filaments in a laser-initiated vacuum discharge.
However, at higher power, filamentary structures play little rôle, probably because the condition
that the mean-free path be less than the collisionless skin depth is not satisfied for very long [158,
see also section 3.12]. In their book Liberman et al [87] discuss several other mechanisms
for filamentation but conclude that the electrothermal [158] overheating instability, such as
discussed later by Imshennik and Neudachen [512] is the most likely explanation. Radiation
loss also enhances the growth rate provided the loss rate has less than a T 2 dependence.
Bremsstrahlung with a n 2 T 1/2 dependence, as used in [214], therefore enhances the instability.
This is because, with ion motion included, a hot filament has a lower density, and radiates less
than the higher density region surrounding it. Adding an inert gas as a dopant can increase the
x-ray radiation loss; this will be discussed further below and in section 8.1.
Attempts have been made to obtain scaling laws not only for larger but also for smaller
plasma focus devices. Lee and Serban [513] defined a ‘drive-parameter’ S by
S =
I p
, (7.14)
aρ1/2 where I p is peak current, a is the inner (anode) radius and ρ is the filling density. For plasma
focus devices optimized for neutron production S is almost the same for all sizes. This was
followed up by Zhang et al [514] for a range of currents from 180 to 400 kA and for aspect
ratios which spanned Mather and Filippov types. Beg et al [515] studied the x-ray emission
from a table-top plasma focus and its application as a backlighter. Soto [516, 517] has extended
this scaling to very small repetitive plasma focus experiments, useful for field applications. A
plasma focus using an energy source of only 1 J has been developed [518].
There is a transition in the structure of the x-ray emitting region as the charge number of the
ion is increased beyond 18. Below Z = 18 there is a well defined pinch column, while above
Z = 18 hot spots with harder x-radiation occur on the axis. These results by Beg et al [515]
are consistent with earlier data by Lebert et al [519] and Kies et al [520]. It is likely that the
transition to hot spots is the result of m = 0 MHD instability in which radiative collapse plays
an important role. Indeed when a heavy gas dopant is added to a deuterium plasma focus, hot
spots are in evidence [521, 522]. This is due to timing of the pinch to coincide with maximum
current at peak compression, and the need to minimize filamentary structures at the insulator
and during the rundown phase.
As in Z-pinches, the long-time behaviour of a dissipative plasma focus could be to
transform via a helical or kink mode into a minimum energy state [219]. This was considered
by Sestero et al [523]. More recently Kukushkin et al [524] proposed that a spheromak-like
magnetic configuration might be produced from a plasma focus by means of a dynamo effect
(see [525]).
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