A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
D–D neutrons were produced at 1 MA on the Frascati 1 MJ machine, greater at the time than
any other controlled fusion experiment (see [43]). The merit of the plasma focus probably
lies in the opportunity during the axial flow stage of building up the current and locally stored
magnetic energy which is then used to compress a reduced mass of plasma. Unfortunately the
main neutron pulse was again associated with a necking or sausage MHD instability, and the
subsequent disruption.
It was during the 1970s that a remarkable technological development occurred. Pioneered
by Martin and co-workers at AWRE (Aldermaston) [6], pulsed power was developed, based at
first on work of Blumlein (1948), [44], a plaque to whom is displayed on his home in Ealing.
What emerged is a technique in which a Marx generator (based on the switching of charged
capacitors from being in parallel to being in series, leading to a large voltage multiplication)
charges up a pulse-forming line to 1–10 MV. At this stage the main inventive step is to realize
that insulators behave perfectly for short enough times. Furthermore the use of oil or water as
the dielectric medium allowed self-healing of the medium after each discharge, and attention
could be given to designing the solid-state insulators at interfaces in a carefully graded way.
From these ideas machines are currently operating at currents rising to 20 MA in 150 ns at
voltages of 8 MV (the Z machine at Sandia National Laboratory, Albuquerque).
In 1978 Haines [45] showed that under fusion conditions with heat losses to electrodes
taken into account the ion Larmor radius is about 0.1–0.3 of the pinch radius. Also, with a
current only somewhat higher at about 1.5 MA, radiative collapse to very high density might
occur [45]. A new programme of Z-pinch research commenced at Imperial College with the
construction of the MAGPIE generator. However, the direct application of pulsed power to
single frozen deuterium fibres gave disappointing results, with the dynamics dominated by
ionization, expansion and MHD m = 0 instabilities before the hot collisionless large Larmor
radius regime could be accessed [46]. Experimental interest then switched to studying the
physics of wire-array implosions. In a renewed effort in 2001, a compression Z-pinch did
indeed demonstrate the stabilizing effect of large ion Larmor radius effects [14].
Meanwhile in the USA and USSR, Z-pinch experiments using the new pulsed power
technology were aimed at producing intense x-ray sources. Exploding wires [47], gaspuffs
[48] and finally wire arrays [49, 50] were explored. A review of x-ray emission from
imploding Z-pinches was given by Pereira and Davis in 1988 [51].
1.2. Various Z-pinch configurations
Figure 3, taken from [52], illustrates the many Z-pinch configurations that have been studied.
The first is the compression Z-pinch in which a cylindrical vessel bounded axially by the two
electrodes is filled with gas. On applying a voltage, breakdown occurs near the insulating
wall and a current shell forms. This current and its self-magnetic field create an inward radial
force. Several models of the inward compression have been developed: the snowplough, a
shock model and a slug model. These will be discussed in section 4.
If the diameter of the vessel is reduced to the order of up to a few millimetres, the
compression pinch becomes a capillary discharge. The wall plays an important role in
controlling the plasma and indeed it can itself ionize and form a conducting path for the current.
The capillary discharge has been remarkably successful in producing a plasma uniform enough
to form a lasing medium [17]. If the plasma density increases towards the ionizing wall, this
plasma can be used to guide a laser beam, and extend the focal region beyond the Rayleigh
length. This idea is being explored in the wakefield acceleration of electrons (see section 8.9).
If the Z-pinch vessel is filled with a high pressure gas (∼ 1 atm) and an ionization path is
3
created along the axis, e.g. by a focused pulsed laser, then, on applying a high voltage, current
8