A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
tendency of the hollow gas jet to expand radially as it flows out of a nozzle from one electrode
to the other, leading to a zippering effect at the implosion.
This axial non-uniformity is overcome by using an array of very fine wires, shown in
figure 3 [20]. The properties of these wire arrays will be discussed in detail later. They could
in principle be replaced by a thin shell metal liner [58], but to keep the mass per unit length
the same as a typical wire array, e.g. 240 wires of 4 µm diameter on an array radius of 12 mm,
would mean a shell thickness of only 40 nm. However for slower compression Z-pinches with
large currents, thicker shells can be employed.
One of the major limitations of the wire-array Z-pinch is the development of RT
instabilities [59]. These instabilities can be partly mitigated by employing double shell or
nested wire arrays [60] shown in figure 3. Further modifications can be considered such as a
central foam or fibre load inside such arrays, as employed in the dynamic hohlraum [61–63].
The staged Z-pinch [64] is one such idea. Recent work by Lebedev et al [65] shows that the
RT instability can be reduced by having incomplete merger of the wire plasmas before the final
implosion, which will have features similar to a snowplough pinch (see section 4.1).
There are a few other variants, e.g. if the Z-pinch is made into a toroidal discharge threading
through multiple cusp magnetic fields (the Polytron configuration [66, 67]), the toroidal current
changes to an ion current through the Hall acceleration effect. Then a plasma stabilized by the
cusp magnetic fields and with greatly reduced ring cusp losses can be formed. See section 8.5.
This configuration has also been studied more recently by Dawson et al [68, 69]. However,
because of the need for cusp magnetic fields provided by external coils which have to be
limited to 5–10 T, the high power-density properties of the Z-pinch cannot be exploited for
this configuration. Reviews of plasma confinement in cusp magnetic fields are to be found
in [70, 71].
Another variant is the X-pinch in which two wires are stretched between electrodes in an
X configuration (Kalantar and Hammer [72]). This crossing point carries twice the current and
this leads to a very hot localized plasma region which is currently being exploited as an x-ray
backlighter source. Another x-ray source can be produced at lower powers using a needle as
the anode [73] in a development of the vacuum spark.
The magnetic fields spontaneously created by ∇T ×∇n effects in laser–plasma interactions
[18] are also in the configuration of a Z-pinch and can develop [74, 75] to the MG level. Many
mechanisms for generation and convection of this azimuthal magnetic field in laser–plasma
interactions have been reviewed [76]. Indeed in the more extreme fast ignitor scheme [19]
the laser-produced channel will have a net current and a similar or larger magnetic field.
When an intense short-pulse laser beam (10 19 Wcm −2 , 1–2 ps) is incident on a solid target an
azimuthal magnetic field of up to 0.7 GG has been measured [77, 78] similar to that predicted
in particle-in-cell simulations [79], in a hybrid model [80] and analytically [81]. It can be
considered as driven by the absorption of photon momentum [81, 82] and leads to a magnetic
field in the opposite direction to that associated with ∇T ×∇n effects. This is a most extreme
Z-pinch. These studies are unfortunately beyond the scope of this review and will be only
briefly discussed in section 7.8.
1.3. Outline of the review
Having presented an introduction to the Z-pinch, highlighting the present exciting results
from high current, wire-array pinches, giving a brief history, and outlining the many Z-pinch
configurations, the review will proceed as follows. In section 2, the properties of the equilibrium
Z-pinch will be explored, followed by the stability analysis (section 3) including the nonlinear
evolution of a disruption and the origin of electron and ion beams. In section 4 the dynamic
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