A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
even more wires are used Coverdale et al [365] and Mazarakis et al [366] have shown that
there is an optimum number of wires for Al and W, respectively. This could be that earlier
merger and plasma shell formation permits a longer time for RT growth, reducing the tightness
and symmetry of the final stagnation. Indeed it is now being recognized in simulations by
Lemke [367] that the precursor could provide an optimal density profile and precursor column
to maximize x-ray power. An alternative explanation could be that with more and finer wires
the final radius could be smaller due to better symmetry, and this smaller radius limits the
area for black-body radiation loss. A detailed experimental study of the precursor plasma has
been carried out by Bott et al [354]. Three stages of the precursor plasma were identified; an
initially broad density profile, with a critical density on axis for formation of the column, then
a shrinkage to a small diameter due to radiative collapse, followed by a slow expansion. Al, W
and other material arrays were compared and modelled, a kinetic model [351] being required
for the first stage. A dynamic pressure balance of the column was found to hold throughout,
where ρVa 2 balances the pressure.
Single and nested nickel wire arrays (8 or 16 wires) are observed to behave rather differently
to aluminium or tungsten [368] in that the precursor plasma column on axis experiences a
m = 1 instability, implying a significant current in the precursor plasma (i.e a higher magnetic
Reynolds’ number), and centrally peaked. Recent low wire number (6) experiments on the
1 MA Zebra facility using copper revealed higher than expected electron temperatures of the
precursor column in the range ∼450 eV [369]. Here there is a significant pulse emission of soft
x-rays prior to that of the main implosion, which might be of interest for multi-shock capsule
implosions.
5.4. Axial structures on wires
The cause or causes of the instability which arises at plasma formation around each wire is
still not fully understood, though it is extremely important as it acts as the seed for the RT
instability in the later implosion phase. It also leads to a filamentary structure of the precursor
plasma, and to the occurrence of trailing mass.
The main experimental features are that the wavelength appears to be only material
dependent (0.5 mm for Al, 0.25 mm for W) for all conditions. It seemed at first that the
wavelength was just equal to the expanded core size [218] but later work by Bland et al [370]
showed that for unequal core sizes on the same wires the wavelength was the same. Jones
et al [219, 220] seeded the instability with controlled modulations on the wires. For Al wires
it was found that for imposed wavelengths of the modulation much larger than the natural
m = 0 mode, magnetic bubbles grow and at the implosion may hit the axis early. On the other
hand, for a seed wavelength of 0.125 mm, smaller than the natural mode of 0.5 mm, while
early flares are seen at the shorter wavelength close to the core, soon the natural wavelength
occurs. This indicates that the natural mode is not seeded by surface perturbations on the wire
nor by mass modulations in the core. Where the instability first arises was partially answered
by x-ray backlighting [218] where the natural mode was found to occur at quite high density
in the plasma around the wire core, as shown in figure 59.
Four theoretical types of instability can be considered; resistive MHD, RT, thermal and
heat-flow-driven electrothermal. But first the parameter space where the instability grows will
be identified, guided by experiments and the simulations of Yu [338]. An electron temperature
in the range 6–12 eV will be taken and a density range (see figure 45) 3–100 kg m −3 . A
density of 3.6 kg m −3 at r = 55 µm and a mass ablation rate ṁ of 4.8 kg m s −1 [338] (for
r w = 5 µm W) leads to a flow velocity from the core to a further 50 µm of3.9 × 10 3 ms −1 ,
(i.e. at approximately the thermal speed) and a transit time of 13 ns.
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