A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
Figure 51. A side-on laser shadowgram of a 16 × 15 µm Al wire array on MAGPIE at 180 ns after
the start of the current [65]. On the right is a similar result from a tungsten 16 × 7.5 µm array.
Reprinted with permission from [65]. Copyright 2001, American Institute of Physics.
between wires so that inside the current-carrying region, the closed line integral ∮ B · dl is
zero. Yu [338] found that the ablation process was confined to an almost azimuthally symmetric
private flux region with R m < 1, and, as described above, developed a theory for the mass
ablation rate.
The mass ablation rate ṁ was very successfully modelled phenomenologically by Lebedev
et al [65] in a rocket model. Assuming R m ≪ 1 and that all the current flows in a narrow
shell-like region, the magnetomotive force leads to ejection of the precursor plasma with an
ablation velocity V a which experimentally is found to be a constant for each material during a
discharge, the rocket equation gives
ṁ =− µ 0I 2
4πRV a
(kg m −1 s −1 ). (5.1)
Knowing all the terms on the rhs from experiment ṁ can be found and integrated in time to
find the mass that has been ablated up to any time t. V a is typically 10 5 ms −1 .
A model developed by the Angara group [339] gave a slightly modified equation for
tungsten
ṁ ∗ =−0.4π I 1.8 (MA)
R 0.8 (cm) (µgcm−1 ns −1 ), (5.2)
where the ablation velocity is implicitly included. Cuneo et al [323] claim that both formulae
agree with experiment within the accuracy of measurement. Yu et al [338] also provide scaling
laws but in terms of current and wire core radius and wire number.
A side-on laser shadowgram, figure 51, clearly shows both the inward filamentary
precursor flow with a wavelength of ∼0.5 mm in Al and the accumulated precursor cylinder
on axis. As can be seen from the radial streak picture in figure 52, the precursor arrives on axis
in MAGPIE at approximately half the time to full implosion, and is a bright emitter. Figure 53
shows gated soft x-ray images of precursor in carbon, aluminium and tungsten. In all cases
the cylindrical column is straight with no sign of MHD instabilities, consistent with it carrying
negligible current. The confinement of the column is because of the ρVa
2 kinetic pressure of
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