A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
Figure 90. Empirical formula and 1D phenomenological predictions for K-shell yields on ZR
at Sandia, as a function of mass for loads 2 cm in length. Fe and Cu predictions are for 55 mm
diameter single wire arrays, Ti predictions for 45 mm, while for argon a standard 1-2-3-4 nozzle
configuration is used. (There is no 1D result for Cu.) [651, figure 11]. Copyright (©) 2006 IEEE.
atomic number A can approximately be related to Z by
A ≈ 1.58Z 1.1 . (8.2)
For Z>10, while the ionization energy E i is approximately
E i ≈ 3.8Z 2.64 (eV/ion) (8.3)
when the plasma is 50% hydrogen-like and 50% helium-like, the minimum energy E min
required is approximately
E min ≈ 1.49Z 3.51 (eV/ion) (8.4)
The demands on the generator are substantial if an efficient radiator is required for high Z,
e.g. for krypton E i > 1 MeV/ion and a current rise time below 30 ns, though the latter could
be increased by increasing the array radius beyond 1 cm.
A more recent paper by Thornhill et al [651] included L-shell losses and opacity, with
the objective of bench marking data and employing 1D MHD to predict what the potential of
the higher current (26 MA) ZR machine at Sandia is for producing multi-keV in x-rays, both
from K-shell line and from free-bound continuum radiation. Argon, titanium, stainless-steel
and copper were considered. The predictions are summarized in figure 90, having first bench
marked the results obtained so far from the Z generator.
Stainless-steel implosions at up to 20 MA on Z have been studied by Jones et al [652]
and show K-shell yield scaling consistent with Thornhill et al [651]. To minimize the effects
of RT instability nested arrays in transparent mode were employed. Optimal x-ray emission
and highest temperatures occurred when there was simultaneous arrival on the axis of the
inner and outer masses. Low mass and large array radius are a key to obtaining electron
temperatures in excess of 3 keV. It is disappointing that the 450 µgcm −1 case which gave
record ion temperatures [130] was omitted from this series, but in terms of coupling maximum
energy to the electrons and hence to radiation it might be justifiable. There is probably an
optimal ratio of equipartition time to Alfvén transit time to maximize x-ray yield, yet benefiting
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