A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
Figure 60. A sequence of side-on soft x-ray images on MAGPIE for an array of 16 wires at 155,
164, 238 and 247 ns. Reprinted figure with permission from [314, figure 4]. Copyright 1998 by
the American Physical Society.
Novel experiments have been carried out using coiled or helical Al wires in an array by
Hall et al [295]. The complex 3D Lorentz forces were modelled by MHD simulations. It was
found that outside the diameter of each helix the flow of ablated plasma is now modulated
at the wavelength of the coils rather than at the fundamental wavelength. Furthermore with
only eight helical wires the resulting x-ray power at stagnation was surprisingly increased to
that of a 32 wire implosion on MAGPIE. However more recently Hall et al [374] have shown
that the fundamental mode does occur initially close to the wire cores. Further details of an
experiment with etched wires can be found in [375].
5.5. Main implosion
The ablation of the wire cores is axially non-uniform due to the occurrence of the instability,
discussed in the previous section and an early implosion adjacent to the cathode. At a certain
stage, typically at a time of 80% of the total time to implosion, gaps appear in the necks of
the instability on each wire, accompanied by correlated bright spots due to the development of
the global MRT instability. A sequence of soft x-ray images is shown in figure 60 from [348].
With no wire cores in the gaps the plasma heats up; the magnetic Reynolds’ number can
be inferred to exceed one, and the J × B global pinching force causes the main implosion.
The implosion’s trajectory is shown in figure 40, and, as discussed in section 5.1, figure 41
illustrates the imploding current shell which acts to a good approximation as a snowplough,
sweeping up the precursor plasma still in its path. This considerably reduces the growth of
RT because the piston is forced to move at almost constant velocity. Lebedev et al [65, 376]
estimated the radial mass distribution ρ(r,t) at a position r at a time t, taking into account the
time delay required for the precursor material to reach the position r to be
ρ(r,t) =
µ 0
8π 2 R 0 rV 2 a
[
I
(
t − R 0 − r
V a
)] 2
, (5.7)
where I(t − ((R 0 − r)/V a )) is the current in the array at the earlier time t − (R 0 − r)/V A .
With r = R p , the radius of the precursor column, the total mass in the precursor column can
be found by integrating equation (5.1) to the time t − (R 0 − R p )/V a .
Using a snowplough model of the implosion as in section 4.1 with ρ(r,t)given by equation
(5.7) and by varying the initial mass in the piston a fit can be made to the trajectory of the final
implosion as shown in figure 40. Similar detailed fitting of Z data from Sandia can be found in
Cuneo et al [323]. A small correction could be made for the motion of the gas being swept up.
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