A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
was always in the direction from cathode to anode. No attempt was made to remove perturbing
fields such as the Earth’s field [557], and it also was not possible to reverse the polarity of
the pinch. In [53] the accretion problem was addressed, and it was suggested that by current
programming to have a larger rate of rise, compression of the hot pinch will occur.
A variant of this was explored by Soto et al [54] who employed two stainless-steel conical
hollow electrodes with 2 mm diameter with edges of 50 µm radius of curvature. A microdischarge
was set up between these. Then a few nanoseconds before the application of the
main current a pulsed laser was focused through the anode on to the cathode. Thus two parallel
conductive paths for the current were set up. With a peak current of 130 kA, interferograms
showed a peak electron density of 3 × 10 25 m −3 on axis. The outer annular hydrogen plasma
coalesced with the central column and there was a compression of the pinch from 1 mm to an
equilibrium radius of 50 µm. The Alfvén transit time was estimated to be 14 ns, and the line
density grew to 1.3 × 10 19 m −1 . This early increase in N is not maintained, inferring that the
neutral gas does not cross the pinch boundary. The pinch appeared to be stable at a temperature
of 150 eV. The enhanced stability is proposed to be due to resistivity at early times, and later
due to FLR because a i /a is about 0.1. It could be worthwhile to extend this compressional gasembedded
pinch to higher currents. So far with no observations of neutrons or x-rays, there are
no disruptions, the achievable temperatures by Joule heating alone are rather modest. This idea
of employing compression both to insulate the plasma from accretion from the neutrals outside,
and to have more heating has been followed up by Veloso et al [558] using a laser-initiated
hollow gas-embedded Z-pinch. The peak current of 150 kA led to an implosion velocity of
5kms −1 , and the plasma column remained hollow and stable for 10 Alfvén transit times at a
Bennett temperature of 150 eV.
7.5. Single wire and frozen deuterium fibre pinches
For single fibres distinction between insulating and conducting materials should be made at
the earliest stage of electrical breakdown and plasma formation. As found by Beg et al [254],
for insulators breakdown was observed to proceed from the cathode, coincident with a pulse of
hard x-rays associated with an electron beam of about 4 kA and >50 keV. This was consistent
with a magnetron type of condition,
√
2me V
I = 2πr 0
(7.15)
µ 0 d e
in a radius r 0 ≫ a, the fibre radius. This is r 0 /d times the Alfvén-Lawson limiting current [95],
(see section 2.2). Carbon and frozen hydrogen or deuterium are examples of insulators used,
while conductors such as aluminium, tungsten, copper and nickel have been widely explored.
The subject of exploding wires has a rather different motivation, but indeed it characterizes
that all fibres initially explode with a typical velocity of 10 4 ms. This is illustrated in figure 81
in an optical radial streak of images of a 25 µm aluminium fibre taken on the IMP generator
in which the current rises to 80 kA in 60 ns. The exploding plasma around the fibre carries the
rising current, but at this stage the J × B pinch force is insufficient to overcome the plasma
pressure, rising under Joule heating. Thus here is another example of the current being less than
that given by the Haines–Hammel curve [103–105]. As the current increases further, however,
simulations [197] show that a re-compression occurs accompanied by the onset of the m = 0
MHD instability. The experimental data and simulation are shown in figure 82. It is interesting
that here the simulation reproduces from noise the same wavelength of instability as occurs
in the experiment, i.e. the resistive MHD approximation is adequate. Thus the fibre pinch
is dominated at the stage of confinement by the m = 0 instability. Furthermore, Chittenden
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