A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
beam-generated neutrons there is experimental evidence, observed by Barnard et al [238]
and Forrest et al [255] of electrostatic turbulence using laser scattering techniques. This is
consistent with the line density locally at the m = 0 neck falling below the critical value,
described in section 3.14.
In most experiments there is an earlier neutron pulse arising at the time of the implosion.
Deutch and Kies [242] have identified this with a Fermi mechanism in which the higher velocity
ions are reflected several times in the inward moving sheath carrying the skin current. Neutrons
resulting from D–D collisions in this case would have an anisotropy in which more neutrons
would be emitted radially.
At currents greater than 1 MA there is a tendency for the neutrons to be more isotropic,
and there could be a significant thermal component which would scale as I 2 , more like the
high current gas-puff experiments (section 7.2). Such results were found on the 1 MJ plasma
focus at Frascati by Maisonnier and Rager [239]. By pinhole-imaging the charged particles
from the fusion reaction zone and correlating with time-resolved neutron detectors Zakaullah
et al [503] showed that at low pressure the neutrons were produced by beam–plasma reactions
with an anisotropy of 3.5. Above the optimum pressure (for this 2.3 kJ low energy machine)
of 2.5 mbar the almost stable plasma moves away as a jet-like boiler. The apparent stability
at this time could be explained by Comisar [504] who theoretically showed that for a curved
Z-pinch (as in a plasma focus) the m = 0 instability grows 10 times more slowly. Hirano
et al [505] found a similar transition from low to high pressure.
The plasma focus does not require pulsed power on the 100 ns time scale but works
conveniently with a capacitor bank with microseconds’ time scale. Instead, the rundown
phase allows magnetic energy to be stored inductively, prior to the final collapse, which can
have a high implosion velocity due to the early shedding of mass, in the rundown phase.
There is a strong polarity dependence, the device having much higher neutron and x-ray
yields with a central anode. (This is the opposite polarity to present-day wire-array experiments
where the cathode and power-feed point are at the same end). There are several mechanisms
which are affected by the polarity. Bostick [506] noted that the shapes of the moving ionizing
shock front and current sheet behind were different. This is because of the Hall effect. Writing
E ∗ = E + v × B + ∇p e /n e e + ∇T e . (7.11)
Ohm’s law becomes
σE ∗ = J + J × β (7.12)
where β = ϖ e τ ei b = σB/n e e is the Hall parameter. There is an angle θ between E ∗ and J
such that
b tan θ = E∗ × J
= β, (7.13)
E ∗ .J
where b is the unit vector in the direction of the magnetic field. If the generalized electric field
E ∗ is normal to the surface of the conducting inner electrode, then when it is the anode the
current will slope backwards, causing the plasma slug to be bullet shaped. In this way much
of the plasma swept up will move radially outwards, so that in the final implosion when the
current has reached its peak and is at the end of the anode, the mass is smaller and a faster
implosion occurs.
In the case of a central cathode the current will slope forward, less radial motion will
occur, and a greater mass will have to be collapsed to the axis.
An apparently different explanation of the polarity ‘riddle’ is presented by Decker et al
[507]. Their theory is that the plasma behaves very differently in the radial electric field
between the electrodes. In an experiment they show that shielding out this field by means of
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