A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
force. Perhaps as a result the growth rate did not follow the usual k 1/2 ideal MHD dependence
for a Z-pinch, but decreased with k.
Introduction of lower hybrid anomalous resistivity will also change the formula for the
Pease–Braginskii current, a point followed up by Robson [125].
In section 3.14 anomalous resistivity will be introduced in a model of disruption when
gaps of low density plasma exist between density islands at the time of a m = 0 disruption
and thereafter.
It is to be hoped that with the new generation of computers further work, perhaps in 3D,
full electromagnetic will be undertaken on lower hybrid turbulence, and the related modified
two-stream instability.
Meanwhile attention could be drawn also to the need for better diagnosed and specially
designed experiments. A paper by Takeda and Imezuka [237] presents measurements of
anomalous resistivity associated with large amplitude noise at the lower hybrid frequency.
Here the ratio v d /v i was large (∼10 2 ) and the anomalous collision frequency was essentially
e . This leads to Bohm diffusion. It is perhaps permissible to speculate that the formula for
ν anom given by equation (3.54) or(3.55) is only valid up to a value of e , when it becomes
independent of (v d /v i ). For a hydrogen plasma this will occur at v d /v i equal to 4.2. A suitable
form for the effective collision frequency νanom ∗ as a function of (v d/v i ) 2 through equation
(3.54) or(3.55) for e τ e > 1isgivenby
νanom ∗ = ν anom/(1+ν anom / e ). (3.56)
3.14. Disruptions; ion beams and neutrons
During the nonlinear evolution of the m = 0 instability of a stagnated compressional Z-pinch or
plasma focus employing deuterium as the working gas, a significant pulse of neutrons appears,
typically a yield of up to 10 12 neutrons [238, 239]. The origin of this has been a great source of
debate and controversy which has still not been resolved. Some of the proposed mechanisms
are fluid-like and others are kinetic in nature. An important test of any hypothetical theory is
whether total axial momentum is conserved during the ion beam formation.
In fact the normally principal pulse of neutrons at the time of m = 0 disruption is often
the second pulse [240]. The likely explanation of the first pulse is essentially kinetic in origin.
It was first hinted at in Trubnikov’s paper [241] and developed more realistically by Deutch
and Kies [242]. Here it is considered that there is a sheet current piston which compresses the
plasma as the first pinch is formed. Unlike the snowplough model, it is postulated that the ions
on encountering this moving piston are reflected by it (in fact by the radial electric field in the
current sheet) with twice the velocity of the piston. During this process they are essentially
collisionless and also conserve their angular momentum (a point made by Trubnikov [241] and
earlier by Haines [243]). On encountering the moving piston a second time, there is another
gain of energy; indeed the faster ions have more reflections and gain even more energy, a feature
of this Fermi acceleration mechanism. There will be, as a result, a high energy ion tail, and the
ion–ion collisions which will grow in number when the piston reaches close to the axis and the
density rises will also yield DD nuclear reactions, but of a suprathermal nature. If the incoming
piston is conical in shape, it will also lead to a growth in axial motion. It should be noted
that multiple collisions of essentially collisionless ions are needed for this, a condition which
might also pertain in certain conditions in the precursor plasma of an imploding wire array.
Turning to the principal pulse of neutrons, there are important features; (i) the neutrons
occur at the time of an m = 0 instability, a point confirmed experimentally by Bernard
et al [238], (ii) the neutrons have an anisotropic distribution consistent with originating from
an ion beam in the z-direction: This was also confirmed by Bernard who employed a deuterated
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