A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
ions leaving the core with a large component of velocity in the −z-direction (i.e. towards the
anode) will almost complete a Larmor orbit before returning. Thus the cores will receive
momentum in the +z-direction for one Larmor period, while, by conservation, the precursor
plasma will acquire momentum in the −z-direction, i.e. towards the anode. Collisions in the
precursor plasma might reduce this effect. Furthermore 3D effects will especially cause the
ions with initial components of velocity in the −z-direction together with a θ-component to
miss the core and join preferentially the precursor flow towards the axis. This is essentially a
finite ion Larmor radius (FLR) effect, and will lead to a component of the inward precursor
plasma flow towards the anode, regardless of the position of the power feed. It is an adaptation
of a theory of the origin of rotation of theta pinches [93] in which ions leaving the vessel-wall
exchange angular momentum with the wall.
Experimental data at the present time show an axial component of precursor flow towards
the anode and away from the power-feed, which is at the cathode. It will be interesting when
experiments with the power-feed at the anode end are undertaken: Then any shorting process
will be electron emission, not from the wires, but from the return conductor. The J × B force
will have a component driving flow away from the power-feed, i.e. towards the cathode. The
FLR mechanism will continue to lead to a component of flow towards the anode.
5.11. Trailing mass and current re-strike
The implosion phase commences when there are gaps in the wire cores. As discussed above,
it could be theorized that the plasma in the gaps, being no longer cooled by the heat flow to
the cores necessary to cause ablation, heats up sufficiently for the magnetic Reynolds’ number
to exceed unity. Thus, this plasma together with the current and associated magnetic field
implodes under the action of the global J × B force. This is illustrated in figure 61 taken from
Lebedev et al [363] for an 8×10 µm Cu wire array. The characteristic wavelength of ∼0.5 mm
of the modulation is seen in the x-ray image at 185 ns. The precursor plasma arrived on the axis
earlier at 130 ns. At 215 ns the implosion has already started, the current sheath being formed
by a large number of magnetic bubbles, moving towards the axis, snowploughing up previously
launched precursor plasma, and now has ∼2 mm wavelength. At 245 ns the imploding plasma
has stagnated leaving behind characteristic trailing mass which has a global m = 0 structure.
Later, these fingers of trailing mass also pinch to the axis, and this is the cause of later x-ray
emission. The peak x-ray emission in this 32 × 10 µm Al wire array occurs at 265 ns, and
so the trailing mass does not contribute to the main x-ray pulse, and indeed could deprive the
stagnated column of some of the current. Figure 69 shows grated x-ray images 2.3 ns before
and 3.2 ns after peak x-ray emission on Z, illustrating the later implosion of the trailing mass
and the relative uniformity of the pinch column.
From analysis of the trajectories it would appear that about 30% of the original mass of the
wires is in the trailing mass [65] though fringe shifts from laser interferograms would merely
estimate that this trailing mass is greater than 7% [363]. After stagnation there is evidence
of a m = 1 component to the dominantly m = 0 stagnated pinch. Bland et al [413] have
compared the evolution of filaments and precursor bubbles for low (8) and high (32) wire
number aluminium wire-array implosions, showing correlation and merging of bubbles in the
latter case. For arrays of ∼300 wires Sinars et al [414] have shown a similar evolution of
trailing mass on Z using x-ray radiography.
Recently, Yu et al [415] have simulated the current trajectories in 3D in the trailing mass.
They find that the growth of bubbles (in the sense of bubble and spike of RT) is reduced
compared with 2D simulations. The trailing mass evolves towards a force-free structure,
implying the presence of significant axial magnetic fields. The azimuthal perturbations and
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