A review of the dense Z-pinch

More documents

Recommendations

Info

Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review Figure 55. End-on laser probing of 32 (a) and 64 (b) Al wires showing collision of plasma streams from neighbouring wires [352, figure 9]. Copyright © 2001 Cambridge University Press. et al [354]. This showed that less than 1% of the current could be present in the precursor on axis for W or Al wire arrays of 16 wires. In a more academic problem, Haines [355] considers the equilibrium problem of a cylinder of plasma under pressure balance in which the Joule heating was balanced by radially inward heat flow to a cold wire acting as a heat sink. The nonlinear second order differential equation has just one free parameter, which is the ratio of the applied axial electric field to the mean radial temperature gradient. The inverse of this ratio scales as T 2 n −1/2 , thus demonstrating again that low magnetic Reynolds’ number, a low Hall parameter and a mean-free path less than the collisionless skin depth occurs in the corona close to the wire core. This last condition is a criterion for the onset of nonlinear heat-flow driven electrothermal instabilities [214]. These dimensionless parameters are discussed further in [315]. A rising total current during the precursor phase and a low R m ensures a skin current and a very small axial electric field in the flowing precursor, which in effect becomes a super- Alfvénic flow e.m. accelerator. Resler and Sears [356] considered various regimes for steady 1D resistive MHD flow, and this was extended by Haines and Thompson [357] for a spatially varying and self consistent magnetic field, finding exact integrals for the flow. In a related model of steady cylindrical 1D precursor flow Chittenden et al [358] have compared a steadystate analytic model with 2D r–θ simulations of precursor flow. Figure 56 is a 2D simulation of plasma ablation from one of 32 wires in an array, showing a concentration of current density on the outside of the wire core and the precursor jets flowing towards the axis (on the left of the diagram). The simulations [359] tend to show far more current in the precursor plasma than is implied by experiments, especially by the lack of m = 1 instabilities, but more data are required. Garasi et al [360] found that in 2D simulations in the r–θ plane the mass ablation rate was overestimated by factors of 10–100, and advects 5× current to the axis in the precursor. Their 3D modelling was closer to experiment. A 1D Cartesian steady-state analytic ablation model by Sasorov et al [361] compares thermal and radiation transport. A transition from subsonic to supersonic flow is claimed in the absence of areal change in the flow, in contrast to [356, 357]. But in addition in a plasma flowing sonically against the heat flow the latter should be nonlinear as discussed later. In contrast to steady models, it can be shown that for a rising current of the form in equation (4.16) and writing γ = I/I ˙ and a magnetic field of the form exp(γ t − kx) in a plasma of conductivity σ and ablation velocity V a , k is given by k =−µ 0 σV a /2+[(µ 0 σV a /2) 2 + µ 0 σγ] 1/2 . (5.3) 81
Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review Figure 56. Contour plots of ln ρ, T e , j z and pressure ρ at 130 ns from a 2D simulation of 1 of 32 × 15 µm Al wires in an array on MAGPIE. Reprinted with permission from [358]. Copyright 2004, American Institute of Physics. For typical precursor plasma conditions, V a ∼ 10 5 ms −1 , σ ∼ 2.5 × 10 5 , the value of k −1 is not sensitive to the value of σ or V a but gives 1.3 mm to 5 mm for γ = (8–2) × 10 7 s −1 . Thus the effective skin depth for fast rising currents appears to dominate even though γ ≪ µ 0 σVa 2/4. If the wires are preheated Beg et al [362] has shown that using a linear ramp current 500 ns long of 1 kA per wire a low density precursor plasma column (n e ∼ 2 × 10 17 cm −3 ) is formed on the array axis before the start of the main current. After the main current pulse the soft x-ray emission shows the growth of an m = 1 helical instability; without a prepulse current the precursor plasma shows no instability. The x-ray pulse at stagnation on axis is at least 30 times smaller. Similar results of onset of a helical instability and reduced x-ray power was found by Lebedev et al [363] in an experiment in which additional current could be diverted into the precursor column on axis. Recent studies by Sarkisov suggest that there is an optimum prepulse condition on current, and also a polarity issue [364]. This is developed further in section 6.4 where improvements in long pulse performance is reported. In [363] there is a study of how the ablation velocity V a varies with gap/core size, x. The mean core size was measured by x-ray radiography as 250 µm approximately when the final implosion begins. The experimental results shown in figure 57 are compared with the 82
Page 1 and 2:
Home Search Collections Journals Ab
Page 3 and 4:
Plasma Phys. Control. Fusion 53 (20
Page 5 and 6:
Page 7 and 8:
Page 9 and 10:
Page 11 and 12:
Page 13 and 14:
Page 15 and 16:
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Page 31 and 32: Plasma Phys. Control. Fusion 53 (20
Page 81: Plasma Phys. Control. Fusion 53 (20
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169:
show all

A review of the dense Z-pinch

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?