Diffusion of a megagauss field into a metal

Abstract

The plane one-dimensional problem of the diffusion of a megagauss field into a metal wall is solved taking into account heat conduction and radiation transfer. At the interface, the magnetic field is assumed to be constant, and in this sense, the problem is close to the self-similar diffusion problem with parameters dependent on the self-similar variable x/ √ t. It is shown that if heat conduction and radiation transfer are taken into account, in megagauss fields (in the examined formulation for fields B > 1.6 MGs) there is no loss of conductivity of the material evaporated by the magnetic field because of the formation of a plasma layer at the interface with a temperature in the electronvolt range. However, the role of the plasma layer in the structure of the skin layer remains insignificant up to fields B ≈ 10 MGs.

Fast penetration of megagauss fields into metallic conductors

“…Hence, at sufficiently large x the deviation of Q from 1 is small whereby the decay of the magnetic field H is governed by a linear diffusion equation; the latter implies a gradual attenuation of H such that H > 0 (and Q > 1) for all x > 0. Contrasting this observation with the singular nature of the leading order terms H 0 and Q -1 leads to the conclusion that the expansions (30) are not uniformly valid for all s > 0. Specifically, they breakdown at a finite value of s, say s f ðtÞ ¼ h Àc=2 x f ðtÞ, where Q -1 , and H 0 , vanish.…”

“…This value corresponds to %2.5 MG for copper; incidentally, this is on the order of the field strengths at which a plasma layer begins to form at the surface. 30 Note that we have arbitrarily chosen the position of the current-density maximum to represent the "exact" wave front. However, the Oðd à h Àc=2 Þ-thickness of the wave-front region decays in the limit h ) 1, hence the leading-order formula (5) is just as well asymptotic to any other equally legitimate "skin-depth" definition 1 associated with this region.…”

“…The question is, then, what is the overall effect of the plasma layer on the penetration process? This question has been addressed by Garanin et al 30 by numerically solving a detailed model of the penetration of a megagauss field into a copper half-space. Their simulations account for hydrodynamics, radiation losses, and the detailed material properties of copper at each phase.…”

“…9,12,13,22 Complementary to such heavy-duty computations, tractable model problems which aim to capture the essential peculiarities of nonlinear magnetic diffusion, and to approximately predict field penetration rates, temperatures, and pressures, have been formulated and studied. 1, [23][24][25][26][27][28][29][30][31][32][33][34] The majority of these models hinge upon the understanding that, excluding ultra-high field magnitudes (տ10 MG), field-penetration rate is dominantly determined by a thermo-magnetic coupling via the strong dependence of electrical conductivity on temperature. Prior to evaporation, and ignoring compression effects [see Sec.…”

“…Prior to evaporation, and ignoring compression effects [see Sec. IV C], this dependence is often modelled as 12,23,26,27,30 …”