Wall Heating and Impurity Mixing Considerations During Magnetic Compression Experiments

We present an analytic treatment of the transport of magnetic field into a metallic material, when the surface field is changing in time. This has many applications in the area of high-current pulsed power. We focus on one of these in this paper, magnetized target fusion (MTF), a simple, potentially inexpensive method of creating burning fusion conditions through fast compression of dense, warm magnetized plasma. Magnetization of the plasma electrons, needed to inhibit thermal transport losses, means that compression, on the order of 10 microseconds (10^-5 seconds), results in large magnetic field compression. Current density, J, proportional to the field gradient in the walls, is also found analytically. Heating in the wall is also a function of etaJ², and so can also be evaluated with these solutions. MTF studies proposed to be conducted at the ATLAS pulsed-power facility (23 MJ, 30 MA, 240 kV), must explicitly determine energy dissipation in the wall. Vaporization, or possibly even melting, of metallic wall material could lead to mixing of such high-Z material with the hot hydrogen plasma. The ensuing radiation losses and plasma cooling would be catastrophic to any MTF scheme.