Electromagnetic field and current waves in a conductor compressed by a shock wave in a magnetic field

A physically correct and mathematically rigorous solution of the problem on the structure of an electromagnetic field formed when a shock wave enters a conducting half–space in a transverse magnetic field is obtained. It is shown that only physically grounded boundary conditions lead to a noncontrovercial pattern of the electromagnetic field and a system of currents in a conductor. The main parameters and characteristic times are found, which determine the structure of current waves in a metal. The solution in the uncompressed region is determined by the parameter $R_1 = \mu_0\sigma_1 D^2t$ and that in the compressed region by the parameter $R_2 = \mu_0\sigma_2(D-U)^2t$ ($\sigma_1$ and $\sigma_2$ are the electric conductivities of the uncompressed and compressed substance, respectively, $\mu_0$ is the magnetic permeability of vacuum, $D$ is the wave–front velocity, $U$ is the mass velocity, and $t$ is the time). The parameter for the compressed substance $R_2$ coincides with the parameter obtained previously for the shock–wave dielectric–metal transition; the governing parameter for the uncompressed substance $R_1$ is obtained for the first time. The asymptotic solutions of the problem for small and large times and the special case $R_1=R_2$ considered help in understanding the physical meaning of the solution found.