Electromagnetic Field and Current Waves in a Conductor Compressed by a Shock Wave in a Magnetic Field

Abstract

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 R₁ = µ₀σ₁D²t and that in the compressed region by the parameter R₂ = µ₀σ₂(D—U)²t (σ₁ and σ₂ are the electric conductivities of the uncompressed and compressed substance, respectively, µ₀ 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.