Theory of the Magnetic Shock Tube with Varying Driving Magnetic Field

Abstract

The inviscid flow of an ionized gas with infinite conductivity in a magnetic shock tube is treated when the driving magnetic field is very strong and varies with time, being induced by the current discharge from capacitors. Two cases are treated; one is the one-dimensional flow with a planar current sheet perpendicular to the flow, and the other is the cylindrically expanding flow with a cylindrical current sheet. The problem is analogous to the hypersonic flow past a slender body, and similarity solutions exist if the driving magnetic field varies proportionally to t^k−1 (t is the time). Numerical results for several values of k are presented. For a general case when the magnetic field varies as an arbitrary function of time, an approximate method of calculation by using the concept of local similarity is also presented.