Nonuniform Expansion of a Piston Into an Ionized Medium with a Weak Magnetic Field

Abstract

The nonuniform expansion of a rigid, perfectly conducting piston into an infinitely conducting fluid wherein there exists a weak uniform magnetic field is considered. A solution for the state of the plasma and the magnetic field between the piston and the magnetohydrodynamic shock is obtained by a small perturbation method; the dependent variables are expressed in double expansions about a zero order (hydrodynamic) solution. The solution is valid for pistons (either cylindrical or spherical) whose expansion velocity is expressible by a small perturbation on a constant velocity. The development includes second order terms; however, numerical results are restricted to first order. Within the first order perturbation, it is shown that the fluid dynamic analysis is uncoupled from the magnetic field, and the shock shape retains its cylindrical or spherical symmetry. Calculations are carried out for a spherical piston, for several values of γ (specific heat ratio), and a∞/v0 where a∞ is the ambient speed of sound and v0 is the uniform piston velocity. The results show that the shock velocity is nearly insensitive to changes in the piston velocity.