Magnetohydrodynamic Flow in a Shock Tube

The effect of a transverse magnetic field on the motion of a perfectly conducting fluid in a shock tube is examined. A generalized form of the Riemann invariant for the continuous motion of such a fluid is combined with the conservation equations for a magnetohydrodynamic shock to obtain an exact description of the fluid motion in a shock tube in terms of arbitrary initial conditions. The fluids are assumed to have constant specific heat ratios. Qualitatively, the effect of the magnetic field is equivalent to that of a pressure, but quantitatively the effect is always greater than merely the hydrodynamic pressure equivalent of the appropriate Maxwell stress. A magnetic field in the high-pressure region alone can produce shocks having Mach numbers for typical laboratory conditions, of the order of hundreds, and in general is in agreement with available experimental results. A magnetic field in the low-pressure region results in weaker, but higher velocity shocks.