Stabilization of plasma flow in a transverse magnetic field

Abstract

Results are given of a theoretical and experimental investigation of the intensive interaction between a plasma flow and a transverse magnetic field. The calculation is made for problems formulated so as to approximate the conditions realized experimentally. The experiment is carried out in a magneto-hydrodynamic (MHD) channel with segmented electrodes (altogether, a total of 10 pairs of electrodes). The electrode length in the direction of the flow is 1 cm, and the interelectrode gap is 0.5 cm. The leading edge of the first electrode pair is at x = 0. The region of interaction (the region of flow) for 10 pairs of electrodes is of length 14.5 cm. An intense shock wave S propagates through argon with an initial temperature To = 293 °K and pressure po = 10 mm Hg. The front S moves with constant velocity in the region x < 0 and at time t = 0 is at x = 0. The flow parameters behind the incident shock wave are determined from conservation laws at its front in terms of the gas parameters preceding the wave and the wave velocity WS. The parameters of the flow entering the interaction region are as follows: temperature T01 = 10,000 °K, pressure P01 = 1.5 atm, conduction σ01 = 3000 Ω−1·m−1, velocity of flow u01 = 3000 m·sec−1, velocity of sounda01 = 1600 m·sec−1, degree of ionization α = 2%, ∼ 0.4. The induction of the transverse magnetic field B = [0, By(x), 0] is determined only by the external source. Induced magnetic fields are neglected, since the magnetic Reynolds number Rem ∼ 0.1. It is assumed that the current j = (0, 0, jz) induced in the plasma is removed using the segmented-electrode system of resistance Re. The internal plasma resistance is Ri = h(σA)−1 (h = 7.2 cm is the channel height; A = 7 cm2 is the electrode surface area). From the investigation of the intensive interaction between the plasma flow and the transverse magnetic field in [1–6] it is possible to establish the place x* and time t* of formation of the shock discontinuity formed by the action of ponderomotive forces (the retardation wave RT), its velocity WT, and also the changes in its shape in the course of its formation. Two methods are used for the calculation. The characteristic method is used when there are no discontinuities in the flow. When a shock wave RT is formed, a system of nonsteady one-dimensional equations of magnetohydrodynamics describing the interaction between the ionized gas and the magnetic field is solved numerically using an implicit homogeneous conservative difference scheme for the continuous calculation of shock waves with artificial viscosity [2].