Monte Carlo Simulation of Nonequilibrium Conductivity Produced by Electron Beam in MHD Flows

Abstract

Fast Monte Carlo code is developed for calculation of the spatial distribution of the energy deposited be e-beam in a substance and the conductivity in the MHD flow sustained by e-beam. The self-consistent approach using the iteration procedure is realized for simulation of the MHD flows with the non-equilibrium conductivity sustained by e-beam. The MHD flows over the plate and the wedge have been calculated and analyzed under different conditions. I. Introduction The MHD influence on the ionized flow causes both the energy and the force action on the flow. Thus the MHD technique seems to be a more flexible method of a flow control in comparison with the plasma technique. In many cases of potential applications of the MHD flow control the equilibrium conductivity of the flow is negligible to produce considerable MHD effect. In order to realize significant level of MHD influence on the flow it is necessary to deposit energy into the flow for creation of the nonequilibrium conductivity. The Lorentz force action in the MHD flow coexists with the Joule heat action, moreover the energy which is deposited into the flow for creation of the flow conductivity also influences on the flow as additional heat release. So in real conditions the positive effect of the Lorentz force may be veiled by the flow heating. The most reasonable approach which allows us to minimize the veiling action of the flow heating is using the means for creation of the flow conductivity characterizing by a minimal power spent on the flow ionization. Now it is universally recognized that e-beam is such type of a flow ionizer. That is why the electron beam is widely considered as the flow ionizer in MHD flow control applications 1,2 . Electrons in an e-beam propagating in a flow participate in elastic and inelastic collisions with molecules of the flow. These collisions lead to changing the energy and the moving direction of electrons. More reliable method for adequate description of the e-beam propagation in a matter is the Monte Carlo method, which allows one to take into account all the processes which influence on the motion of electrons. In paper 3 it is shown that for correct description of the e-beam propagation through the MHD flow the self-consistent character of the processes in the MHD flow should be taken into account. Namely: 1) The electron beam propagating in a flow creates and sustains a conductivity in a local region of the flow; 2) MHD interaction on the locally ionized flow leads to modification of the flow parameters; 3) Propagation of e-beam in a flow depends on the flow parameters, thus modification of the flow parameters leads to modification of the spatial distribution of the conductivity in the flow. This self-consistent character of the MHD interaction with the flow imposes heavy demands on the Monte Carlo code to be used in the modeling the MHD flow with e-beam ionization. The Monte Carlo code should provide a required precision of calculations and should be very fast. Thus reasonable simplifications of physical description of e-beam propagation in MHD flows must be done to create fast but precise Monte Carlo code. II. Fast Monte Carlo Code for Calculation of E-Beam Energy deposition in matter