A numerical method for the solution of the magnetic convection-diffusion equation for high magnetic Reynolds numbers

In plasma technological applications with high electrical conductivity, magnetic convection can become comparable to or even exceed magnetic diffusion. The physical formulation, derived from the Maxwell equations and Ohm's law, yields the convection-diffusion equation of the magnetic flux density. For high magnetic Reynolds numbers, the first order space derivatives dominate over the second order derivatives. Under these circumstances, special attention must be paid to the numerical solution of the problem. A numerical method based on a finite element formulation for the solution of the magnetic convection-diffusion equation has been developed. The method proposed utilizes an upwinding technique as in the finite difference methods mentioned above. A first order set of shape functions has been utilized to approximate the unknown function. In applying the weighted residual method, a second order weighting function has been adopted. An optimal value of the convexity of the weighting function is chosen to obtain an oscillation free solution with a good accuracy. The method has been utilized to solve the electrodynamics of a discharge in SF/sub 6/ at a pressure of 10 MPa and a current of 2 kA.