Universal mode with diffusive electrons: Linear instability and nonlinear saturation

Abstract

The effect of spatial electron diffusion on the stability properties of the universal drift mode in a sheared magnetic field are studied using an initial value code, TEDIT. In previous studies of this problem Hirshman and Molvig relied on an approximation to the electron resonance function equivalent to making a Krook approximation for the spatial diffusion operator, D ∂2/∂x2. The present work treats the diffusion operator precisely and also allows the treatment of a realistic parallel velocity dependence of the diffusion coefficient, D=D(v∥). For the case of a velocity-independent diffusion coefficient, the qualitative features found by Hirshman and Molvig are observed. The modes with kyρi>1 destabilize at small values of the diffusion coefficient and saturate at higher values, corresponding to several orders of magnitude in D. There are quantitive discrepancies with the previous work that, near the saturation point, can be accounted for reasonably well by a simple asymptotic theory. However, when the code uses a more realistic form, D=D0 (ve/‖v∥‖) exp(−v2c/v2∥)+Dc, where Dc corresponds to the (small) collisional diffusion, and D0 parametrizes the turbulence level, then a quantitative difference is observed. Instability persists down to zero turbulence levels, D0=0. This is essentially linear instability due to collisional diffusion alone.