Dielectric linear response of magnetized electrons: Drag force on ions

The drag force on ions moving in a magnetized electron plasma is calculated in dielectric linear response. Various representations of the dielectric function ε(k, ω) are investigated for their suitability to display the limits for an infinite and a vanishing magnetic field. While the influence of the magnetic field is negligible in certain regions of k-space, it introduces in other regions a strong oscillatory structure in the dielectric function. This requires a careful treatment of the multidimensional integrations necessary for the drag force. The contributions from oscillatory integrands are treated by the saddle point method. Explicit results are obtained for the dependence of the drag force on the magnetic field, the direction of motion of the ion relative to the magnetic field, the shielding in the electron plasma, its density and the anisotropy of the electron temperature. The importance of the collective response of the electrons is investigated for limiting cases of the magnetic field. The validity of the linearization of the dielectric theory is checked by comparison with results obtained by numerical simulation of the nonlinear Vlasov-Poisson equation. For strong magnetic fields and low ion velocities, the simulations rather agree with the complementary binary collision model than with linear response.