Shear Alfvén waves with Landau and collisional effects

Shear Alfvén waves can be driven unstable by hot particles such as alpha particles in an ignited fusion device or hot ions in existing devices. Motivated by rather collisional Wendelstein 7 Advanced Stellarator (W7-AS) [Phys. Rev. Lett. 72, 1220 (1994)] beam-driven global Alfvén instability experiments, the effect of electron and ion collisions on these modes has been examined. Collisions broaden and suppress the peak associated with Landau effects. This broadening makes ion damping more important, while the electron damping is suppressed. Additional resistive effects provide increased damping for the main part of the spectrum, which can have a rather high phase velocity. Of more general interest is the fact that collisional and collisionless resistivity has a numerically stabilizing effect that is known to be important for nonlinear resistive magnetohydrodynamics (MHD). This can preclude the need for introducing and testing the sensitivity to similar ad hoc effects. Numerical and analytic results for both a particle-conserving Krook collision operator and a Lorentz (pitch angle) collision operator are compared and contrasted.