Investigation of multiple roots of the resistive wall mode dispersion relation, including kinetic effects

The resistive wall mode instability in tokamak plasmas has a complex frequency which can be determined by a dispersion relation that is cubic, in general, leading to three distinct roots. A simplified model of the dispersion relation, including kinetic effects, is presented and used to explore the behavior of these roots. By changing the plasma rotation frequency, it is shown that one root has a slow mode rotation frequency (less than the inverse wall time) while the other two rotate more quickly, one leading and one lagging the plasma rotation frequency. When realistic experimental parameters from the National Spherical Torus Experiment M. Ono, Nucl. Fusion 40, 557 (2000) are used, however, only one slow rotating, near-marginal stability root is found, consistent with present experiments and more detailed calculations with the MISK code B. Hu, Phys. Plasmas 12, 057301 (2005). Electron collisionality acts to stabilize one of the rotating roots, while ion collisionality can stabilize the other. In devices with low rotation and low collisionality, these two rotating roots may manifest themselves, but they are likely to remain stable.