Collisional ballooning mode dispersion relation in the banana regime

Collisional ballooning mode theory in the banana regime is developed for tokamak configurations from the gyrokinetic formalism. A general dispersion relation is obtained, which in principle can deal with a collision operator of any type. However, investigation of an approximate Fokker--Planck collision operator developed in recent neoclassical transport theory is detailed. The most significant feature of the present theory as compared to the customary treatment lies in that the distinction between particle and fluid velocities is made in the ordering analyses. This reveals that the eigenfrequency of modes is determined by balancing the small-parallel-ion-velocity (SPIV) effect [L.-J. Zheng and M. Tessarotto, Phys. Plasmas 1, 3928 (1994)], instead of the fluid inertia one, with the instability drives. Since the parallel-electric-field effect is found to be negligible as compared to the SPIV effect, in contrast to the customary resistive ballooning mode picture, the leading collisional effect is demonstrated to be the modification of the SPIV effect instead of the relaxation of the frozen-in-law. The ion--ion collisions are the cause for this modification, while the electron collisional effect is shown to be negligible. copyright 1995 American Institute of Physics