Meanwhile, as the ion collision rate increases, the GAM frequency decreases from the collisionless value, \sqrt while externally introducing the Krook type collision model in the one-dimensional electrostatic PIC simulation. The results from the Krook operator with both number and energy conservation terms, the Lorentz operator with an energy-dependent collision rate and the full Hirshman-Sigmar-Clarke collision operator are very close.

The collision damping is much overestimated with the number-conserving-only Krook operator on the other hand, using the Lorentz operator with a constant collision rate, the damping is overestimated at low collision rate but underestimated at high collision rate. Different collision operators do not change the overall trend but influence the magnitude of the damping rate. As the ion collision rate increases, the damping rate increases at low collision rate but decays at high ion collision rate. The collisional damping rate and real frequency of the geodesic acoustic mode (GAM) are solved from a drift kinetic model with different collision operators.

Comparison of collision operators for the geodesic acoustic mode

Moho pro 12 particles crash