Gyrokinetic Fokker-Planck Collision Operator

The gyrokinetic linearized exact Fokker-Planck collision operator is obtained in a form suitable for plasma gyrokinetic equations, for arbitrary mass ratio. The linearized Fokker-Planck operator includes both the test-particle and field-particle contributions, and automatically conserves particles, momentum, and energy, while ensuring non-negative entropy production. Finite gyroradius effects in both field-particle and test-particle terms are evaluated. When implemented in gyrokinetic simulations, these effects can be precomputed. The field-particle operator at each time step requires the evaluation of a single two-dimensional integral, and is not only more accurate, but appears to be less expensive to evaluate than conserving model operators.

Figure 1

Typical wave number dependence of gyrophase integral $I/I_0$ for self-collisions. Here $v^{\prime }=1$, ${\xi }^{\prime }=0$, $v=0.5$, $\xi =1$ (solid line), $\xi =0.8$ (dashed line), $\xi =0.5$ (dash-dotted line).