Collisional $δf$ method

A general method for including various collisional effects, such as the drag and diffusion of test particles due to background plasmas, the effect of particle source and sink, and the like-particle Coloumb collisions, is presented. The marker density $g$ is generally unknown along the particle trajectory, and its evaluation depends on the way particles are initially loaded and new particles are injected into the simulation. The method is demonstrated for the problem of the nonlinear evolution of the toroidicity induced Alfvén eigenmode, driven by energetic α particles. The saturation amplitude is found to scale with the collision rate in a way as predicted by theory.