Collision operators for partially linearized particle simulation codes

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Abstract
Algorithms are presented for energy- and momentum-conserving like-particle Coulomb collisions in partially linearized (δf) particle simulations. They are developed and implemented in particular for gyrokinetic simulation models of a strongly magnetized plasma. The collision operators include both drag and diffusion terms, are not restricted to a single or few Fourier modes, and approximately conserve both momentum and energy locally in space in a statistical sense. The first algorithm is a many-mode generalization of a test-particle–plus–source algorithm previously proposed. The second is easier to implement and improves upon the first significantly by not requiring many time steps for good conservation. Implementations for the case for ion-ion collisions are given and conservation properties are demonstrated, both directly with non-self-consistent test simulation runs and indirectly with self-consistent runs. The computational cost of particle pushing and solving for fields depends on the relative collisionality and can result in a tripling of the total computational costs if collisions are done at each time step, but typically will be a small fraction of the total simulation cost. It is also shown that binary-collision-based algorithms are unsuitable for partially linearized simulations.