Am. Dimits et Bi. Cohen, COLLISION OPERATORS FOR PARTIALLY LINEARIZED PARTICLE SIMULATION CODES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 49(1), 1994, pp. 709-721
Algorithms are presented for energy- and momentum-conserving like-part
icle Coulomb collisions in partially linearized (delta f) particle sim
ulations. They are developed and implemented in particular for gyrokin
etic 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 moment
um and energy locally in space in a statistical sense. The first algor
ithm is a many-mode generalization of a test-particle-plus-source algo
rithm previously proposed. The second is easier to implement and impro
ves 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 sel
f-consistent runs. The computational cost of particle pushing and solv
ing for fields depends on the relative collisionality and can result i
n a tripling of the total computational costs if collisions are done a
t each time step, but typically will be a small fraction of the total
simulation cost. It is also shown that binary-collision-based algorith
ms are unsuitable for partially linearized simulations.