Brief description

There are basically 2 versions of the collision operator: a linear and a non linear version. Each version can be used either by taking into account only intraspecies collisions or by considering all collisions consistently.

The collision operators are derived by using a truncated moment expansion of the distribution function to compute Rosenbluth potentials. In practice, 4 moments are kept, corresponding to the density, the parallel velocity, the temperature and the parallel heat flux. Numerically, the moments are computed in spatial bins.

This leads to a collision operator in the form of a Fokker-Planck operator which is equivalent to a Langevin equation which can be efficiently implemented in a PIC code. Note that if one keeps only the first moment in the truncated moment expansion of the distribution function to compute Rosenbluth potentials, the procedure leads to the derivation of the test-particle part of the linear collision operator.

A second part of the collision operator is added to ensure conservation of density, total momentum and total energy (over species). This procedure, inspired from a work of Lin in the context of linear collsions, allows a conservation up to machine precision in each spatial domain.

Noise control adapted to collisions

Usually a modified Krook operator is used in ORB5 for noise control. The problem is that the typical frequency of this Krook operator is in the range of the collision frequency. Therefore this Krook operator is in direct competition with the collision operator and leads to an unphysical deformation of the distribution function.

Another noise control scheme adapted to the presence of collisions has therefore be implemented. It is called "quadtree" method in ORB5 jargon. The procedure is performed in two main steps. The one consists in creating chunks of neighbouring markers (typically 10) using a quadtree procedure. The second step, performed in each chunk, consists in taking groups of 4 markers on reduce the weight dispersion while maintening the conservation of density, parallel momentum and energy. This noise control can be used in all types of simulations.