Metriplectic particle-in-cell integrators for the Landau collision operator
This provides a structure-preserving discretization for the Landau collision operator in plasma physics, enabling accurate long-time simulations.
The authors developed a new particle-in-cell framework for the nonlinear Landau collision operator that conserves density, momentum, and energy while ensuring entropy production. The method is fully compatible with existing Vlasov-Maxwell integrators.
In this paper, we present a new framework for addressing the nonlinear Landau collision operator in terms of particle-in-cell methods. We employ the underlying metriplectic structure of the collision operator and, using a macro particle discretization for the distribution function, we transform the infinite-dimensional system into a finite-dimensional time-continuous metriplectic system for advancing the macro particle weights. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of density, momentum, and energy, as well as the positive semi-definite production of entropy in both the time-continuous and the fully discrete system is demonstrated algebraically. The new algorithm is fully compatible with the existing particle-in-cell Poisson integrators for the Vlasov-Maxwell system.