Energy and charge conserving semi-implicit particle-in-cell model for simulations of high-pressure plasmas in magnetic traps

Abstract

The paper presents a new particle-in-cell model for fully kinetic simulations of plasma confinement regimes with high relative pressure. These regimes are considered as the most promising ones for fusion reactor proposals based on field reversed configurations, mirror and multi-cusp magnetic traps. Formation of an equilibrium high-pressure plasma with a fully excluded or reversed magnetic field cannot be investigated using the simplified magnetohydrodynamic and gyrokinetic approaches. A correct description of the electron dynamics under close proximity of zero and strong magnetic field regions can only be achieved within the framework of the kinetic theory that can be implemented most efficiently by the particle-in-cell method. The full-scale particle-in-cell simulations of modern fusion experiments require the use of finite-difference schemes in which temporal steps exceed the period of fastest electron oscillations at the plasma or even cyclotron frequencies and spatial steps do not have to resolve the Debye radius. This requirement is satisfied by implicit schemes capable of conserving the total energy of the system. The particle-in-cell model presented in this paper is based on the energy conserving semi-implicit approach as a predictive step and a new method for suppressing the electrostatic noise inherent in it as a corrective step. This two-step algorithm provides not only accurate energy conservation, but also the exact local fulfillment of the Gauss law.