A fully implicit, scalable, conservative nonlinear relativistic Fokker-Planck 0D-2P solver for runaway electron

Abstract

Upon application of a sufficiently strong electric field, electrons break away from thermal equilibrium and approach relativistic speeds. These highly energetic runaway electrons (MeV) play a significant role in tokamak disruption physics, and therefore their accurate understanding is essential to develop reliable mitigation strategies. For this purpose, we have developed a fully implicit solver for the 0D-2P (i.e., including two momenta coordinates) relativistic nonlinear Fokker-Planck equation (rFP). As in earlier implicit rFP studies (NORSE, CQL3D), electron-ion interactions are modeled using the Lorentz operator, and synchrotron damping using the Abraham-Lorentz-Dirac reaction term. However, our implementation improves on these earlier studies by 1) ensuring exact conservation properties for electron collisions, 2) strictly preserving positivity, and 3) being scalable algorithmically and in parallel. Key to our proposed approach is an efficient multigrid preconditioner for the linearized rFP equation, a multigrid elliptic solver for the Braams-Karney potentials [Braams and Karney, Phys. Rev. Lett. 59, 16 (1987)], and a novel adaptive technique to determine the associated boundary values. We verify the accuracy and efficiency of the proposed scheme with numerical results ranging from small electric-field electrical conductivity measurements to the accurate reproduction of runaway tail dynamics when strong electric fields are applied.

arXiv comment27 pages, 21 figures

References in corpus (6)

• Conductivity of a Relativistic Plasma
• Differential Form of the Collision Integral for a Relativistic Plasma
• NORSE: A solver for the relativistic non-linear Fokker-Planck equation for electrons in a homogeneous plasma
• Positivity-preserving scheme for two-dimensional advection-diffusion equations including mixed derivatives
• Structure-preserving strategy for conservative simulation of relativistic nonlinear Landau--Fokker--Planck equation
• Conservative finite-element method for the relativistic Coulomb collision operator

Cited by in corpus (4)

• DREAM: a fluid-kinetic framework for tokamak disruption runaway electron simulations
• Structure-preserving marker-particle discretizations of Coulomb collisions for particle-in-cell codes
• Multispecies structure-preserving particle discretization of the Landau collision operator
• An asymptotic-preserving 2D-2P relativistic Drift-Kinetic-Equation solver for runaway electron simulations in axisymmetric tokamaks