An asymptotic-preserving 2D-2P relativistic Drift-Kinetic-Equation solver for runaway electron simulations in axisymmetric tokamaks

Abstract

We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated by analysis of the dominant numerical errors, as well as by numerical experiments. We demonstrate the ability of the algorithm to provide accurate answers regardless of plasma collisionality on a circular axisymmetric tokamak geometry.

References in corpus (6)

• Numerical calculation of the runaway electron distribution function and associated synchrotron emission
• Effect of partially ionized impurities and radiation on the effective critical electric field for runaway generation
• Asymptotic preserving schemes for highly oscillatory kinetic equation
• 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
• A fully implicit, scalable, conservative nonlinear relativistic Fokker-Planck 0D-2P solver for runaway electron