Numerical calculation of the runaway electron distribution function and associated synchrotron emission

TL;DR

This paper presents a fast numerical framework for calculating runaway electron distribution functions and their synchrotron emission in tokamaks, incorporating primary and secondary generation, with applications in plasma diagnostics.

Contribution

The paper introduces an efficient continuum numerical method for solving the relativistic Fokker-Planck equation with an electric field, including primary and secondary runaway generation, and computes associated synchrotron spectra.

Findings

Numerical verification of an analytic model for secondary runaway distribution.

Realistic distribution functions produce synchrotron spectra not well approximated by single-electron emission.

The framework enables rapid simulation of runaway electron behavior for plasma diagnostics.

Abstract

Synchrotron emission from runaway electrons may be used to diagnose plasma conditions during a tokamak disruption, but solving this inverse problem requires rapid simulation of the electron distribution function and associated synchrotron emission as a function of plasma parameters. Here we detail a framework for this forward calculation, beginning with an efficient numerical method for solving the Fokker-Planck equation in the presence of an electric field of arbitrary strength. The approach is continuum (Eulerian), and we employ a relativistic collision operator, valid for arbitrary energies. Both primary and secondary runaway electron generation are included. For cases in which primary generation dominates, a time-independent formulation of the problem is described, requiring only the solution of a single sparse linear system. In the limit of dominant secondary generation, we present the first numerical verification of an analytic model for the distribution function. The numerical electron distribution function in the presence of both primary and secondary generation is then used for calculating the synchrotron emission spectrum of the runaways. It is found that the average synchrotron spectra emitted from realistic distribution functions are not well approximated by the emission of a single electron at the maximum energy.