Adjoint Fokker-Planck equation and runaway electron dynamics

TL;DR

This paper applies the adjoint Fokker-Planck equation to analyze runaway electron behavior, providing efficient computation of runaway probability and slowing-down time, revealing slow decay rates near the critical electric field and contributing to understanding hysteresis effects.

Contribution

It introduces an adjoint Fokker-Planck approach for runaway electron analysis, offering improved efficiency and new insights into decay rates and hysteresis phenomena.

Findings

Runaway probability function is smooth across the separatrix.

Adjoint method is more efficient than Monte Carlo for the same accuracy.

High-energy electron decay rate is very slow near the critical electric field.

Abstract

The adjoint Fokker-Planck equation method is applied to study the runaway probability function and the expected slowing-down time for highly relativistic runaway electrons, including the loss of energy due to synchrotron radiation. In direct correspondence to Monte Carlo simulation methods, the runaway probability function has a smooth transition across the runaway separatrix, which can be attributed to effect of the pitch angle scattering term in the kinetic equation. However, for the same numerical accuracy, the adjoint method is more efficient than the Monte Carlo method. The expected slowing-down time gives a novel method to estimate the runaway current decay time in experiments. A new result from this work is that the decay rate of high energyelectrons is very slow when E is close to the critical electric field. This effect contributes further to a hysteresis previously found in the runaway electron population.