Effect of partially ionized impurities and radiation on the effective critical electric field for runaway generation

TL;DR

This paper derives a new formula for the effective critical electric field for runaway electrons in tokamaks, considering impurities and radiation, showing it is significantly higher than classical estimates and impacts mitigation strategies.

Contribution

It introduces a comprehensive formula for the effective critical electric field accounting for impurities and radiation, improving understanding of runaway electron dynamics.

Findings

Effective critical field is much larger than classical estimates.

Runaway current decay is linear and proportional to the effective critical field.

Impurity injection efficacy for runaway mitigation is enhanced.

Abstract

We derive a formula for the effective critical electric field for runaway generation and decay that accounts for the presence of partially ionized impurities in combination with synchrotron and bremsstrahlung radiation losses. We show that the effective critical field is drastically larger than the classical Connor-Hastie field, and even exceeds the value obtained by replacing the free electron density by the total electron density (including both free and bound electrons). Using a kinetic equation solver with an inductive electric field, we show that the runaway current decay after an impurity injection is expected to be linear in time and proportional to the effective critical electric field in highly inductive tokamak devices. This is relevant for the efficacy of mitigation strategies for runaway electrons since it reduces the required amount of injected impurities to achieve a certain current decay rate.