Relativistic limitations on runaway electrons

Abstract

The non-relativistic theory of a plasma in an electric field E predicts that there will always be runaway electrons, although their number will be exponentially small for fields less than the Dreicer field ED. However, when E/ED ∼ kT/mec2, the ratio of the electron thermal energy to the rest mass energy, relativistic effects become important. After comparing earlier non-relativistic calculations we extend the approach of Kruskal and Bernstein to take account of relativistic effects and also to investigate the influence of impurities. It is found that below the critical electric field ER = ED (kT/mec2) absolutely no runaways are generated. In addition, the number of runaway electrons produced by electric fields in excess of ER is calculated and we find significant modifications to the non-relativistic estimates when (ED/E)2 (kT/mec2) > 1.

Efficiency of current drive by fast waves

“…The electron-electron collision term then drops out (from momentum conservation) and the electron-ion term is proportional to the numerator in Eq. (21).…”

First dedicated observations of runaway electrons in the COMPASS tokamak

“…This is the reason why there are REs in real tokamaks even if the strength of the electric fi eld never reaches the Dreicer value. A non-relativistic analysis was taken for the calculation of the Dreicer fi eld, but if relativistic effects are taken into account then a different expression for the critical (threshold) electric fi eld E C = {(n e e 3 ln)/(4 0 2 c 2 )} is obtained [6]. The critical electric fi eld E C represents the lower limit for the RE generation.…”

The effect of ITER-like wall on runaway electron generation in JET

“…Runaway electrons in cooling plasmas can be generated by various mechanisms: Dreicer generation [13], hot tail generation [14] and runaway avalanching [15]. The time evolution of the current density profile is determined by the runaway electron generation and the diffusion of the electric field governed by the parallel component of the induction equation…”