Velocity-space structure of runaway electrons

Abstract

The region of velocity space is determined in which electron runaway occurs because of a dc electric field. Phase‐space analysis of the relaxation equations describing test electrons, corroborated by two‐dimensional (2‐D) numerical integration of the Fokker–Planck equation, reveals that the Dreicer condition for runaway v²_∥≥(2+Z_i)E_c/E is only sufficient. A weaker condition v²_∥≥(2+Z_i)^1/2E_c/E is established, and it is shown, in general, that runaway in velocity space only occurs for those electrons that are outside one of the separatrices of the relaxation equations. The scaling with v_∥ of the parallel distribution function and of the perpendicular temperature is also derived.