Velocity-space structure of runaway electrons

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+Zi)Ec/E is only sufficient. A weaker condition v2∥≥(2+Zi)1/2Ec/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.