Effect of Multiple Scattering on the Critical Electric Field for Runaway Electrons in the A.pdf

Effect of Multiple Scattering on the Critical Electric Field for Runaway Electrons in the Atmosphere Ya. S. Elensky Institute for Nuclear Research, Russian Academy of Sciences, pr. Shestidesyatiletiya Oktyabrya 7a, Moscow, 117312 Russia e-mail: yansa@gcnet.ru A simple method for taking into account the multiple Coulomb scattering in construction of a sep- aratrix (the line separating the regions of runaway and decelerating electrons in an electric field) is described. The desired line is obtained by solving a simple transcendental equation. DOI: 10.3103/S1062873807070428 INTRODUCTION of momenta p = p (z) or p = p (t); here, n is the number The so-called separatrix—a line separating the run- away and deceleration regions is reported in almost of particles per volume unit dp, and ∫n (p )dp = N (one each study devoted to runaway electrons. In the sim- particle with the probability density function f (p ) can plest case, the kinetic electron energy T is plotted on the be also considered; in this case, f (p ) = n(p )/N and horizontal axis and the energy losses or the correspond- f ( ) ing strength of the accelerating field (F = dT/dx or F = ∫ p dp = 1). loss el dU/dx) is plotted on the vertical axis. In this case, the We can easily determine the fraction of runaway separatrix is a dependence of the loss on energy; the electrons if the function n(p ) is known. To this end, we point corresponding to a given electron energy T and a have to solve the kinetic equation with appropriate ini- given field Eel lies either