Toroidal runaway beams

Abstract

We investigate the dynamics of a special group of runaway electrons which possibly play an important role in toroidal fusion devices. Starting from the torus center they are accelerated by a toroidal electric field and are hence forced to move across the toroidal magnetic field into regions with rising poloidal field in order to compensate for the centrifugal forces. Can such particles finally form a tight beam of relativistic runaways in the outboard region or is this prevented due to the perpendicular momentum they gain by passing the toroidal field? Since neither the energy nor the magnetic momentum of the particles is conserved this question has been treated by invoking the relativistic equations of motion. It turns out, however, that the problem can be essentially simplified since, apart from the centrifugal forces associated with the toroidal motion, the inertia forces are negligible. The resulting first order equation can be solved analytically. From the solution it is concluded that the formation of narrow runaway beams with diameters in the range of micrometers and very small pitch angles ($v_{\perp }/v_{\left|\right|}<{10}^{-6}$) appears feasible. Such electrons would perform low-frequency oscillations about three to four orders of magnitude lower than the gyrofrequency in the toroidal field. When passing the maximum poloidal magnetic field strength they are suddenly lost from the plasma region. DOI: http://dx.doi.org/10.1103/PhysRevE.87.013105 ©2013 American Physical Society