Kinetic treatment of alpha-particle loss and energy deposition in ELMO Bumpy Torus

Abstract

A formalism has been developed in terms of a drift kinetic equation with a Fokker-Planck collision operator to calculate alpha particle loss and energy deposition rate coefficients for one position in space and for steady-state operating conditions. A bounce-averaged drift kinetic equation for an ELMO Bumpy Torus (EBT) is expressed in invariant variables E = v/sup 2//2 and lambda = v/sub perpendicular//sup 2/B/sub MID//v/sup 2/B(l) and is used with energy scattering and pitch angle scattering terms in the collision operator. The alpha particle distribution function is expanded in terms of energy coefficients and pitch angle eigenfunctions. For the case of a square well magnetic field shape, the pitch angle eigenfunctions are the Legendre polynominals. With an expression for the distribution function the particle loss and energy deposition rates are calculated by taking the zeroth and first-order energy moments, respectively, of the kinetic equation.