Variational calculation of the trapping rate in thermal barriers

A variational calculation of the trapping rate and trapped ion density in thermal barriers is presented. The effects of diffusion in energy as well as pitch angle scattering are retained. The variational formulation uses the actual trapped-passing boundary in velocity space. The boundary condition is that the trapped ion distribution function matches the passing ion distribution function, which is taken to be a Maxwellian, on the boundary. The results compare well with two-dimensional Fokker-Planck code calculations by Futch and LoDestro