A one-dimensional model for lower-hybrid current drive including perpendicular dynamics

The two-dimensional (velocity space) Fokker–Planck equation for lower-hybrid current drive is approximated by its perpendicular moments hierarchy closed in the second moment equation. The closure is derived on the basis of a distribution function composed of a central thermal Maxwellian plus a perpendicularly broadened distribution of fast particles that are diffused into, and pitch-angle scattered out of, the quasilinear plateau region. The resulting one-dimensional model reproduces the relevant features of the solutions obtained from numerically integrating the two-dimensional Fokker–Planck equation. An analytic estimate of the perpendicular temperature on the plateau and the plateau height as a function of spectrum width and position is presented. Also predicted are the current density generated and its figure of merit (the current density per unit power density dissipated).