Reduced order methods for full wave ICRF calculations in tokamaks

Reduced order methods have been used extensively to eliminate ion Bernstein waves (IBWs) from full wave calculations in the ion cyclotron range of frequencies (ICRF). These reduced order methods replace higher order derivatives in the finite Larmor radius (FLR) expansion of the plasma current with algebraic terms depending on the local perpendicular wavenumber k⊥ determined from the fourth order plasma dispersion relation. However, the dispersion relation determines only the magnitude of k⊥, not the direction. If k⊥ is assumed to be perpendicular to the flux surface, energy conservation is violated near the magnetic axis. One method of dealing with this problem is to solve algebraically for the parallel electric field E||, in which case the direction of k⊥ drops out of the problem completely. Another method, which allows for the complete differential solution of E||, assumes a direction for k⊥. Both methods are limited by assumptions. A better approach is to apply the reduced order algorithm to the ion FLR current alone, while treating the electron current differentially. Since the direction of k⊥ enters only through electron terms, this method resolves the ambiguity in the direction of k⊥ while still suppressing the IBW, which originates in the ion current. Comparison with the simpler models suggests that it is necessary to include the differential electron current for an accurate description of direct electron heating and fast wave current drive near the ion second harmonic.