Toroidal and electric field effects on current drive in tokamaks by lower hybrid and electron cyclotron waves

The current drive by HF waves in a tokamak with longitudinal electric field is studied on the basis of the two-dimensional kinetic equation for electrons. Analytical formulas for current and current drive efficiency are obtained for a low level of absorbed power. Numerical methods are used to solve the kinetic equation at high HF power level. It is shown that the dependence of the efficiency on the effective charge of the plasma changes with increasing power absorption. The existence of trapped particles reduces current drive efficiency. An analysis of the calculation results leads to simple approximate expressions for current and efficiency, convenient for comparisons with the experiments.