A weakly relativistic theory of current drive by parallel acceleration of electrons in toroidal geometry is presented. Analytic expressions of efficiency are obtained for superthermal and subthermal electrons. By using a few adjustable parameters for intermediate energies, an accurate formula for the efficiency is obtained by fitting numerical results. This includes trapping effects and is valid for all frequencies up to the lower hybrid range of frequencies. It is found that for low-frequency

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... ast-wave current drive, the relativistic and nomelativistic efficiencies agree to within 15% up to 500 keV, although the relativistic corrections to power absorption and current density can be much larger separately. Relativistic effects on the efficiency become prominent at lower energies for Landau damping. 0 199.5 American Institute of Physics.