Relativistic description of electron Bernstein waves

The application of the extraordinary and ordinary electron cyclotron waves for heating and current drive in overdense, magnetized plasmas is restricted. For frequencies near low harmonics of the electron cyclotron frequency these waves are cutoff near the edge of the plasma. For higher frequencies the interaction of the waves with electrons is weak leading to very low absorption of wave power. However, electron Bernstein waves provide means for heating and current drive in overdense plasmas since they have no density cutoffs and are strongly damped near harmonics of the electron cyclotron resonance. This paper discusses properties of electron Bernstein waves that make them an attractive means for delivering energy and momentum to electrons. An approximate analytical model for electrostatic waves in the weakly relativistic and weak damping limits is developed. From this model the propagation and damping characteristics of electron Bernstein waves and their dependence on plasma parameters are derived. It is found that relativistic effects are necessary to properly describe the resonant interaction of electron Bernstein waves with electrons. The characteristics of electron Bernstein wave propagation and damping are very different depending on whether the electron cyclotron harmonic resonance is approached from the low- or high-field side. The results from the analytical model and the associated analysis agree well with the results from the exact numerical calculations. This validates the physics of the simplifying assumptions on which the model is based. The electron Bernstein waves are completely damped well before the electron cyclotron resonance due to the Doppler shift. Within the damping region the waves interact with suprathermal electrons thereby having the potential for efficient current drive.