Effective time and resonance width in cyclotron resonance heating

The concepts of effective time and interaction time are examined in a unified context that includes electron cyclotron resonance heating as well as fast and slow wave ion cyclotron resonance heating. Here effective time t e is defined by Delta nu perpendicular to =(eE + /m)t e , while interaction time t i is the period over which the phase between the particle and the wave is slowly changing. Elliptically polarized travelling waves are assumed obliquely incident upon an arbitrary magnetic mirror field. Arbitrary harmonics and Doppler shift are included in the analysis. It is shown that, for ECRH and slow wave ICRH, t e approximately=0.7t i for particular resonance locations, but both t e and t i become ill-defined in between, owing to overlapping resonances. A new expression is derived relating t e and t i for fast wave IRCH. A cubic equation, valid for t i <<t b , the bounce time, is derived for a general magnetic well and solved numerically for a parabolic well. A simple condition for resonance overlap is given by the vanishing of the discriminant of the cubic. The results are applied to ECRH with k/sub /// to 0 and to fast wave midplane heating, for which k/sub /// nu /sub ///<< omega . In general, resonances are found to be much broader in typical ICRH experiments than for ECRH.