TheECRwaveheatingisnowaroutinemethodforplasmaheatingandprofilecontrolinfusiondevicesandalsoinplasmaapplications.TheoreticalstudyofECRwavepropagationandabsorptionbeganveryearlyin1950's.Basictheoreticalworkhadaccomplishedin1970~1980.Fortoroidaldeviceslikethetokamak,thefundamentalO-modeandX-modewithnearlyperpendicularpropagationwereusedveryoften.ForpureO-modeandX-modewithkx=O,