Synchrotron radiation and absorption at 3ωce with X‐mode–O‐mode coupling

The mode conversion‐tunneling equation with weakly relativistic absorption at 3ωce has been solved by using the Green function method. The numerical results show that the reflection and conversion coefficients are dramatically reduced when relativistic absorption is included, while the transmission coefficients and the conversion coefficient from the X‐mode on the high field side to the O‐mode on the low field side are independent of absorption. The reduction of these coefficients leads to the reduction of the asymmetry in the absorption between different wave branches. The numerical results also show that the relativistic effect is important even for a relatively low temperature plasma. An important relationship between solutions is expressed by the reciprocity relations which have been proved for any harmonic number. These analyses modify the interpretation of electron cyclotron emission (ECE).