Features of Fundamental- and Subharmonics ECR Heating in a Magnetic Trap

We compare the efficiency of microwave heating of electrons in a dense plasma at the fundamental harmonics ( = eH/(mc)) and at the subharmonics ( = eH/(2mc)) of the electron gyrofrequency. In particular, recent experimental results showing a higher efficiency of microwave heating at the frequency equal to one half of the electron gyrofrequency are analyzed. Equations describing the nonlinear subharmonic electron cyclotron resonance (ECR) heating are derived for an arbitrary geometry of the microwave field. If the microwave field has the vacuum polarization, then the microwave power absorbed by electrons at the fundamental harmonic of the electron gyrofrequency in rarefied plasmas exceeds by many orders of magnitude the corresponding power absorbed by electrons in the case of nonlinear heating at one half of the electron gyrofrequency. However, it is shown that this difference in a dense plasma does not exceed one order of magnitude, which is explained by the effect of depression of the resonance component of the microwave field. In this case, the efficiency of the formation of high-energy electron population can be influenced not only by the energy-deposition rate but mainly by the stability condition of an electron in the magnetic trap. It is shown that a twofold decrease in the magnetic field, necessary to satisfy the ECR condition at one half of the electron gyrofrequency, leads to a dramatic shortening of the hot-electron lifetime in a magnetic trap and, in turn, to a dramatic decrease in the energy-deposition efficiency. We discuss the dependence of the electron heating on the effect of quasi-static enhancement of the microwave field near a target located in a magnetic trap for the generation of X-ray emission.