Direct Voltage Depression Calculation of Arbitrary Electron Beams in Misaligned Coaxial Gyrotron Cavities

Coaxial-cavity gyrotrons for electron cyclotron heating in plasma experiments for nuclear fusion can operate with very high-order modes, having reduced mode competition and decreased voltage depression compared with hollow-cavity tubes. However, since exact alignment of coaxial insert and cavity wall can only be ensured up to a certain precision, the effects of misalignment must be properly understood. In this paper, an efficient method is presented to determine the voltage depression on beam electrons for arbitrary misalignment between cavity wall and insert, and for a beam with arbitrary shape and density distribution. The method has been verified using a 3-D code, and it can be generalized to some other geometries.