Numerical simulation of electromagnetic fields and impedance of CERN LINAC4 H$^−$ source taking into account the effect of the plasma

Numerical simulation of the CERN LINAC4 H− source 2 MHz RF system has been performed taking into account a realistic geometry from 3D Computer Aided Design model using commercial FEM high frequency simulation code. The effect of the plasma has been added to the model by the approximation of a homogenous electrically conducting medium. Electric and magnetic fields, RF power losses, and impedance of the circuit have been calculated for different values of the plasma conductivity. Three different regimes have been found depending on the plasma conductivity: (1) Zero or low plasma conductivity results in RF electric field induced by the RF antenna being mainly capacitive and has axial direction, (2) Intermediate conductivity results in the expulsion of capacitive electric field from plasma and the RF power coupling, which is increasing linearly with the plasma conductivity, is mainly dominated by the inductive azimuthal electric field, (3) High conductivity results in the shielding of both the electric and magnetic fields from plasma due to the skin effect, which reduces RF power coupling to plasma. From these simulations and measurements of the RF power coupling on the CERN source, a value of the plasma conductivity has been derived. It agrees well with an analytical estimate calculated from the measured plasma parameters. In addition, the simulated and measured impedances with and without plasma show very good agreement as well demonstrating validity of the plasma model used in the RF simulations.