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

Abstract

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.

Plasma ignition and steady state simulations of the Linac4 H− ion source

“…Plasma heating takes place by coupling of the RF fields with the charged particles. As shown by Grudiev et al 3 , the E RF field points primarily in the r and z direction, which causes the electrons to move in the opposite direction to the electric field, leading to a push-pull effect of the electrons during the initial phase, as illustrated in Fig. 4.…”

“…The electric field E and the magnetic field B are the sum of two contributions. The fields generated by the RF solenoid antenna (E RF and B RF ) are simulated separately by the HFSS software, taking into account the real 3D ion source geometry with its respective material properties 3 . The fields are then averaged in the θ-direction and exported as a field map to the PIC model.…”

Kinetic simulations and photometry measurements of the E-H transition in cylindrical inductively coupled plasmas

“…Details of the simulations are described in [23]. From HFSS we export a field map of E RF , B RF that we average in the ✓ direction.…”

Status and operation of the Linac4 ion source prototypes

“…With a purely inductive coupling, it was used to determine the minimal RF-power required to sustain and heat the plasma as a function of the H 2 pressure 7 thus providing results similar to the experimental Paschen discharge characteristics. With the RF field 4 , initial electron-ionsand neutrals density distributions and the geometry of the cesiated surface prototype as input (but neglecting the permanent magnetic fields), the evolution of the plasma was studied for low electron density specific to plasma ignition and for densities up to 10 18 m -3 typical for steady state operations 8 . The resulting time dependent electron densities and electron Energy Distribution Function (eEDF) were used as input into a collision radiation models to calculate the light emission from excited neutrals 9 (see Fig.…”

“…Complex simulations are mandatory towards the engineering of plasmas dedicated to volume or cesiated surface H -production. The electromagnetic RF-field distribution was simulated as a function of isotropic average plasma conductivity over several orders of magnitude 4 . RF to plasma coupling modes characterized by the penetrability of the electrical field into the plasma were identified.…”