Computational and analytical optimization of helicon antenna power coupling with a fast full wave solver exploiting Fourier decomposition of antenna currents

Abstract

Plasma wakefield accelerators, such as the Advanced Proton Driven Plasma Wakefield Acceleration Experiment (AWAKE), require homogeneous high-density plasmas. The Madison AWAKE Prototype (MAP) has been built to create a nearly uniform argon plasma in the 1020 m-3 density range using helicon waves. Optimization of MAP plasmas requires calculating the helicon wavefields and power deposition. This task is computationally expensive due to the geometry of high-performance half-helical antennas and the small wavelengths involved. We show here for the first time how the 3D wavefields can be accurately calculated using just four 2D-axisymmetric simulations. Our approach exploits an azimuthal Fourier decomposition of the non-axisymmetric antenna currents to massively reduce computational cost and is implemented in the Comsol finite-element framework. This new tool allows us to calculate the power deposition profiles for 640 combinations of core plasma density, antenna length, and radial density profile shape. We find that certain combinations of antenna length and core density maximize axial power deposition asymmetry, independent of the exact radial profile shape. We can reproduce this relationship analytically by engineering a good overlap between the antenna power spectrum and the helicon dispersion relation. The result is a simple analytical expression that enables the optimization of power coupling in any linear helicon device by calculating the ideal antenna length for a given plasma density, RF frequency and magnetic field.