Investigation of the effectiveness of non-inductive `multi-harmonic' electron cyclotron current drive through modeling multi-pass absorptions in the EXL-50 spherical tokamak

The effectiveness of multiple electron cyclotron resonance (ECR) harmonics has been thoroughly investigated in context of high current drive efficiency, generally observed in fully non-inductive operation of the low aspect ratio EXL-50 spherical tokamak (ST) powered by electron cyclotron (EC) waves. The Fokker-Plank equation is numerically solved to obtain electron distribution function, under steady state of the relativistic nonlinear Coulomb collision and quasi-linear diffusion operators, for calculating plasma current driven by the injected EC wave. For the extra-ordinary EC wave, simulation results unfold a mechanism by which electrons moving around the cold second harmonic ECR layer strongly resonate with higher harmonics via the relativistic Doppler shifted resonance condition. This feature is in fact evident above a certain value of input EC wave power in simulation, indicating it to be a non-linear phenomenon. Similar to the experimental observation, high efficiency in current drive (over 1 A/W) has indeed been found in simulation for a typical low density ($\sim 1\times10^{18}~m^{-3}$), low temperature ($\lesssim 100$ eV) plasma of EXL-50 by taking into account multi-pass absorptions in our simulation model. However, such characteristic is not found in the ordinary EC-wave study for both single-pass and multi-pass simulations, suggesting it as inefficient in driving current on our ST device.