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The effectiveness of multiple electron cyclotron resonance (ECR) harmonicshas been thoroughly investigated in context of high current drive efficiency,generally observed in fully non-inductive operation of the low aspect ratioEXL-50 spherical tokamak (ST) powered by electron cyclotron (EC) waves. TheFokker-Plank equation is numerically solved to obtain electron distributionfunction, under steady state of the relativistic nonlinear Coulomb collisionand quasi-linear diffusion operators, for calculating plasma current driven bythe injected EC wave. For the extra-ordinary EC wave, simulation results unfolda mechanism by which electrons moving around the cold second harmonic ECR layerstrongly resonate with higher harmonics via the relativistic Doppler shiftedresonance condition. This feature is in fact evident above a certain value ofinput EC wave power in simulation, indicating it to be a non-linear phenomenon.Similar to the experimental observation, high efficiency in current drive (over1 A/W) has indeed been found in simulation for a typical low density ($\sim1\times10^{18}~m^{-3}$), low temperature ($\lesssim 100$ eV) plasma of EXL-50by taking into account multi-pass absorptions in our simulation model. However,such characteristic is not found in the ordinary EC-wave study for bothsingle-pass and multi-pass simulations, suggesting it as inefficient in drivingcurrent on our ST device.

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