Electron cyclotron resonance during plasma initiation

Electron-cyclotron resonance heating (ECRH) is the main heating mechanism in the Wendelstein 7-X (W7-X) stellarator. Although second-harmonic ECRH (X2) has been used routinely for plasma startup, startup at third harmonic (X3) is known to be much more difficult. In this work, we investigate the energy gain of particles during nonlinear wave-particle interaction for conditions relevant to second- and third-harmonic startups in W7-X. We take into account both the beam and the ambient magnetic field inhomogeneities. The latter is shown to significantly increase the mean energy gain resulting from a single wave-particle resonant interaction. In W7-X-like conditions, the improvement in maximum gained energy is up to 4 times the analogous uniform magnetic field case. However, this improvement is not enough to ensure X3 startup. The optimal magnetic field inhomogeneity length scale for average energy gain and start up in W7-X-like conditions is found to be in the range of $1$ to $3 km^{-1}$. A possibility of using multiple beams with neighbouring resonances is also considered. A considerable enhancement of the energy gain is demonstrated.