Model for second harmonic ECRH plasma start-up in stellarators

Plasma ionisation avalanche under constant electric field is well described by classical theory. It is the standard tokamak start-up method. In this work, we investigate an analogous avalanche process driven by electron cyclotron resonance (ECR). This is a typical plasma initiation method in stellarators. At low plasma temperatures, the typical wave–particle interactions result in complex trajectories. These allow electrons to gain energy beyond their initial value in a single wave encounter. We present a heating model applicable to the standard second-harmonic start-up in stellarators. The model is based on scaling laws derived from wave–particle Hamiltonian dynamics. It relies on a dimensionless numerical coefficient that encapsulates geometric and experimental specifics. This coefficient is calibrated via test-particle simulations. The absorption model is coupled with a collisional-radiative description of hydrogen ionisation, radiation losses, and recombination to simulate the evolution of the ECR-driven ionisation avalanche. The breakdown condition is shown to be related to the maximum temperature achieved during the early stages of start-up. A semi-analytical expression for this temperature is given. The predicted plasma breakdown times show reasonable agreement with experimental observations in the Wendelstein 7-X and TJ-II stellarators.