Stellarator Plasma Start-up Model Based on Energy Confinement Time Scaling Laws, Experimental Verification and Numerical Simulation Results

Based on the energy confinement time scaling law of stellarator in the low-confinement mode, combined with energy balance equation and the plasma propagation and power deposition equations of the electron cyclotron wave in the three-dimensional magnetic field, a stellarator plasma start-up model including electron cyclotron resonance heating (ECRH) and impurity radiation power loss is established. Validation against W7-X experimental data demonstrates good agreement in the temporal evolution of electron temperature and radiation losses, which verified that the model can correctly give the plasma start-up results of the stellarator under ECRH. This model is applied to predict the results of plasma start-up under 28 GHz ECRH for China Helical Device 1 (CN-H1) stellarator. The effects of the initial electron-to-ion temperature ratio (Te/Ti), ECRH injection power (Pinj), deposition position and effective charge number Zeff on start-up are systematically studied and analyzed. The results show that the initial Te/Ti ratio affects only the ramp-up rate, while the final steady-state electron and ion temperature remain unaffected. Higher Pinj accelerates electron temperature rise and increases flat-top electron temperature, whereas the ion temperature exhibits the opposite trend, decreasing with increasing Pinj. The deposition location has a decisive impact on the start-up outcome: only core deposition on the low-field side leads to a successful start-up, while high-field side and off-axis low-field side depositions fail owing to refractive deviation of the ray trajectory and insufficient absorption, respectively. The steady-state electron and ion temperatures are insensitive to {Z}eff within a reasonable range.