Numerical analysis of electron distribution function under electron cyclotron heating during tokamak start-up

Start-up of a large tokamak with a superconducting central solenoid (CS) is challenging due to its low loop voltage. Non-inductive start-up using radio-frequency waves such as electron cyclotron (EC) waves has been studied using the trapped-particle configuration (TPC) designed to confine collisionless electrons. In recent years, TPC was found to be effective not only for non-inductive start-up but also for EC assisted ohmic start-up as well. The global phase-space structure of the collisionless electrons during EC heated TPC start-up was numerically analyzed in terms of the orbit-averaged distribution function. Transport of collisionless electrons generated by EC waves was simulated with orbit-averaged Fokker–Planck equation solver that can treat open field-lines. The result of the Fokker–Planck simulation was introduced to equilibrium reconstruction code based on extended magnetohydrodynamics (MHD) that included the kinetic electron current. Finite-orbit effects and relativistic effects were considered consistently for both the Fokker–Planck simulation and the extended MHD equilibrium reconstruction. Time evolution of the global electron distribution function was simulated for the first time starting from the vacuum TPC up to closed flux surface formation. The results of the newly developed model suggest that the kinetic electron current generated by EC heating under the TPC is sufficient to form closed flux surfaces. The electron distribution function was predicted to have a characteristic phase-space structure resulting from strong acceleration of trapped electrons with turning points at the EC resonance layer.