The physical origin of H-mode: the most important problem of plasma physics

Four decades of H-mode experiments revealed many features of heating power threshold (P_th) for the low to high confinement (L-H) transition, where P_th is proportional to the toroidal magnetic field (B_T), inversely proportional to the ion mass (m_i), and P_th has U-shaped dependence on the plasma density. It is found for the first time that this U-shaped rollover dependence came from P_th is inversely proportional to the multiplication of plasma density (n_i) and the squire of neutral density (n_n). The reason for the neutral density involved in the L-H transition is that the turbulence suppression takes place by the viscous force of the ion-neutral friction. When the plasma is in the equilibrium by the compensation of turbulence-induced return current to the gyro-center shift current generated by the ion-neutral charge exchanges, the Reynolds number (Re), the ratio of inertial force to the viscous force, can predict the onset of laminar to turbulent flow [1]. Re for the plasma-neutral interaction is proportional to B_T / (m_i n_in²_n) which is well agreed with the experimental results of P_th. Re is also proportional to the second gradient of radial electric field which is agreed with experiments. Finally, the feature of P_th having favorable dependence on the ion grad B drift toward the x-point is explained by the increased neutral due to the ion grad B drift.

[1] K. C. Lee, Plasma Phys. Control. Fusion 51, 065023 (2009).