A linear empirical threshold condition ω E×B /γ ITG > 0.68s − 0.095 has been found for the onset of the ion internal transport barriers in the JET optimised shear database. Here, s is the magnetic shear, ω E×B the flow shearing rate and γ ITG is an approximate of the linear growth rate of the ion temperature gradient instability. The present empirical threshold condition for the ITB formation will provide a first clear indication of the strong correlation of s and ω E×B at the ITB transition. The empirical analysis consists of ITB discharges from a wide plasma parameter range; the toroidal magnetic field varies between 1.8-4.0 T, the auxiliary heating power between 10-30 MW and the diamagnetic energy between 3-12 MJ. The predictive simulations of several ITB discharges with the empirical ITB threshold condition reproduce the experiments with time averaged prediction errors of the order of 10-25% in T i and T e profiles and 10-15% in n e profiles as well as the toroidal flow velocity with errors of the order of 10-20%. The simulated times of the onset of the ITB compared to the experimental ones are typically within 0.4 s and the simulated ITB widths within 0.1 in r/a throughout the whole simulations.

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The direction and magnitude of power and momentum exchange between fast ions and electrostatic waves in slab and toroidal systems are obtained from global Monte Carlo simulations that include the quasilinear wave-induced ion diffusion both in velocity space and through a radially localized (lower hybrid) wave structure with propagation in one preferential poloidal direction in tokamaks. The model considers a full linearized collision model, finite fast ion orbits, and losses in toroidal geometry, and can properly treat the boundary effects on the particle–wave interaction in the configuration space. For an isotropic steady ion source, reduction of wave Landau damping but no wave amplification by wave localization is found for a Gaussian wave intensity distribution in radius, irrespective of the steepness of the radial gradient of the fast ion source rate. Enhanced wave-driven fast ion current, with magnitude, direction, and profile determined by the boundary conditions, net power transfer, and fast ion radial transport, is found to follow from the asymmetry in the parallel wave number spectrum created by the finite poloidal magnetic field. In the presence of intense well-penetrated waves the current carried by fusion α particles can be controlled by the choice of the poloidal wave number spectrum and the total current can greatly exceed the neoclassical bootstrap current of the α particles in a reactor.