Nonlinear trapping in the bounce-transit and drift resonance and neoclassical toroidal plasma viscosity in tokamaks

Bounce-transit and drift resonance is one of the resonances in tokamaks with broken toroidal symmetry. It plays an important role in the wave-particle interactions. The nonlinear consequence of the resonance is the nonlinear particle trapping in the magnetic well, created by the radial drift motion resulting from the perturbed magnetic fields. These nonlinearly trapped particles form superbananas. When the effective collision frequency is less than the bounce frequency of the superbananas, the resonance is resolved by the nonlinear orbits. The transport theory for the superbananas is developed by solving the drift kinetic equation using the Eulerian approach. The neoclassical toroidal plasma viscosity, and the non-axisymmetric transport coefficients have a scaling nu r(2) root delta B/BU, which can be significant even for weakly perturbed tokamaks. Here, nu is the collision frequency, r is the minor radius, delta B is the typical magnitude of the perturbed magnetic field strength, delta B is the equilibrium magnetic field strength, and U is a function of the magnetic shear parameter, mode numbers, and rho(p)/r with rho(p) being the poloidal gyro-radius. The magnitude of the energy flux can be comparable to that of the axisymmetric tokamaks for energetic alpha particles when delta B/B similar to 10(-4) and rho(p)/r similar to 0.1. Thus, the theory sets a maximum magnitude of the tolerable perturbed magnetic field strength in fusion reactors, when nonlinear trapping is significant.