Eulerian approach to bounce-transit and drift resonance and neoclassical toroidal plasma viscosity in tokamaks

An Eulerian approach to treat the bounce-transit and precession drift resonance in tokamaks is developed by expanding the poloidal angle dependence in terms of a Jacobian elliptic function in the low collisionality regime instead of integrating along the unperturbed particle trajectories. One of the advantages is that a complex Coulomb collision operator can be adopted in the approach. The full thermodynamic forces are kept to conserve momentum in the collision processes. To illustrate the method, the approach is applied to calculate the neoclassical toroidal plasma viscosity in both the resonant plateau regime and the Pfirsch-Schluter regime. Both trapped particles and circulating particles contribute to the resonant plateau regime through the bounce and drift resonance and the transit and drift resonance, respectively. The dependences on plasma parameters for both regimes are found to be the same as that of the nonlinear plasma viscosity. The resonant plateau regime naturally connects to the Pfirsch-Schluter regime in the collisional limit.