Neoclassical transport in strong gradient regions of large aspect ratio tokamaks

Applicability of standard neoclassical theory in transport barriers is limited because of sharp gradients of temperature, density, and radial electric field. We have developed a new neoclassical approach that sets the scale length in transport barriers to be the ion poloidal gyroradius. This ordering implies that the poloidal component of the ExB-drift becomes of the order of the poloidal component of the typical ion parallel velocity, and the trapped particle region is shifted. Using large aspect ratio and low collisionality expansions, we derive equations describing the ion transport of particles, parallel and perpendicular momentum, and energy. Previous work which only accounted for strong gradients in density and electric field or neglected the mean parallel velocity gradient is extended by keeping the poloidally varying part of the electric potential and by allowing the temperature gradient to have the same scale length as the density gradient. We find that a neoclassical ion particle flux requires parallel momentum input. Due to the nonlinear character of the equations, we can show that for certain sources and boundary conditions there are no solutions.