  We present a new neoclassical transport model for large aspect ratio tokamaks
where the gradient scale lengths are of the size of the poloidal gyroradius.
Previous work on neoclassical transport across transport barriers assumed large
density and potential gradients but a small temperature gradient, or neglected
the gradient of the mean parallel flow. Using large aspect ratio and low
collisionality expansions, we relax these restrictive assumptions. We define a
new set of variables based on conserved quantities, which simplifies the drift
kinetic equation whilst keeping strong gradients, and derive equations
describing the transport of particles, parallel momentum and energy by ions in
the banana regime. The poloidally varying parts of density and electric
potential are included. Studying contributions from both passing and trapped
particles, we show that the resulting transport is dominated by trapped
particles. We find that a non-zero neoclassical particle flux requires parallel
momentum input which could be provided through interaction with turbulence or
impurities. We derive upper and lower bounds for the energy flux across a
transport barrier in both temperature and density and present example profiles
and fluxes.
