Finite Banana-Width Effect on Neoclassical Transport Theory

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The purpose of this research project is to extend the conventional neoclassical transport theory by relaxing the constraints ρ_p/L ≪ 1 and ρ_p/γ ≪ 1, where ρ_p is the poloidal Larmor radius, L is the gradient scale length and γ is the local minor radius.1. The finite banana-width effect modifies the conventional neoclassical transport theory around the magnetic axis in the collisionless regime. The neoclassical transport theory on the magnetic axis is proposed in an axisymmetric magnetic field. Using this theory, a simple interpolation formula between the neoclassical transport coefficients on the magnetic axis and the conventional ones is presented, and the analytic expressions for the transport coefficients are derived. The bootstrap current due to the fusion-produced alpha particles is also obtained. In addition, it is shown that the finite banana-width effect leads to the concept of a tokamak sustained only by the bootstrap current. The properties of this completely bootstrapped tokamak are also studied.2. An ion energy flux across a magnetic field in a presence of steep gradient has been studied. In a uniform magnetic field, the perpendicular energy flux is found to be nonlocally related to the density and pressure profiles. This flux is explicitly calculated for a simple density and pressure profile model and its dependency on ρ/L is obtained, where ρ is the Larmor radius. In the similar method, the nonlocal transport equation for the radial energy flux is derived in the plateau regime. These classical and neoclassical transport equations are valid for the arbitrary values of ρ/L and ρ_p/L.3. A kinetic equation for a distribution function ensemble-averaged over fluctuations has been studied in order to estimate the effect of radial anomalous transport on the current along the magnetic field.