Plasma equilibrium with fast ion orbit width, pressure anisotropy, and toroidal flow effects

We formulate the problem of tokamak plasma equilibrium including the toroidal flow and fast ion (or energetic particle, EP) pressure anisotropy and the finite drift orbit width (FOW) effects. The problem is formulated via the standard Grad-Shafranov equation (GShE) amended by the solvability condition which imposes physical constraints on allowed special dependencies of the anisotropic pressure. The GShE problem employs the pressure coupling scheme and includes the dominant diagonal terms and non-diagonal corrections to the standard pressure tensor. The anisotropic tensor elements are obtained via the distribution function represented in the factorized form via the constants of motion. Considered effects on the plasma equilibrium are estimated analytically, if possible, to understand their importance for GShE tokamak plasma problem. The novelty of the proposed approach is in the way FOW is included into the GShE via the non-diagonal pressure tensor, factorized distribution function of the fast ions representation and in the prescription of the spacial dependence of P⊥ given the spacial dependence of p∥.