Canonical Profiles in Tokamak Plasmas with an Arbitrary Cross Section

Two principles are used to determine a canonical profile: the principle of the minimum of free plasma energy with the constraint that the total current is conserved and the principle of profile consistency. A second-order differential equation for the canonical profile of the function (mu) = 1/q is deduced in the natural coordinate system. Soft and hard boundary conditions are proposed to find an unambiguous solution to this equation. The range of their applicability is discussed. Numerical calculations show that the half-width of the canonical profile increases with decreasing aspect ratio, increasing plasma elongation, and decreasing q[sub a] value. The canonical profiles obtained make it possible to determine the critical gradients for the heat and particle fluxes in transport models.