Anomalous diffusion and transport beta limits in dense tokamak plasmas

For tokamak plasmas which are sufficiently large and/or dense that the ionization source on axis may be neglected, particle balance is achieved by the inward diffusion due to the Ware pinch compensating the outward flow due to both neoclassical and anomalous diffusion. Insertion of measured data into the particle flux balance relation determines the anomalous particle diffusion coefficient D A ; comparison of the results from a variety of tokamaks implies that the dominant dependence on machine and/or plasma parameters is D A ∝ 1/n. Particle flux balance also implies an upper bound on the central value of β e , the limiting value being obtained when the plasma parameters are chosen such that D A ≪D NEO . This limit has been computed for circular-cross-section tokamaks, and the results so obtained are of the same order as magnetohydrodynamic beta limits.