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Anomalous transport in magnetically confined plasmas is investigated by radial fractional transport equations. It is shown that for fractional transport models, hollow density profiles are formed and uphill transports can be observed regardless of whether the fractional diffusion coefficients (FDCs) are radially dependent or not. When a radially dependent FDC D α r < 1 is imposed, compared with the case under D α r = 1.0 , it is observed that the position of the peak of the density profile is closer to the core. Further, it is found that when FDCs at the positions of source injections increase, the peak values of density profiles decrease. The non-local effect becomes significant as the order of fractional derivative α → 1 and causes the uphill transport. However, as α → 2 , the fractional diffusion model returns to the standard model governed by Fick’s law.

Fluid equations with transport effects have been derived from summing up discrete particle effects in the configuration space. The diffusion coefficient takes a form different from, but equivalent to, the Kubo formula. By taking into account the decoherence along the field lines, the diffusive damping in the perpendicular direction, and the finite Larmor radius effect in the cyclotron resonance, it is shown that the diffusion of magnetized 3d plasma has a regime of B−3/2 scaling which lies between the Bohm diffusion of B−1 and the classical diffusion of B−2.