Analysis of anomalous transport based on radial fractional diffusion equation

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.