Anomalous particle pinch and scaling of vin/D based on transport analysis and multiple regression

Predictions of density profiles in current tokamaks and ITER require a validated scaling relation for vin/D where vin is the anomalous inward drift velocity and D is the anomalous diffusion coefficient. Transport analysis is necessary for determining the anomalous particle pinch from measured density profiles and for separating the impact of particle sources. A set of discharges in ASDEX Upgrade, DIII-D, JET and ASDEX is analysed using a special version of the 1.5-D BALDUR transport code. Profiles of ρsvin/D with ρs the effective separatrix radius, five other dimensionless parameters and many further quantities in the confinement zone are compiled, resulting in the dataset VIND1.dat, which covers a wide parameter range. Weighted multiple regression is applied to the ASDEX Upgrade subset which leads to a two-term scaling with x' = ρ/ρs, effective radius ρ and average value . The rmse value of the scaling equals 15.2%. The electron temperature gradient length is the key parameter of the anomalous particle pinch which yields the main contribution. A further parameter is the loop voltage UL which introduces the electron collisionality parameter νe*. All exponents are statistically significant. The parameters UL and νe* suggest a new anomalous particle pinch term driven by the Ohmic inductive electric field. The nonlinearities in the two-term scaling show that quasilinear theory is disproved by experiment. Regression analysis of the whole dataset VIND1.dat from four tokamaks shows that the scaling covers the dependence of ρsvin/D on the effective plasma radius. It is further found that the ρsvin/D values from transport analysis do not respond to a change in collisionality regime and are not clearly related to the prevailing turbulence type. The new scaling law predicts for ITER high values of ρsvin/D and peaked density profiles, caused by the term and central heating due to alpha particles. The density peaking improves the energy confinement by some 20%.