Anomalous particle pinch in tokamaks

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Abstract
The diffusion coefficient in phase space usually varies with the particle energy. A consequence is the dependence of the fluid particle flux on the temperature gradient. If the diffusion coefficient in phase space decreases with the energy in the bulk of the thermal distribution function, the particle thermodiffusion coefficient which links the particle flux to the temperature gradient is negative. This is a possible explanation for the inward particle pinch that is observed in tokamaks. A quasilinear theory shows that such a thermodiffusion is generic for a tokamak electrostatic turbulence at low frequency. This effect adds to the particle flux associated with the radial gradient of magnetic field. This behavior is illustrated with a perturbed electric potential, for which the trajectories of charged particle guiding centers are calculated. The diffusion coefficient of particles is computed and compared to the quasilinear theory, which predicts a divergence at low velocity. It is shown that at low velocity, the actual diffusion coefficient increases, but remains lower than the quasilinear value. Nevertheless, this differential diffusion between cold and fast particles leads to an inward flux of particles.