Anomalous pinch flux in tokamaks driven by the longitudinal adiabatic invariant

The turbulent particle flux in tokamaks has an inward component, the pinch flux, which is independent of the density gradient. It is proposed that this flux represents a tendency of the particle distribution to approach turbulent equipartition, which means that the phase space density is constant on hypersurfaces defined by those invariants that are not destroyed by the turbulence. For tokamaks the two first adiabatic invariants give the peaked density profile n∼1/q of trapped particles. Sharp gradients are predicted near the separatrix of divertor plasmas. The physical mechanism of the pinch is as follows. When a parcel of trapped particles is displaced inward by the turbulent fluctuations, their parallel velocity must increase in order to keep the longitudinal invariant J constant. This is equivalent to adiabatic compression, and increases the density. The turbulence is assumed to be caused by thermally driven electrostatic modes.