Invariant measure and turbulent pinch in tokamaks

It is shown that electron transport due to a generic low-frequency electrostatic turbulence in tokamak geometry results in the relaxation to a peaked, self-sustained plasma density profile n0(r), rather than to a diffusion-induced flat distribution. The relaxed density profile depends on the magnetic geometry and the distribution of turbulence. The associated inward pinch velocity Vr=D∇lnn0 results from the competition of the turbulent diffusion of trapped electrons over the poloidal magnetic flux coordinate ψ and the collisional relaxation toward a Maxwellian distribution function