Turbulent equipartition and up-gradient transport

Abstract

Turbulent transport in tokamaks is often observed to be directed up-gradient. It is proposed that such up-gradient fluxes represent a tendency to approach turbulent equipartition (TEP). At TEP the phase space fluid is well mixed along surfaces defined by those invariants that are not destroyed by the turbulence. This implies that the distribution function f depends only of these invariants, since, according to Liouville's theorem, f is a Lagrangian invariant of the phase space flow. The nature of the TEP depends entirely on what the invariants are. Assuming that the magnetic moment of the particles is conserved, the general form of the transport equations is found for a two-dimensional electrostatic plasma model. These equations describe the relaxation to TEP, and show that in the presence of turbulence there may be fluxes without gradients in the thermodynamic variables. For tokamaks the two first adiabatic invariants of the single-particle motion are assumed to be conserved in the presence of the turbulence. This leads to the density profile n ~ 1/q of trapped particles, which has a maximum in the centre. The proposed model implies that trapped particle modes dominate turbulent transport in tokamaks. Since negative shear stabilizes these modes, it is predicted that negative shear improves confinement significantly.