Equipartition and Transport in Two-Dimensional Electrostatic Turbulence

Abstract

Turbulent equipartition is investigated for the nonlinear evolution of pressure driven flute modes in a plasma in an inhomogeneous magnetic field. Numerical solutions of the model equations on a bounded domain with sources and sinks show that the turbulent fluctuations give rise to up-gradient transport, a pinch flux, of heat or particles. The averaged equilibrium density and temperature profiles approach the profilesn B and T B 2=3 predicted by turbulent equipartition. Recently, a new approach has been suggested for predicting the quasi-steady profiles in tokamak plasmas [1, 2, 3, 4]. It is based on the existence of Lagrangian invariants in the presence of turbulence. The basic assumption is that the turbulent mixing causes the equipartition of these invariants over the accessible phase space, a state denoted Turbulent EquiPartition (TEP) [1]. Since the Lagrangian invariants depend on the magnetic fieldB, a homogeneous distribution of these invariants implies that if B is inhomogeneous, so are the density and the temperature. Therefore, the fluxes that drive the plasma towards TEP may be up-gradient. In a two-dimensional plasma model the corresponding mechanism is easily understood.