TURBULENT EQUIPARTITION AND UP-GRADIENT TRANSPORT

Turbulent transport in tokamaks is often observed to be directed up-gr adient. It is proposed that such up-gradient fluxes represent a tenden cy to approach turbulent equipartition (TEP). At TEP the phase space f luid is well mixed along surfaces defined by those invariants that are not destroyed by the turbulence. This implies that the distribution f unction f depends only of these invariants, since, according to Liouvi lle's theorem, f is a Lagrangian invariant of the phase space flow. Th e nature of the TEP depends entirely on what the invariants are. Assum ing that the magnetic moment of the particles is conserved, the genera l form of the transport equations is found for a two-dimensional elect rostatic plasma model. These equations describe the relaxation to TEP, and show that in the presence of turbulence there may be fluxes witho ut gradients in the thermodynamic variables. For tokamaks the two firs t adiabatic invariants of the single-particle motion are assumed to be conserved in the presence of the turbulence. This leads to the densit y profile n similar to 1/q of trapped particles, which has a maximum i n the centre. The proposed model implies that trapped particle modes d ominate turbulent transport in tokamaks. Since negative shear stabiliz es these modes, it is predicted that negative shear improves confineme nt significantly.