Turbulent sources in axisymmetric plasmas

Successful operation of tokamaks and other magnetic confinement schemes of fusion interest rely on the tailoring of the parallel momentum/current density and temperature profiles via resonant absorption of externally injected waves. Similarly, it is to be expected that a turbulent spectrum of waves, internally generated to free the energy stored in the gradients of the equilibrium profiles, could transfer locally momentum and energy to the particle degree of freedom of the plasma. Turbulent sources stem out nicely from the action-angle transport formalism, as a detailed derivation of the general transport law from the collision operator (which includes both the diffusion and the friction coefficients) in action-space shows. The special case of magnetic turbulence is considered, and explicit expressions for the electron parallel momentum and energy sources are presented. An interesting feature of the sources resides in their dependence on the first and second powers of the safety factor derivative, a dependence that is often found in turbulent fluxes as well. One term in the energy source depends, in a determinant way, also on the relative magnitude of the electron and ion temperature. This dependence, an output of the retention of the friction term in the collision operator, leads to an energy flow that is always directed from the hotter to the cooler species, a desirable property that is missed when a quasilinear approach is employed.