Electron energy and current density: coupled transport, symmetry breaking and degradation

We propose that, in regimes where the applied electric field drives the plasma current and at the same times heats the plasmas, the transport of electron thermal energy and the redistributino of the electron current density are strongly coupled. Thus we introduce a matrix equation that described the transport of both quantities. The energy degradatino that occurs when auxiliary heating is dominant is interpreted in terms of the breaking of the symmetry properties of the transport matrix. This matrix equation contains, besides the thermal conductivity, a "thermo-viscous" coefficient that accounts for the energy and current density transport arising from the relative shape of their profiles. The energy transport related to the thermo-viscous coefficient takes the form of a thermal energy inflow, associated with the gradient of the current density, and provides a natural formulation for the so called "heat pich". Thi appraoch has been implemented in a 1 D transport code and tested against the experimental data of a TFTR ohmic discharge. The overall results fit the experimental data well.