Transport equations in tokamak plasmas

Tokamak plasma transport equations are usually obtained by flux surface averaging the collisional Braginskii equations. However, tokamak plasmas are not in collisional regimes. Also, ad hoc terms are added for neoclassical effects on the parallel Ohm’s law, fluctuation-induced transport, heating, current-drive and flow sources and sinks, small magnetic field nonaxisymmetries, magnetic field transients, etc. A set of self-consistent second order in gyroradius fluid-moment-based transport equations for nearly axisymmetric tokamak plasmas has been developed using a kinetic-based approach. The derivation uses neoclassical-based parallel viscous force closures, and includes all the effects noted above. Plasma processes on successive time scales and constraints they impose are considered sequentially: compressional Alfvén waves Grad–Shafranov equilibrium, ion radial force balance , sound waves pressure constant along field lines, incompressible flows within a flux surface , and collisions electrons, parallel Ohm’s law; ions, damping of poloidal flow . Radial particle fluxes are driven by the many second order in gyroradius toroidal angular torques on a plasma species: seven ambipolar collision-based ones classical, neoclassical, etc. and eight nonambipolar ones fluctuation-induced, polarization flows from toroidal rotation transients, etc. . The plasma toroidal rotation equation results from setting to zero the net radial current induced by the nonambipolar fluxes. The radial particle flux consists of the collision-based intrinsically ambipolar fluxes plus the nonambipolar fluxes evaluated at the ambipolarity-enforcing toroidal plasma rotation radial electric field . The energy transport equations do not involve an ambipolar constraint and hence are more directly obtained. The “mean field” effects of microturbulence on the parallel Ohm’s law, poloidal ion flow, particle fluxes, and toroidal momentum and energy transport are all included self-consistently. The final comprehensive equations describe radial transport of plasma toroidal rotation, and poloidal and toroidal magnetic fluxes, as well as the usual particle and energy transport. © 2010 American Institute of Physics. doi:10.1063/1.3335486