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Predicting the dynamics of a thermonuclear plasma during a magneticconfinement experiment is fundamental in order to make nuclear fusion areliable source of energy. The development of a set of equations describing theplasma evolution on a given time scale is the main requirement to reach thisgoal. A limited amount of works have studied in a self-consistent waycollisional transport and fluctuation induced transport. The motivation of thiswork stems from the fundamental importance of the self-consistency of theadopted description in order to understand transport processes on the energyconfinement (transport) time scale because of the mutual interaction betweencollisions and turbulence. In turn, this is crucial in order to predict fluxesof particle and energy and, ultimately, the overall plasma evolution. Usingflux coordinates and the drift ordering we derive a set of evolutions equationsfor the number of particles and the energy density on the transport time scale.These equations show the interplay between collisions and fluctuations and, inparticular, show that fluctuations may enhance collisional transport while thecollisions can damp long lived structures formed by saturated instabilities,i.e zonal structures. Fluctuation induced fluxes are described usinggyrokinetic field theory, which makes a comparison with the theory of phasespace zonal structures possible, revealing that the fluctuations induced partof the transport equations can be obtained by taking the proper moment of thelong length scale limit of the equation governing the evolution of phase spacezonal structures. Finally, we show that plasma nonlinear evolution can yield tostructures formation that are characterized by mesoscales, intermediate betweenthe typical ones of plasma turbulence and those of the reference plasmaequilibrium.

Gyrokinetic theory for particle transport in fusion plasmas