Thermodynamic fluctuation levels of drift modes and transport coefficients

A statistical model is presented, of a collective electrostatic configuration, described by the Vlasov equation, interacting, through exchange of charged particles, with an infinite homogeneous medium of individual particles. The marginal linear instability of a collective mode is related to a negative dielectric constant of the mode in the medium and to a minimum of the entropy of the collective configuration calculated with suitable coarse graining and physical constraints. When the nonlinear terms are taken into account the entropy has a maximum corresponding to an equilibrium with a definite fluctuation level of the interacting systems. The model is applied to the electrostatic drift modes destabilized by the toroidal geometry of the Tokamak. The interaction with the medium also produces a fluctuation of the charges, which participate to the electron parallel current of the Tokamak. This fluctuating current is divergenceless and creates a braided magnetic field and anomalous thermal diffusivity of the electrons. The magnitude and the scaling of the electron thermal conductivity are consistent with the observations in ohmic discharges.