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Turbulent correlations and anomalous transport in tokamaks-I. Development of the theory

A parallel kinetic approach to the calculation of turbulent correlations and transport properties in Tokamaks is presented. The non-linear kinetic equations of the theory with suitable collision operators are derived from the well-known drift kinetic theory. The specification of a single fluctuation spectrum (say that of the parallel vector potential) leads to a problem of determining the quasi-neutral plasma response to the spectrum in question. The solution of the problem using a Born-Feynman perturbation series in the assumed smallness of the fluctuation amplitude is developed in detail. Subject to rather weak restrictions, the specified spectral function is shown to determine (under quasi-neutral conditions neglecting trapped particle and anisotropic pressure effects) all other fluctuation spectra and transport properties.