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### Abstract

A transport theory of fluctuations with frequencies less than the gyrofrequency in toroidal plasmas is developed to calculate particle and heat fluxes, bootstrap current, Ware pinch flux, and modification to plasma conductivity. It is found that the particle and heat fluxes are proportional to ∑_{ m,n,ω} *m* ^{2}(*e*Φ̃_{ m nω}/*T* _{ e })^{ 2 }, the bootstrap current and Ware pinch flux are proportional to ∑_{ m,n,ω} *m*[(*m*−*n* *q*)/‖*m*−*n* *q*‖] (*e*Φ̃_{ m nω}/*T* _{ e })^{2}, and the modification

to plasma conductivity is proportional to ∑_{ m,n,ω}‖*m*−*n* *q*‖(*e*Φ̃_{ m nω} /*T* _{ e })^{2}, where *m* (*n*) is the poloidal (toridal) mode number for the (*m*,*n*) mode with frequency ω, Φ̃_{ m nω} is its mode amplitude, *e* is the electric charge, *T* _{ e } is the electron temperature, and *q* is the safety factor. Alternatively, in terms of the poloidal wave vector *k* _{θ} and the parallel wave vector *k* _{∥}, the particle and heat fluxes are proportional to 〈*k* ^{2} _{θ}〉〈(*e*Φ̃/*T* _{ e })^{2}〉, the bootstrap current and Ware pinch flux are proportional to 〈*k* _{θ} *k* _{∥}/‖*k* _{∥}‖〉〈(*e*Φ̃/ *T* _{ e })^{2}〉, and the modification to plasma conductivity is proportional to 〈‖*k* _{∥}‖〉〈(*e*Φ̃/*T* _{ e })^{2}〉, where 〈Φ̃^{2}〉 is the averaged fluctuation level. Thus the sensitivities of various transport fluxes to plasma fluctuations are different: the most sensitive ones are particle and heat fluxes, the less sensitive ones are bootstrap current and Ware pinch flux, and the least sensitive one is the modification to plasma conductivity. The effects of fluctuations on bootstrap current and Ware pinch flux and on modification to plasma conductivity are smaller than those on particle and heat fluxes by factors of 〈*k* _{θ} *k* _{∥}/‖*k* _{∥}‖〉/〈*k* ^{2}

_{θ}〉 and 〈*k* _{∥}‖〉/〈*k* ^{2} _{θ}〉, respectively. It is demonstrated explicitly that the matrix consisting of these transport coefficients satisfies Onsager symmetry. Furthermore, it is shown that the electron and ion transport are coupled through plasma flows. The theory is employed to discuss some qualitative transport properties observed in toroidal plasma experiments.

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