Magnetic fluctuations can contribute to plasma transport, ‘‘self-consistency constraints’’ notwithstanding

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Abstract
The recent conclusion of Terry, Diamond, and Hahm (TDH) [Phys. Rev. Lett. 5 7, 1899 (1986)] that in a turbulent, collisionless plasma ‘‘magnetic transport including quasilinear magnetic flutter transport . . . does not contribute to the relaxation of 〈f〉, and thus is not responsible for electron energy or momentum transport’’ is argued to be irrelevant or incorrect for a variety of situations of physical interest, including saturation by quasilinear plateau formation, induced scattering, and, most important, conventional mode coupling. The well‐established theory of the mean infinitesimal response function and the spectral balance equation provides a unifying framework for understanding the work of TDH. In particular, the cancellations which lead to the TDH conclusion are special cases of well‐known relationships between the response functionparticle propagator, and dielectric function. A more general, concise, and manifestly gauge‐invariant algebraic derivation of the cancellations is given. Although the cancellations occur in a certain limit, the conclusions of TDH do not follow in general: The TDH picture of steady‐state turbulence as consisting of small‐scale ‘‘incoherent’’ ballistic ‘‘clumps’’ shielded by long‐wavelength ‘‘coherent’’ dielectric response is misleading physically and incomplete mathematically since it does not describe correctly the often dominant process of renormalized n‐wave coupling, particularly important for the ions. Although ion ballistic response is negligible, ions are important nevertheless: Their nonlinear contribution to the saturated potential can drive parallel electron currents, hence magnetic fluctuations, through linear mechanisms. Thus, when ion nonlinearities are considered, formulas for the magnetic contribution to transport emerge which are quite similar to the quasilinear formula.