On zero-frequency magnetic fluctuations in plasmas

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  • T. Tajima
    Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712
  • S. Cable
    Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712
  • R. M. Kulsrud
    Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08540

Abstract

<jats:p>A plasma sustains fluctuations of electromagnetic fields and particle density even in thermal equilibrium and such fluctuations have a large zero-frequency peak. The level of fluctuations in the plasma for a given wavelength and frequency of electromagnetic fields is calculated through the fluctuation–dissipation theorem. The frequency spectrum shows that the energy contained in this peak is complementary to the energy ‘‘lost’’ by the plasma cutoff effect. The level of the zero (or nearly zero) frequency magnetic fields is computed as 〈B2〉0/8π = (1/2π3)T(ωp/c)3, where T and ωp are the temperature and plasma frequency. The relation between the nonradiative and radiative fluctuations is elucidated. Both a simple collision model and a kinetic theoretic treatment are presented with essentially the same results. The size of the fluctuations is λ ∼ (c/ωp)(η/ω)1/2, where η and ω are the collision frequency and the (nearly zero) frequency of magnetic fields oscillations. Perhaps the most dramatic application of the present theory, however, is to the cosmological plasma of early epoch (say t = 10−2–100 sec after the Big Bang). Implications of these magnetic fields in the early Universe are discussed.</jats:p>

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