Kinetic theory of linear fluctuations in magnetized and unmagnetized collisionfree plasmas

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Fluctuations are a generic feature of all plasmas with finite random velocities of the plasma particles. Past research has concentrated predominantly on the fluctuations from collective weakly amplified/damped modes in the plasma using non-relativistic kinetic plasma equations. It is proposed to (1) extend the kinetic linear plasma fluctuation theory in unmagnetized plasmas calculating in particular the associated density and velocity fluctuation spectra of weakly propagating and weakly amplified/damped modes (collective and non-collective modes), and (2) develop the linear fluctuation theory for magnetized plasmas using the existing fluctuation theory of unmagnetized plasmas. These magnetized plasmas harbour an ordered magnetic field, uniform on spatial scales which are large compared to the wavelengths of the fluctuations. Due to the high conductivity of cosmic plasmas. no large-scale stationary electric fields exist in these systems. The most important unmagnetized cosmic plasma is the partially-ionized intergalactic medium (IGM) immediately after the reionization onset. The generation of aperiodic magnetic fluctuations in the IGM has been proposed by us as an important mechanism for the generation of cosmological seed magnetic fields. The associated turbulent density and velocity fluctuations can be used to place observational constraints on the strength of these fluctuations from dispersion measure, rotation measure and scintillation data as well as turbulent Doppler broadening of atomic and molecular lines, respectively. The general (with no restriction on the frequency of the fluctuations) kinetic linear fluctuation theory in magnetized plasmas using covariantly correct kinetic plasma equations has not been systematically studied before. The derivation of the generalized Kirchhoff laws for collective modes in magnetized plasmas allows us the quantitative calculation of the fluctuation intensities of electric and magnetic fields from collective modes for any given gyrotropic equilibrium plasma particle distribution $f_{a0}(\pper, \ppa )$ in magnetized plasmas, that take into account the effects of spontaneous emission and absorption. This permits in particular the quantitative modelling of the observed fluctuating magnetic field intensities in the solar wind plasma.