International School of Cosmic Ray Astrophysics <<Maurice M. Shapiro>>

21^st Course: Astroparticle Physics: Yesterday, Today, and Tomorrow
1-7 August, 2018

The classical theory of linear uctuations in unmagnetized and magnetized plasmas is presented for given stationary, homogeneous and gyrotropic equilibrium plasma particle distribution functions f(0) a (~p). The most prominent gyrotropic equilibrium distribution functions are the Maxwellian, Kappa and power law distributions, supported by in-situ observations in the interplanetary solar wind plasma. For isotropic particle distribution functions f(0) a (p) with p = j~pj the equilibrium uc- tuation intensities can be calculated resulting from the competition of their spontaneous emission by the particles and their collisionless damping. Collective eigenmodes with a dispersion relation !(~k) provide most of the intensities. The theoretical results agree well with particle-in-cell simulations. Of particular interest for cosmic ray transport are transverse MHD waves (Alfven waves, magnetosonic waves) whose electric elds jEj are much smaller than their magnetic elds jBj. For anisotropic gyrotropic particle distribution functions f(0) a (p?; pk) kinetic instabil- ities with positive growth rates =(!) > 0 occur, so that the uctuation intensities grow exponentially in time. In this case coupled time-dependent kinetic equations for the particles and the uctuations have to be considered.