Thermal fluctuation levels of magnetic and electric fields in unmagnetized plasma: The rigorous relativistic kinetic theory

<jats:p>Any fully ionized collisionless plasma with finite random particle velocities contains electric and magnetic field fluctuations. The fluctuations can be of three different types: weakly damped, weakly propagating, or aperiodic. The kinetics of these fluctuations in general unmagnetized plasmas, governed by the competition of spontaneous emission, absorption, and stimulated emission processes, is investigated, extending the well-known results for weakly damped fluctuations. The generalized Kirchhoff radiation law for both collective and noncollective fluctuations is derived, which in stationary plasmas provides the equilibrium energy densities of electromagnetic fluctuations by the ratio of the respective spontaneous emission coefficient and the true absorption coefficient. As an illustrative example, the equilibrium energy densities of aperiodic transverse collective electric and magnetic fluctuations in an isotropic thermal electron-proton plasmas of density ne are calculated as |δB|=(δB)2=2.8(nemec2)1/2g1/2βe7/4 and |δE|=(δE)2=3.2(nemec2)1/2g1/3βe2, where g and βe denote the plasma parameter and the thermal electron velocity in units of the speed of light, respectively. For densities and temperatures of the reionized early intergalactic medium, |δB|=6·10−18G and |δE|=2·10−16G result.</jats:p>