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 n e are calculated as jdBj ¼ ffiffiffiffiffiffiffiffiffiffiffi ðdBÞ 2 q ¼ 2:8ðn e m e c 2 Þ 1=2 g 1=2 b 7=4 e and jdEj ¼ ffiffiffiffiffiffiffiffiffiffiffi ðdEÞ 2 q ¼ 3:2ðn e m e c 2 Þ 1=2 g 1=3 b 2 e , where g and b e 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, jdBj ¼ 6 Á 10 À18 G and jdEj ¼ 2 Á 10 À16 G result. V C 2014 AIP Publishing LLC. [http://dx.

No abstract

Starting from the recently derived general expressions for the electromagnetic fluctuation spectra (electric and magnetic field) from uncorrelated plasma particles in plasmas with an uniform magnetic field, the case of strictly parallel (k⊥=0) oriented wave vectors with the respect to the uniform magnetic field direction is investigated. To derive fluctuation spectra valid in the entire complex frequency plane, the relevant dispersion functions and form factors are analytically continued to negative values of the imaginary part of the frequency for arbitrary gyrotropic plasma particle distribution functions. The generalized fluctuation-dissipation theorems for non-collective fluctuations in isotropic equal-temperature thermal distribution functions for general complex values of the frequency of the fluctuations with parallel wave vectors are derived.

SUMMARYStarting from the principle of virtual work and applying the transformation of Legendre, a mixed finite element method is presented. This is done for the geometrically linear and nonlinear beam analysis including shear deformation. Lagrange polynomials of order six are chosen as element shape functions, and several examples are calculated, in order to show the efficiency of the numerical algorithm.

During the past myon and prior electron annihilation epoch of the early universe the electron–positron pair number density was very high as the pairs were in thermal equilibrium with the intense superluminal photons at temperatures k B T > 1 MeV. With classical plasma fluctuation theory, it is shown that these pairs generate random electric and magnetic fields in the form of collective damped aperiodic fluctuations with very high tera-Gauss strengths on spatial scales greater than cm with a 100% volume filling factor. The associated field decay with time by damping is compensated by their perpetually re-excitation due to the spontaneous emission by the pairs to maintain a lasting fluctuation level.