The linear electron acoustic waves propagating in plasmas with two kappa-distributed electrons and stationary ions are investigated. The temperatures of the two electrons are assumed to be same, but the kappa indices are not. It shows that if one kappa index is small enough and the other one is large enough, a weak damping regime of the electron acoustic waves exists. The dispersions and damping rates are numerically studied. The parameter spaces for the weakly damped electron acoustic waves are analyzed. Moreover, the electron acoustic waves in the present model are compared with those in other models, especially the plasmas with two-temperature electrons. At last, we perform Vlasov–Poisson simulations to verify the theory.

Transport processes in the fully ionized plasma with kappa-distribution and in strong magnetic field are studied. By analyzing the current density and the heat flux in the κ-distributed plasma, we derive the corresponding transport coefficients, including the electric conductivity, the thermal conductivity and thermoelectric coefficient. Besides, we derive the coefficients of Hall, Nernst and Leduc-Righi effects in the κ-distributed plasma. It is shown that these new transport coefficients depend strongly on the κ-parameter and only in the limit κ→∞, they recover the traditional forms in the plasma based on a Maxwellian distribution. We also numerically analyze the role of the κ-parameter in the κ-dependent transport coefficients.

Abstract:The rate coefficient formulae of unimolecular reactions are generalized to the systems with the power-law distributions based on nonextensive statistics, and the power-law rate coefficients are derived in the high and low pressure limits, respectively. The numerical analyses are made of the rate coefficients as functions of the ν-parameter, the threshold energy, the temperature and the number of degrees of freedom. We show that the new rate coefficients depend strongly on the ν-parameter different from one (thus from a Boltzmann-Gibbs distribution). Two unimolecular reactions, CH 3 CO→CH 3 +CO and CH 3 NC→CH 3 CN, are taken as application examples to calculate their power-law rate coefficients, which obtained with the ν-parameters slightly different from one can be exactly in agreement with all the experimental studies on these two reactions in the given temperature ranges.

We study the slowing down of a particle beam passing through the dusty plasma with power-law -distributions. Three plasma components, electrons, ions, and dust particles, can have a different -parameter. By using Fokker-Planck theory, the deceleration factor and slowing down time are derived and expressed by a hyper-geometric -function. Numerically, we study the slowing down property of an electron beam in the -distributed dusty plasma. We show that the slowing down in the plasma depends strongly on the -parameters of plasma components, and dust particles play a dominant role in the deceleration effects. We also show dependence of the slowing down on mass and charge of a dust particle in the kappa-distributed plasma.

We study the time behavior of the Fokker-Planck equation in Zwanzig's rule (the backward-Ito's rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation-dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker-Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution.