Time evolution of plasmas using the exact solution of the Boltzmann equation in the presence of an intense laser field

Abstract

In a recent paper, using the Volkov solution of the minimally coupled Dirac equation, we developed the concept of the quasifree states of the electron from a kinematical point of view [Rashid, Phys. Rev. A 38, 2525 (1988)]. Using these concepts, we present a coupling (decoupling) scheme that separates the kinematical factors from the dynamical ones. When the electrons in a gas are assumed to be in quantum states having quasi-four-momentum, then the Boltzmann equation reduces to a form that lends itself easily to the methods of separation of the variables. The solution is obtained as the product of a time-dependent part and a time-independent part. The latter is assumed to be just the initial distribution function, in which case the time-dependent part is found to be linked to the scattering cross section of the electrons. We assume a high-Z plasma where electron-ion collisions dominate over electron-electron collisions. The complete solution is finally obtained by normalizing the product solution. The first case we consider is a cold plasma, so that the energy of the photon is much greater than the mean kinetic energy of the electron and the electrons are assumed to form a Maxwellian gas. The cross section calculated under the Born approximation from our previous paper is used and the laser intensity is assumed to be such that the Kibble parameter is much smaller than unity. The time-dependent solution is surprisingly found to be Maxwellian still but with the temperature increasing with time. The second case concerns a hot plasma with a mean electron energy much greater than the photon energy but still less than its rest mass energy. The final normalization gives us a non-Maxwellian distribution but is reduced to an analytically closed form so that it is easily tractable. The temperature is still found to be increasing, but now we get a difference in the time dependence between the amplitude part and the exponential part.