Models of Nonlinear Propagation of Relativistically Intense Ultrashort Laser Pulses in Plasmas

Abstract

In this chapter, we examine a number of basic mathematical models of interactions of relativistically intense, ultrashort laser pulses with cold underdense plasmas. The general equations discussed in Chap. 2 are too complicated to treat directly to describe the nonlinear propagation of powerful laser radiation in plasmas (this would entail extremely massive computations and make it hardly possible to derive any analytical results); substantial model simplifications can stem from the fact that in plasmas obtained by ionization of gaseous targets, the laser pulse frequency is much greater than the plasma electron frequency. First, this circumstance makes it possible to average the equations describing the medium’s response to the laser pulse electromagnetic field, after which the fluid dynamics equations become much simpler. Second, the traditional nonlinear optics approach of introducing an envelope approximation appears productive in the powerful laser—plasma interactions theory as well. The electromagnetic field’s slow amplitude and fast phase can be introduced, assuming that this amplitude varies slowly on the laser radiation wavelength scale. As a result, the evolution of this amplitude is described by a nonlinear Schroedinger equation instead of the wave equation.