<title>Application of solitons to the study of laser propagation into a thermonuclear plasma in the inertial confinement fusion</title>

Abstract

In this work we study the laser propagation in a thermonuclear plasma corresponding to implosion of Deuterium-Tritium pellets in the Inertial Confinement Fusion, by injecting energy provided by high power laser devices into a quiescent plasma and generating solitons. Having in mind that the electric field inside of plasma can be studied by means of a particular Non Linear Schrodinger Equation, we solve this equation as an inverse problem using the Inverse Scattering Transform method, that is a 2 by 2 eigenvalue problem, known as AKNS scheme, developed by Ablovitz, Kamp, Newell and Shabat. We obtain the pseudo potentials q and r if we suppose that the eigenvalue is invariant in time, and is representative of wave eigenvector, obtaining a solution that has a structure of soliton type. In the process, one change of variable for space and another for time are applied, and the relation between the pseudo potentials is given by r equals -q. Discretization of Non Linear Schrodinger Equation, solved by Inverse Scattering Transform are give by Ablovitz et al. These solitons are generated near critical layer where w<SUB>0</SUB> approximately equals w<SUB>p</SUB>, being w<SUB>0</SUB> the laser frequency and w<SUB>p</SUB> the plasma frequency, exhibit a change in electronic density profile and are caused by ponderomotive force of laser radiation. The electronic density is a function of mean square of electric field. The dispersion relation is representative of an inhomogeneous plasma. Finally, the electric field is obtained as a function of space and time, showing a structure of soliton type.