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

Abstract

In this work, we study the laser propagation in a thermonuclear plasma corresponding to implosion of deuterium-tritium pellets in 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 Schrödinger equation, we solve this equation as an inverse problem, using the Inverse Scattering Transform method, that is a 2 × 2 eigenvalue problem, known as the AKNS scheme, developed by Ablovitz, Kamp, Newell, and Shabat. We obtain the pseudopotentials q and r if we suppose that the eigenvalue is invariant in time, and is representative of a wave eigenvector, obtaining a solution that has a structure of the soliton type. In the process, one change of variable for space and another for time are applied, and the relation between the pseudopotentials is given by r = −q^*. Discretization of the non-linear Schrödinger equation, solved by inverse scattering transform are given by Ablovitz et al. (1999). These solitons are generated near the critical layer where w₀ ≅ w_p, w₀ being the laser frequency and w_p the plasma frequency, exhibit a change in electronic density profile and are caused by the ponderomotive force of laser radiation.