Numerical investigation of guiding of Gaussian laser pulse in plasma channel with radial variation in presence of Kerr effect by Runge–Kutta and extrapolation methods

• Published in: Indian journal of physics 2022-12, Vol.96 (14), p.4307-4314
• Main Authors: Ghalandari, M., Babayar-Razlighi, B.
• Format: Article
• Language: English
• Subjects: Astrophysics and Astroparticles; Boundary value problems; Extrapolation; Kerr effects; Numerical methods; Original Paper; Physics; Physics and Astronomy; Pulse amplitude; Runge-Kutta method; Wave fronts
• ISSN: 0973-1458; 0974-9845
• DOI: 10.1007/s12648-022-02357-5

In this paper, guiding of Gaussian laser pulse in plasma channel in the presence of Kerr effect is studied numerically. We assume that the plasma channel has radial variation. We obtain matched condition to guide intense laser pulse through plasma channel in presence of Kerr effect. Using the SDE method, four coupled equations for the pulse amplitude, phase, spot size and wave front curvature will be derived. We apply two numerical methods for solving these equations, Runge–Kutta and extrapolation methods. We give the functional form of the nonlinear initial value problem and obtain some properties about the convergence of the methods. Since these are pure mathematical considerations, they are mentioned in Appendix section. The solutions obtained by the methods are compared together and we see that the solutions are the same. Hence, the proposed methods are applicable and have the sufficient accuracy for the current system of equations.