United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS INTERACTIONS OF TWO CO-PROPAGATING LASER BEAMS IN UNDERDENSE PLASMAS USING A GENERALIZED PEACEMAN-RACHFORD ADI FORM

A generalized Peaceman-Rachford (P-R) ADI form based on the regularized finite difference scheme is employed in order to study the interactions of two co-propagating laser beams in underdense plasmas. A numerical algorithm using the P-R ADI form is constructed for solution of coupled 2D time-dependent non-linear Shrödinger equations for quasineutral plasmas in paraxial approximation. The ability of the form to solve the equations is discussed, and its performance in simulating phenomena associated with the interactions in the presence of pondermotive nonlinearity and relativistic nonlinearity is examined. It is shown that the generalized P-R ADI form can accurately solve the coupled NLS equations. With simulation results, the form is shown to be suitable to simulate the interactions of two co-propagating laser beams with underdense plasma, and it can successively simulate the associated phenomena at varying conditions. MIRAMARE – TRIESTE December 2005