Propagational quasi-Hamiltonian functional and stability analysis of finite Airy-Gaussian beams in uniform dense plasma

Abstract This paper investigates the nonlinear propagation dynamics of finite Airy-Gaussian (AiG) laser beams in a uniform dense collisionless plasma using the Wentzel-Kramers-Brillouin (WKB) and paraxial ray approximations. Instead of treating the coupled beam width parameter differential equations (BWPDEs) solely as evolution equations, the beam propagation is analysed within an equivalent classical dynamical framework. The beam width evolution is reformulated as a two-dimensional dynamical system governed by propagational quasi-Hamiltonian functional and an effective pseudo-potential. An energy-like propagational quasi-Hamiltonian functional is derived characterizes the nonlinear beam dynamics. The evolution of the system is further interpreted through kinetic energy-like and effective pseudo-potential terms. The analysis reveals that, the quasi-Hamiltonian functional governs the self-trapping, oscillatory self-focusing and defocusing behavior of the beam. Different propagation regimes are identified according to the evolution of the quasi-Hamiltonian functional; near-zero values correspond to self-trapping, bounded oscillations indicate stable propagation and divergent behaviour signifies beam defocusing. The condition for self-trapping, self-focusing, defocusing and beam stability are further examined through a Hessian matrix analysis. The proposed framework provides deeper physical insights into the nonlinear dynamics of finite AiG beams and extends the conventional beam width parameter approach by revealing the underlying dynamical structure of beam propagation in plasma.