ANALYSIS OF SELF-FOCUSING OF LASER BEAMS IN QUANTUM PLASMA

Abstract

The relativistic self-focusing of laser beams in quantum plasma has drawn considerable inter est because of its applications in inertial confinement fusion, charged-particle acceleration, and high-energy-density physics. In this dissertation, we study the propagation and self-focusing of non-conventional beam profiles, namely Bessel-Gaussian and Elliptical-Gaussian beams, in magnetized quantum plasmas with spatial density gradients. The paper considers combinations of beam geometry, magnetic fields and plasma inhomogeneity which have never been system atically treated in previous work. The study uses the quantum hydrodynamic (QHD) model, incorporating the Bohm potential, exchange-correlation effects, relativistic ponderomotive forces, and the influence of an exter nal magnetic field. Applying the paraxial approximation and the Wentzel–Kramers–Brillouin (WKB) method reduces Maxwell’s equations to a differential equation governing beam-width evolution along the propagation axis. For Paper-1 on Bessel-Gaussian beams, this results in a second-order nonlinear ordinary differential equation, solved numerically using the fourth-order Runge-Kutta method. Simulations are carried out for high laser frequencies of (1.78×1020s−1), electron densities of (n0 = 4 × 1019cm−3) satisfying (χ ≥ 1), an axial magnetic field of (ωc/ω = 0.3), and exponential density ramp parameters (d = 5,10,20). Key findings from Paper-1 show that: (1) thermal quantum plasma enables much stronger and more sustained self-focusing than classical and cold quantum plasmas; (2) exponential den sity ramps greatly accelerate self-focusing, maintaining high intensity over multiple Rayleigh lengths; (3) Bessel-Gaussian beams outperform Gaussian beamsbecauseoftheirring-shaped in tensity profile; (4) the transverse wave parameter µ significantly enhances self-focusing; and (5) beyond a threshold, increasing laser intensity reduces self-focusing due to relativistic mass satu ration and exchange-correlation effects introducing competingnonlinearities. Paper-2(Elliptical Gaussian beams in magnetized quantum plasma with tangential densityramps)isinanadvanced stage with mathematical framework and numerical analysis under way.