Abstract
In this article we present a discussion and overview of mathematical result of the self-focusing of a Langmuir wave which governs Zakharov system and has studied the self- focusing of a Langmuir wave following by Gaussian distribution. Langmuir wave propagates through uncharged plasma which governed by Zakharov systems. The phenomenon plays a vital role in the Dynamics. We present the article mathematical model with effect of Landou damping. Relativistic mass oscillation and ponderomotive force on electrons of the ionized plasma encouraged the Langmuir wave which resists the self-focusing effect when damping is ignored. The Beam radius gets narrow. when it further propagates considering the paraxial ray’s approximation, the self-focusing length Rn. It shows that characteristics of varying bandwidth distance of propagation in relativistic plasma.
Highlights
Laboratory and many space observations have proved that there have been lots of evidences for the existence of Langmuir wave [1]
Langmuir wave propagates in a unmagnetized or less magnetic plasma can be described with the help of Zakharov systems
In 1920 Langmuir wave discovered by Irvin Langmuir and Levi Tonks [5]. when plasma wave accelerate electron and its acceleration is in the comparision of phase velocity of the wave and this process performs in the form of damp mode which is known as Landau damping [6] when in any conducting media electron density changes its value fast oscillatory form in the ultraviolet region [7]
Summary
Laboratory and many space observations have proved that there have been lots of evidences for the existence of Langmuir wave [1]. Collective charged particle accelerator has been centre of both theoretical and experimental research from last few years [8] In this process two laser beam of different frequencies ω1 & ω2 and wave number K1 and K2 respectively are established in plasma. The propagation of Langmuir wave in homogeneous plasma can outcomes as self-focusing by developing a density depression in the ionized plasma and by increasing the electron mass through relativistic effect [11]. Present applied process ignores an important effect, for example the parametric coupling of Langmuir mode to the ionized acaustic wave This opposes the analysis to νosc < νoscth where represents the thershold value of varying velocity for parametric excitation. In part 2 we discussed a simple overview and analysis of self-focusing using eikonal approach. we determined an expression for the beam width parameter and in part 3 study its characteristics with distance of propagation
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