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arXiv 2005.08565physics.plasm-ph
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相对论简并laser等离子体中电磁孤子的稳定性和演化

Stability and evolution of electromagnetic solitons in relativistic degenerate laser plasmas

Sima Roy, A. P. Misra

摘要:

研究了线偏振强激光与相对论简并等离子体非线性相互作用形成的电磁孤子的动力学行为。在相对论动力学的慢运动近似下,弱非线性电磁包络的演化由具有局域和非局域非线性的广义非线性薛定谔(GNLS)方程描述.利用Vakhitov-Kolokolov准则,研究了GNLS方程的电磁孤子解的稳定性.利用孤子速度、孤子本征频率以及简并参数$R=p_{Fe}/m_ec$(其中$p_{Fe}$为费米动量,$m_e$为电子质量,$c$为真空中光速)的影响,给出了不同的稳定区和不稳定区.结果表明,从弱相对论$(R\ll1)$到超相对论$(R\gg1)$简并态,稳定区向不稳定区移动,并显著减小.分析预测结果与GNLS方程的模拟结果吻合较好。结果表明,孤立子解是稳定的。然而,运动孤子可以是稳定的或不稳定的,这取决于孤子的速度,本征频率或简并参数的值。后者具有强简并$(R>1)$,最终导致孤子坍缩。

英文摘要:

The dynamical behaviors of electromagnetic (EM) solitons formed due to nonlinear interaction of linearly polarized intense laser light and relativistic degenerate plasmas are studied. In the slow motion approximation of relativistic dynamics, the evolution of weakly nonlinear EM envelope is described by the generalized nonlinear Schr{ö}dinger (GNLS) equation with local and nonlocal nonlinearities. Using the Vakhitov-Kolokolov criteria, the stability of an EM soliton solution of the GNLS equation is studied. Different stable and unstable regions are demonstrated with the effects of soliton velocity, soliton eigenfrequency, as well as the degeneracy parameter $R=p_{Fe}/m_ec$, where $p_{Fe}$ is the Fermi momentum and $m_e$ the electron mass, and $c$ is the speed of light in vacuum. It is found that the stability region shifts to an unstable one and is significantly reduced as one enters from the regimes of weakly relativistic $(R\ll1)$ to ultrarelativistic $(R\gg1)$ degeneracy of electrons. The analytically predicted results are in good agreement with the simulation results of the GNLS equation. It is shown that the standing EM soliton solutions are stable. However, the moving solitons can be stable or unstable depending on the values of soliton velocity, the eigenfrequency or the degeneracy parameter. The latter with strong degeneracy $(R>1)$ can eventually lead to soliton collapse.

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