arXiv 1606.025822016-06-09physics.plasm-ph

冷等离子体中的相对论性准孤子和圆偏振嵌入孤子

Relativistic quasi-solitons and embedded solitons with circular polarization in cold plasmas

G. Sánchez-Arriaga, E. Siminos

备注：: 11 pages, 12 figures, corrected a reference
发表信息：: J. Phys. A: Math. Theor. 50 185501 (2017)
DOI：: 10.1088/1751-8121/aa65a0

摘要：

在一维相对论麦克斯韦流体模型的框架下，讨论了含不动离子的冷等离子体中局域电磁结构的存在性。新的部分本地化的解决方案被发现与有限差分算法，旨在定位数值精确解的麦克斯韦流体系统。这些解被称为准孤子，它是由一个局域的电磁波陷在一个空间扩展的电子等离子体波中构成的。它们被组织在以矢量势的节点数$p$为特征的族中，并且存在于$ω-V$平面中的连续参数范围中，其中$V$是传播速度，$ω$是矢量势角频率。参数研究表明，常见的完全局域相对论孤子是部分局域准孤子族中的特殊成员。因此，孤子解分支$p>1$参数嵌入准孤子的连续。另一方面，几何论证和数值模拟表明，$p=0$孤子只存在于小振幅或零速度的极限。Maxwell流体模型的直接数值模拟表明，$p>0$准孤子（和嵌入孤子）是不稳定的，会导致尾流激发，而$p=0$准孤子是稳定的.这有助于解释在激光-等离子体相互作用的数值模拟中普遍观察到的类似于$p=0$孤子的结构。

英文摘要：

The existence of localized electromagnetic structures is discussed in the framework of the 1-dimensional relativistic Maxwell-fluid model for a cold plasma with immobile ions. New partially localized solutions are found with a finite-difference algorithm designed to locate numerically exact solutions of the Maxwell-fluid system. These solutions are called quasi-solitons and consist of a localized electromagnetic wave trapped in a spatially extended electron plasma wave. They are organized in families characterized by the number of nodes $p$ of the vector potential and exist in a continuous range of parameters in the $ω-V$ plane, where $V$ is the velocity of propagation and $ω$ is the vector potential angular frequency. A parametric study shows that the familiar fully localized relativistic solitons are special members of the families of partially localized quasi-solitons. Soliton solution branches with $p>1$ are therefore parametrically embedded in the continuum of quasi-solitons. On the other hand, geometric arguments and numerical simulations indicate that $p=0$ solitons exist only in the limit of either small amplitude or vanishing velocity. Direct numerical simulations of the Maxwell-fluid model indicate that the $p>0$ quasi-solitons (and embedded solitons) are unstable and lead to wake excitation, while $p=0$ quasi-solitons appear stable. This helps explain the ubiquitous observation of structures that resemble $p=0$ solitons in numerical simulations of laser-plasma interaction.

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