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arXiv 2408.04404physics.plasm-phastro-ph.HE
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相对论简并天体物理磁等离子体中电子声孤子的横向不稳定性

Transverse instability of electron-acoustic solitons in a relativistic degenerate astrophysical magnetoplasma

A. P. Misra, A. Abdikian

AI总结:

本文研究了相对论简并磁等离子体中电子声孤子的演化与横向不稳定性,推导出 ZK 和 mZK 方程,分析了相对论参数和简并参数对增长率的影响,并讨论了其在白矮星等天体环境中的应用。

摘要:

我们研究了相对论天体物理磁等离子体中小振幅电子声孤子(EASs)的非线性理论,该等离子体由双温电子组成:稀疏的相对论非简并经典电子群和完全简并的稠密相对论电子群(主要成分),并浸没在具有中和性静止离子背景的静态磁场中。通过使用带洛伦兹变换的多尺度约化摄动技术,推导出 Zakharov-Kuznetsov(ZK)方程和修正的 Zakharov-Kuznetsov(mZK)方程,以描述在两种不同相对论简并区间 $r_{d0}<50$ 和 $r_{d0}\gtrsim50$ 中电子声孤子的演化。研究了 ZK 和 mZK 方程的平面孤子解的特性以及孤子能量。我们表明,以与外部磁场成角度 $α$ 运动的孤子在横向长波扰动下可能是不稳定的。获得了不稳定性的增长率,并分析了相对论参数 $β_{\rm{cl}}=k_BT_{\rm{cl}}/m_ec^2$ 和简并参数 $r_{d0}$ 的影响,其中 $k_B$ 是玻尔兹曼常数,$T_{\rm{cl}}$ 是经典电子的温度。有趣的是,ZK 孤子即使对一阶扰动是稳定的,也可能在二阶修正中变得不稳定。此外,当 $α\rightarrow 38^\circ$ 时,ZK 孤子扰动的一阶增长率趋于消失,而 mZK 孤子的增长率在 $α\rightarrow 90^\circ$ 时趋于零。然而,根据角度 $α$ 的不同,发现增长率可以通过增大 $β_{\rm{cl}}$ 的值或减小 $r_{d0}$ 的值来降低。我们讨论了这些结果在天体物理等离子体中的应用,例如白矮星环境中的等离子体。

英文摘要:

We study the nonlinear theory of small-amplitude electron-acoustic solitons (EASs) in a relativistic astrophysical magnetoplasma consisting of two-temperature electrons: a sparse population of relativistic nondegenerate classical electrons and a group of fully degenerate dense relativistic electrons (main constituent) immersed in a static magnetic field with a neutralizing stationary ion background. By using the multiple-scale reductive perturbation technique with the Lorentz transformation, the Zakharov-Kuznetsov (ZK) and the modified Zakharov-Kuznetsov (mZK) equations are derived to describe the evolution of EASs in two different regimes of relativistic degeneracy: $r_{d0}<50$ and $r_{d0}\gtrsim50$. The characteristics of the plane soliton solutions of ZK and mZK equations and the soliton energy are studied. We show that the solitons moving at an angle $α$ to the external magnetic field can be unstable under transverse long-wavelength perturbations. The growth rates of instabilities are obtained and analyzed with the effects of the relativity parameter $β_{\rm{cl}}=k_BT_{\rm{cl}}/m_ec^2$ and the degeneracy parameter $r_{d0}$, where $k_B$ is the Boltzmann constant and $T_{\rm{cl}}$ is the temperature of classical electrons. Interestingly, the ZK solitons, even if it is stable for the first-order perturbations, can be unstable in the second-order correction. Furthermore, while the first-order growth rates of perturbations for ZK solitons tend to vanish as $α\rightarrow 38^\circ$, that for the mZK soliton goes to zero as $α\rightarrow 90^\circ$. However, depending on the angle $α$, the growth rates are found to be reduced either by increasing the values of $β_{\rm{cl}}$ or by decreasing the values of $r_{d0}$. The applications of our results to astrophysical plasmas, such as those in the environments of white dwarfs are discussed.

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