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arXiv 1012.1139physics.plasm-ph
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超相对论简并稠密等离子体中二维静电波包的调制不稳定性和非线性演化

Modulational instability and nonlinear evolution of two-dimensional electrostatic wave packets in ultra-relativistic degenerate dense plasmas

A. P. Misra, P. K. Shukla

摘要:

研究了超相对论(UR)简并稠密电子-离子等离子体中静电波包的非线性传播,其动力学过程由非局域二维非线性类薛定谔方程控制.然后利用耦合方程组研究了均匀波列对多维形式的微扰的调制不稳定性。得到了MI的条件,并证明了与简并电子UR压力相关的无量纲参数$β\proptoλ_C n_0^{1/3}$($λ_C$是约化康普顿波长,$n_0$是粒子数密度)使$n_{0}\sim10^{30}$ cm $^{-3}$处的稳定(不稳定)区域向更高密度处的不稳定(稳定)区域(即$n_{0}\gtrsim7\times10^{33}$)移动.研究还发现,$n_{0}$的值越高,调制波数越低时截止MI的增长率越低。此外,数值研究了波包的动力学演化。我们表明,它们要么分散或爆破在有限的时间内,当波的作用是低于或高于阈值。这些结果对于理解UR简并致密等离子体中调制波包的性质及其多维演化,例如白矮星{和/或}前超新星恒星内部的调制波包的性质具有重要意义.

英文摘要:

We consider the nonlinear propagation of electrostatic wave packets in an ultra-relativistic (UR) degenerate dense electron-ion plasma, whose dynamics is governed by the nonlocal two-dimensional nonlinear Schr{ö}dinger-like equations. The coupled set of equations are then used to study the modulational instability (MI) of a uniform wave train to an infinitesimal perturbation of multi-dimensional form. The condition for the MI is obtained, and it is shown that the nondimensional parameter, $β\proptoλ_C n_0^{1/3}$ (where $λ_C$ is the reduced Compton wavelength and $n_0$ is the particle number density), associated with the UR pressure of degenerate electrons, shifts the stable (unstable) regions at $n_{0}\sim10^{30}$ cm$^{-3}$ to unstable (stable) ones at higher densities, i.e. $n_{0}\gtrsim7\times10^{33}$. It is also found that {the} higher the values of $n_{0}$, the lower is the growth rate of MI with cut-offs at lower wave numbers of modulation. Furthermore, the dynamical evolution of the wave packets is studied numerically. We show that either they disperse away or they blowup in a finite time, when the wave action is below or above the threshold. The results could be useful for understanding the properties of modulated wave packets and their multi-dimensional evolution in UR degenerate dense plasmas, such as those in the interior of white dwarfs {and/or} pre-Supernova stars.

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