Pattern formation and spatiotemporal chaos in relativistic degenerate plasmas

TL;DR

The paper investigates nonlinear interactions between high-frequency EM waves and electron-acoustic density perturbations in relativistic degenerate plasmas using a one-dimensional Zakharov-like model for two electron populations. Through MI analysis and extensive numerical simulations across moderate, strong, and ultra-relativistic degeneracy, it demonstrates that many solitary patterns initially excited by modulational instability can collide and fuse, transferring energy to higher harmonics and transitioning from coherent envelope solitons to temporal, spatial, and spatiotemporal chaos. The emergence of STC, quantified via positive Lyapunov exponents and decaying correlation and mutual information, becomes more pronounced as degeneracy increases, suggesting EM wave turbulence as a potential feature of radiation spectra from compact astrophysical objects. These results highlight the role of degeneracy-driven nonlocal and nonlinear effects in pattern formation and energy redistribution, with implications for understanding spectral broadening and variability in astrophysical plasmas, while acknowledging the need for higher-dimensional studies and observational validation.

Abstract

We numerically study the nonlinear interactions of high-frequency circularly polarized electromagnetic (EM) waves and low-frequency electron-acoustic (EA) density perturbations driven by the EM wave ponderomotive force in relativistic plasmas {(moderate, strong, and ultra-relativistic)} with two groups of electrons--the population of relativistic degenerate dense electrons (bulk plasma) and the sparse relativistic nondegenerate (classical) electrons, and immobile singly charged positive ions. By pattern selection, we show that many solitary patterns can be generated and drenched through modulational instability of EM waves at different spatial length scales and that the EM wave radiation spectra emanating from compact astrophysical objects may not settle into stable envelope solitons but into different incoherent states, including the emergence of temporal and spatiotemporal chaos due to collisions and fusions among the patterns with strong EA wave emission. The appearance of these states is confirmed by analyzing the Lyapunov exponent spectra, correlation function, and mutual information {as quantitative evidence}. As a result, the redistribution of wave energy from initially exciting many solitary patterns at large scales to a few new incoherent patterns with small wavelengths in the system occurs, leading to the onset of turbulence in astrophysical plasmas.

Figures (13)

• Figure 1: The modulational instability growth rate ($\Gamma$) is plotted against the modulation wave number $(k)$ for different values of the degeneracy parameter $R_0$ as in the legend. In the inset, a zoomed in part of the variation of $\Gamma$ in a small interval of $k$, especially when $R_0$ is small $(<1)$, is shown.
• Figure 2: Initial excitations of master and harmonic solitary patterns for the EM wave field ($|A|$) and the associated density perturbation ($N$) are shown over the spatial domain in the moderate relativistic degenerate regime with $R_0=5$. It is seen that the pattern selections lead to the excitations of three, five and thirteen solitary modes corresponding to $k=0.15$ [subplot (a)], $k=0.11$ [subplot (b)], and $k=0.043$ [subplot (c)] respectively. The other fixed parameter values are $A_0=2$ and $b=0.5$.
• Figure 3: The EM wave field $|A(x,t)|$ is contour plotted with respect to space and time in the regime of moderate relativistic degeneracy with $R_0=5$ to show the excitation of solitary patterns (master mode and harmonic modes with different wavelengths) and their collisions and fusions into a new incoherent pattern. Subplots (a), (b) and (c) are corresponding to $k=0.15$, $k=0.11$, and $k=0.043$ respectively.
• Figure 4: The largest Lyapunov exponent (LLE) spectra of the time series is shown over the spatial domain $x$ in the moderate relativistic degenerate regime with $R_0=5$ corresponding to $k=0.15$ [Subplot (a)], $k=0.11$ [Subplot (b)], and $k=0.043$ [Subplot (c)].
• Figure 5: The correlation function [$C(r)$, subplot (a)] and the mutual information [$I(r)$, subplot (b)] are plotted against the distance $r$ between any two data points in the moderate relativistic degenerate regime with $R_0=5$ for different values of the modulation wave number $k$ as in the legends.