Chaos in the dynamics of electromagnetic solitons in relativistic degenerate plasmas

Abstract

We propose a coupled system for the nonlinear interaction between high-frequency, circularly polarized, intense electromagnetic (EM) waves and low-frequency electron-density perturbations, driven by the EM-wave ponderomotive force, in an unmagnetized plasma composed of fully degenerate relativistic electrons and stationary positive ions, including a higher-order correction to the nonlocal nonlinearity. We show that the modulational instability (MI) growth rate associated with the generation of EM envelope solitons gets significantly reduced with a slight increase in either the nonlocal nonlinear correction or the degeneracy parameter. Furthermore, a three-wave temporal model predicts the existence of quasiperiodic and chaotic states of EM solitons while interacting with longitudinal electron density perturbations. We show that the greater the degeneracy (or the higher the contribution from the nonlocal correction), the smaller the instability domain of modulation wave numbers; thus, degeneracy favors the stability of EM soliton evolution. The existence of temporal chaos in a low-dimensional model could be a signature of the development of spatiotemporal chaos in the complete nonlinear model, in which many electromagnetic solitons can be excited and saturated as they interact with electron plasma waves.

Figures (14)

• Figure 1: The modulationsl instability growth rate $\Gamma$ is plotted against the modulation wave number ($k$) for different values of the degeneracy parameter $R_0$ and $\sigma$ as in the legend.
• Figure 2: The real parts of the eigenvalues corresponding to Eq. \ref{['ch-eq']} are shown for the parameters, $R_0=1.2,~\sigma=0.16,~\beta_0=0.34$, and $N=1$. We observe that there is at least one positive eigenvalue in the entire domain of $k$, predicting the existence of chaos in the temporal model [Eq. \ref{['eq-reduced']}]. The overlapping of two curves with $\Re\lambda>0$ appears due to a pair of complex-conjugate eigenvalues.
• Figure 3: Bifurcation diagram and the LLE are shown for the set of parameters, $R_0=0.8,~\sigma= 0.06,~N=1$, and $\beta_0=0.05$.
• Figure 4: The same as in Fig. \ref{['fig-bifur-lyap1']} but for a different value of $R_0$, $R_0=1.2$.
• Figure 5: The same as in Fig. \ref{['fig-bifur-lyap1']} but for a different value of $\sigma$, $\sigma= 0.12$.