Asymmetry-driven structure formation in pair plasmas

The nonlinear propagation of electromagnetic waves in pair plasmas, in which the electrostatic potential plays a very important but subdominant role of a “binding glue” is investigated. Several mechanisms for structure formation are investigated, in particular, the “asymmetry” in the initial temperatures of the constituent species. It is shown that the temperature asymmetry leads to a (localizing) nonlinearity that is qualitatively different from the ones originating in ambient mass or density difference. The temperature-asymmetry-driven focusing-defocusing nonlinearity supports stable localized wave structures in 1–3 dimensions, which, for certain parameters, may have flat-top shapes.

Figure 1

The effective potential $V$ vs the amplitude $A$ for different values of the nonlinear frequency shift $\lambda$. The curve “a” corresponds to $\lambda >{\lambda }_{cr}^{\left(1\text{D}\right)}\simeq 0.2162$, the curve “b” has $\lambda ={\lambda }_{cr}^{\left(1\text{D}\right)}$, and the curve “c” corresponds to $0<\lambda <{\lambda }_{cr}^{\left(1\text{D}\right)}$.

Figure 2

Nonlinear dispersion relations: the effective eigenvalue $\lambda$ as a function of $A_m$. The boundary line (dotted) corresponds to critical value $\lambda ={\lambda }_{cr}^{\left(1\text{D}\right)}$ analytically found only for 1D. The other three lines represent, respectively, the 1D, 2D, and 3D dispersion relations.

Figure 3

Stationary soliton solution for 1D for different critical eigenvalues. Plot a corresponds to ${\lambda }_{cr}=0.19315$ with $A_m=1$; plot b corresponds to ${\lambda }_{cr}=0.21583$ with $A_m=1.4$ and plot c corresponds to ${\lambda }_{cr}=0.21622$ with $A_m=1.47$, respectively. The plot c represents the flat-top soliton solution.

Figure 4

Stationary soliton solution for 2D for different critical eigenvalues. Plot a corresponds to ${\lambda }_{cr}=0.12789382$ with $A_m=1$; plot b corresponds to ${\lambda }_{cr}=0.17891793$ with $A_m=1.4$ and plot c corresponds to ${\lambda }_{cr}=0.20299496$ with $A_m=1.57$ respectively. The plot c represents the flat-top soliton solution.

Figure 5

Stationary soliton solution for 3D for different critical eigenvalues. Plot a corresponds to ${\lambda }_{cr}=0.6774722$ with $A_m=1$; plot b corresponds to ${\lambda }_{cr}=0.12451945$ with $A_m=1.4$ and plot c corresponds to ${\lambda }_{cr}=0.19222242$ with $A_m=1.67$, respectively. The plot c represents the flat-top soliton solution.

Figure 6

The dependence of the photon number $N$ on the amplitude $A_m$ for 2D and 3D. Normalized photon numbers correspond to $N^{\left(2\text{D}\right)}$ (solid line) and ${10}^{-1}{N}^{\left(3\text{D}\right)}$ (dashed line). For 2D (3D) the threshold energy for the existence of soliton is $N_{cr}=11.6$ (236.8).