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Anderson self-localization of light in pair plasmas

Maxim Lyutikov, Victor Gurarie

TL;DR

The paper identifies a novel regime of Anderson self-localization of light in pair plasmas, where a weakly nonlinear EM wave generates large, random density fluctuations that create a disordered dielectric environment. It develops three complementary viewpoints—PIC simulations of wave reflection and back-scattering, linear instability analysis with the Pierce-like parameter $\rho_L$, and a wave-equation approach including delta-disorder and adiabatic onset—to show that localization and even bulk reflection can occur for $a_0 \le 1$. It also uses Clemmow-frame PIC simulations to study localization of waves that originate inside the plasma, revealing bright-localized EM pockets with linearly polarized fields and random polarization structure between pockets. The results illuminate a kinetic, self-consistent mechanism for light confinement in relativistic plasmas and suggest possible implications for astrophysical fast radio bursts, as well as fundamental connections to Brillouin/Bragg scattering and FEL-like growth phenomena.

Abstract

We demonstrate that in pair plasma weakly nonlinear electromagnetic waves, $a_0 \leq 1$, experience Anderson self-localization. The beat between the driver and a back-scattered wave creates charge-neutral, large random density fluctuations $δn/n_0 \gg 1$, and corresponding fluctuations of the dielectric permittivity $ε$ (random plasma density grating). Propagating in quasi-1D, waves in a medium with spatially random self-created fluctuations of dielectric permeability experience localization. {In the linear regime, the instability can be classified as Induced Brillouin Scattering; it is described by the parameter $ρ_L = \left( a_0 { ω_{p}/ }ω\right)^{2/3} \leq 1 $, related to the Pierce parameter of Free Electron Lasers. In the cold case, the growth rate is $Γ\approx ρ_{L} ω$ ($a_0 $ is laser nonlinearity parameter, $ω_p$ is plasma frequency, $ω$ is the laser frequency). } Anderson self-localization of light leads to (i) reflection of EM waves by the under-dense pair plasma; (ii) a wave already present inside the plasma separates into bright trapped pockets and dark regions. Mild initial thermal spread with $Θ\equiv k_B T/(m_e c^2) \approx a_0^2$, restores wave propagation by suppressing the seeds of parametrically unstable density fluctuations. A circularly polarized driver produces linearly polarized structures, with position angle varying randomly between the bright pulses. Time-variability of the resulting density structures does not suppress localization due to remaining corrections (not white noise). We discuss possible applications to astrophysical Fast Radio Bursts.

Anderson self-localization of light in pair plasmas

TL;DR

The paper identifies a novel regime of Anderson self-localization of light in pair plasmas, where a weakly nonlinear EM wave generates large, random density fluctuations that create a disordered dielectric environment. It develops three complementary viewpoints—PIC simulations of wave reflection and back-scattering, linear instability analysis with the Pierce-like parameter , and a wave-equation approach including delta-disorder and adiabatic onset—to show that localization and even bulk reflection can occur for . It also uses Clemmow-frame PIC simulations to study localization of waves that originate inside the plasma, revealing bright-localized EM pockets with linearly polarized fields and random polarization structure between pockets. The results illuminate a kinetic, self-consistent mechanism for light confinement in relativistic plasmas and suggest possible implications for astrophysical fast radio bursts, as well as fundamental connections to Brillouin/Bragg scattering and FEL-like growth phenomena.

Abstract

We demonstrate that in pair plasma weakly nonlinear electromagnetic waves, , experience Anderson self-localization. The beat between the driver and a back-scattered wave creates charge-neutral, large random density fluctuations , and corresponding fluctuations of the dielectric permittivity (random plasma density grating). Propagating in quasi-1D, waves in a medium with spatially random self-created fluctuations of dielectric permeability experience localization. {In the linear regime, the instability can be classified as Induced Brillouin Scattering; it is described by the parameter , related to the Pierce parameter of Free Electron Lasers. In the cold case, the growth rate is ( is laser nonlinearity parameter, is plasma frequency, is the laser frequency). } Anderson self-localization of light leads to (i) reflection of EM waves by the under-dense pair plasma; (ii) a wave already present inside the plasma separates into bright trapped pockets and dark regions. Mild initial thermal spread with , restores wave propagation by suppressing the seeds of parametrically unstable density fluctuations. A circularly polarized driver produces linearly polarized structures, with position angle varying randomly between the bright pulses. Time-variability of the resulting density structures does not suppress localization due to remaining corrections (not white noise). We discuss possible applications to astrophysical Fast Radio Bursts.

Paper Structure

This paper contains 26 sections, 83 equations, 17 figures.

Table of Contents

  1. Introduction
  2. Reflection of weakly nonlinear EM wave by under-dense pair plasma: PIC simulations
  3. Mildly non-linear $a_0 =10^{-2}$ EM pulse
  4. Mild intensities $a_0 =0.1$: onset of Stimulated Raman Scattering in e-i case, strong bulk compression in $e^\pm$ case
  5. Bulk acceleration of pair plasma by in-falling EM wave
  6. Large density modulations created by EM wave in pair plasma
  7. Induced Brillouin and Bragg's scattering in pair plasma
  8. Linear regime of parametric instability
  9. Cold limit
  10. Thermal effects
  11. PIC simulations of the linear stage, temperature-induced transparency, and seeded back-scattering
  12. Scaling of the "nose" part with $a_0$ and density
  13. Temperature-induced transparency
  14. Seeded back-scattered wave
  15. Summary of important parameters
  16. ...and 11 more sections

Figures (17)

  • Figure 1: Interaction of weakly nonlinear waves $a_0 =10^{-2}$ with under-dense $n = 0.0125 n_{\rm cr}$ plasmas. Top panel: values of Poynting flux $F$ normalized to the incoming one for CP (so, LP is two times smaller); red lines are for pair plasma, blue lines for e-i plasma; circular (CP) and linear (LP) polarizations. Bottom row: density for CP (left) and LP (right) for the $e^\pm$ plasma. We observe huge density variations $\delta n/n_0 \gg 1$.
  • Figure 2: Reflection of a CP EM pulse by under-dense pair plasma (solid blue curve) if compared with e-i case (black dashed). Negative values of Poynting flux (zoomed insert) indicate reflection. Same parameters as Fig. \ref{['a001']}. In the pair plasma case, persistently negative Poynting flux is observed when the head to the pulse propagated thousands of wavelengths into the plasma.
  • Figure 3: Temporal evolution of a pulse in e-p and e-i cases; CP. $a_0=10^{-2}$. Shown are Poynting fluxes at different times $t_1, \, t_2, \, t_3$; blue line: e-i case, red lines: e-p case.
  • Figure 4: Annotated longer simulations of CP pulse with $a_0 =10^{-2}$ propagating in pair plasma. Shown are Poynting flux (red curves) and density (dark blue), both normalized to the incoming flux and unperturbed density. The EM wave penetrates into plasma only for a finite distance; the wave is Anderson-localized. For this run $n_x =20$.
  • Figure 5: The case of $a_0 =10^{-1}$, CP. Top panel: Poynting $F$ for $e-i$ and $e^\pm$ cases. Bottom panel: density sweep-up for pair plasma (notice that even for $a_0^2 = 10^{-1} \ll 1$ the resulting density increases is of the order of unity); parallel electric field for e-i plasma (notice onset of plasma oscillations - SRS - corresponding to the dip in EM intensity in the range $2000 \leq x/\lambda \leq 4000$).
  • ...and 12 more figures