Unified kinetic theory of induced scattering: Compton, Brillouin, and Raman processes in magnetized electron and positron pair plasma

TL;DR

The work develops a unified kinetic framework to describe induced scattering—comprising ICS, SBS, and SRS—in strongly magnetized electron-positron plasmas. It derives dispersion relations for three density-fluctuation modes (ordinary, neutral, charged) from a ponderomotive-force-based coupling and provides analytic growth rates across weak/strong coupling and noncollective/collective density regimes. The study reveals how magnetic-field strength and density regulate which instability dominates in each mode, and shows that SRS can operate in the charged mode under magnetization, unlike in unmagnetized pair plasmas. It also extends results to broadband incident waves, clarifies physical interpretations, and discusses implications for FRB emission and magnetar magnetospheres, with numerical validations matching the analytic predictions.

Abstract

We present a unified theoretical framework for induced (stimulated) scattering-parametric instabilities of electromagnetic waves, including induced Compton, stimulated Brillouin, and stimulated Raman scattering (SRS) in strongly magnetized electron-positron pair plasma. By solving the dispersion relations derived from kinetic theory, taking into account the ponderomotive force due to the beat of incident and scattered waves, we obtain analytical expressions for the linear growth rates of the ordinary, neutral, and charged modes of density fluctuations. Our results clarify which type of scattering dominates under different thermal coupling, resonance, and density conditions. In strong magnetic fields, scattering of perpendicularly polarized waves is generally suppressed, but by different powers of the cyclotron frequency. Moreover, SRS, which is forbidden in unmagnetized electron and positron pair plasma, becomes possible in the charged mode. This framework enables a comprehensive evaluation of induced scattering in extreme astrophysical and laboratory plasma, such as fast radio burst (FRB) emission and propagation in magnetar magnetospheres.

Figures (6)

• Figure 1: The maximum linear growth rate of induced scattering excited by the ordinary mode as a function of the strength parameter of the incident EM wave. The orange solid line represents the growth rate of ICS, given by Eq. \ref{['eq:maximum_growth_rate_no_magnetic_Compton_Brillouin']}. The red dashed-dotted line corresponds to the growth rate of SBS in the strong coupling regime, given by Eq. \ref{['eq:induced_Brillouin_nomagnetic_maximum_growth_rate']}. The green dotted line indicates the growth rate of SBS in the weak coupling regime, given by Eq. \ref{['eq:stimulated_Brillouin_weak_ordinary']}. The purple vertical dotted line marks the value of the strength parameter at the transition from weak to strong coupling, as described by Eq. \ref{['eq:transition_point_for_ordinary_mode']}. The blue dots show numerical solutions of the dispersion relation, Eq. \ref{['eq:dispersion_relation_no_magnetic_Brillouin']}. The following parameters are used: electron thermal velocity $v_{\mathrm{th}}/c=10^{-3}$, plasma frequency $\omega_{\mathrm{p}}/\omega_0=10^{-2}$, and incident wave frequency $\omega_0=2\pi \times 10^9~\mathrm{Hz}$.
• Figure 2: The dependence of the maximum linear growth rate of induced scattering for the neutral mode on the incident wave amplitude \ref{['eq:definition_of_eta']}. The orange solid line represents the growth rate of ICS, as given by Eq. \ref{['eq:growth_rate_induced_Compton_subdominant_Brillouin']}. The red dashed-dotted line corresponds to the SBS growth rate in the strong coupling regime, as given by Eq. \ref{['eq:induced_Brillouin_neutral_maximum_growth_rate']}. The green dotted line denotes the SBS growth rate in the weak coupling regime, given by Eq. \ref{['eq:stimulated_Brillouin_weak_neutral']}. The purple vertical dashed line indicates the incident wave amplitude at the transition point from weak to strong coupling, as given by Eq. \ref{['eq:Transition_point_eta_neutral']}. Blue dots represent the numerically obtained solutions of the dispersion relation in Eq. \ref{['eq:dispersion_relation_neutral_Brillouin2']}. The parameters used are $v_{\mathrm{th}}/c=10^{-4}$, $\omega_{\mathrm{p}}/\omega_0=10^{-2}$, $\omega_{\mathrm{c}}/\omega_0=10^{2}$, and $\omega_0=2\pi\times 10^9~\mathrm{Hz}$.
• Figure 3: The further subdivision of the charged mode instability classification, as summarized in Tab. \ref{['tab:roadmap_coupling']}, according to plasma density and temperature. The horizontal axis shows the dimensionless plasma frequency, while the vertical axis represents the dimensionless thermal velocity. The solid black diagonal line denotes the boundary between the low density and intermediate/high density regimes, as defined by Eqs. \ref{['eq:charged_mode_instability_thin_condition_Brillouin']} and \ref{['eq:induced_Raman_condition_Brillouin']}. The black dashed line indicates the boundary between the intermediate and high density regimes, following Eqs. \ref{['eq:induced_Raman_condition_Brillouin']} and \ref{['eq:charged_mode_instability_dense_condition_Brillouin']}. The dominant induced scattering process in each density regime (ICS: induced Compton scattering, SRS: stimulated Raman scattering, SBS: stimulated Brillouin scattering) is indicated within the diagram. For simplicity, the subluminal effect $(1+\omega_{\mathrm{p}}^2/\omega_{\mathrm{c}}^2)$ appearing in Eq. \ref{['eq:Alfven_velocity_Brillouin']} is neglected by assuming it is of order unity 2025PhRvD.111f3055N. Note also that, in the high density regime, strong coupling does not occur because, as discussed in Eq. \ref{['eq:weak_coupling_Debye_screening_henkei']}, the incident wave amplitude $a_{\text{e}} \omega_0/\omega_{\text{c}}$ always satisfies the weak coupling condition as long as it remains within the linear regime.
• Figure 4: Dependence of the maximum linear growth rate of induced scattering excited by the charged mode on the strength parameter of the incident EM wave in the low density regime \ref{['eq:charged_mode_instability_thin_condition_Brillouin']}. The orange solid curve represents the linear growth rate of ICS, given by Eq. \ref{['eq:maximum_growth_rate_magnetic2_Brillouin']}. The red dashed-dotted curve shows the linear growth rate of SBS in the strong coupling regime, as given by Eq. \ref{['eq:induced_Brillouin_charged_maximum_growth_rate']}. The purple vertical dotted line indicates the incident wave amplitude at the transition from the weak to strong coupling regime, as given by Eq. \ref{['eq:Transition_point_eta_neutral']}. Blue dots represent the results obtained from the numerical solution of the dispersion relation, Eq. \ref{['eq:dispersion_relation_charged_Brillouin2']}.
• Figure 5: The dependence of the maximum linear growth rate of induced scattering in the charged mode on the incident wave amplitude \ref{['eq:definition_of_eta']} for the intermediate density regime \ref{['eq:induced_Raman_condition_Brillouin']}. The orange solid line represents the growth rate of ICS as given by Eq. \ref{['eq:maximum_growth_rate_magnetic2_Brillouin']}, while the red dash-dotted line corresponds to the growth rate of SBS in the strong coupling regime as given by Eq. \ref{['eq:induced_Brillouin_charged_maximum_growth_rate']}. The purple vertical dotted line indicates the transition point of the incident wave amplitude between the weak and strong coupling regimes, as described by Eq. \ref{['eq:Transition_point_eta_neutral']}. The blue dots show the results obtained from numerical solutions of the dispersion relation in Eq. \ref{['eq:dispersion_relation_charged_Brillouin2']}.