Coherent Rayleigh-Brillouin scattering: influences of intermolecular potentials and chirp rates

TL;DR

The paper presents a fast deterministic solver for coherent Rayleigh-Brillouin scattering spectra by solving the linearized Boltzmann equation using a fast spectral method, enabling each line shape to be computed in about one minute. It systematically analyzes how intermolecular potentials (via the viscosity index $\omega$) and chirp rate (via $\beta$ or $\tau$) shape the CRBS spectrum for monatomic and polyatomic gases, revealing pronounced sensitivity in the kinetic regime and characteristic asymmetries and Rayleigh ripples with rapid chirps. The polyatomic extension incorporates rotational degrees of freedom through a Wu et al. non-vibrating model with parameters $d_r$, $Z$, $f_t$, and $f_r$, showing how rotational energy exchange modulates Brillouin positions and spectral features. Overall, the work provides both physical insight and a practical computational tool for high-fidelity, non-intrusive diagnostics of rarefied gas flows, with potential for real-time interpretation of CRBS experiments.

Abstract

Chirped coherent Rayleigh-Brillouin scattering (CRBS) is a flow diagnostic technique that offers high signal-to-noise ratios and nanosecond temporal resolution. To extract information of dilute gas flow, experimental spectra must be compared with theoretical predictions derived from the Boltzmann equation. In this work, we develop a MATLAB code that deterministically solves the Boltzmann equation to compute CRBS spectra, enabling each line shape to be obtained in about one minute. We find that the CRBS spectrum is highly sensitive to the intermolecular potential, and that rapid chirping generates fine ripples around the Rayleigh peak along with spectral asymmetries.

Figures (5)

• Figure 1: Chirp-free CRBS spectra of a Maxwellian gas with $\omega = 1$ at different Knudsen numbers. In this and following figures, all spectra are normalized to their maximum magnitude.
• Figure 2: Comparisons of chirp-free CRBS spectra for different power-law intermolecular potentials.
• Figure 3: Chirped CRBS spectra for Maxwell gas at different chirp duration $\tau$.
• Figure 4: Chirp-free CRBS spectra of polyatomic gas with different values of rotational collision number $Z$, with rotational degrees of freedom $d_r=2$, translational Eucken factor $f_t=2.4$, and rotational Eucken factor $f_r=1.5$.
• Figure 5: Chirped CRBS spectra for a polyatomic Maxwell gas at different chirp duration $\tau$, with the rotational degrees of freedom $d_r=2$, rotational collision number $Z=1$, translational Eucken factor $f_t=2.4$, and rotational Eucken factor $f_r=1.5$.