Monte Carlo simulation method for incoherent Thomson scattering spectra from arbitrary electron distribution functions

TL;DR

The paper addresses computing incoherent Thomson scattering spectra from arbitrary electron distribution functions in high-temperature plasmas using a Monte Carlo forward model. It treats the scattering process as a superposition of photon-electron interactions and leverages macro-particles to reduce computational cost while yielding natural statistical uncertainties. Validation against relativistic Maxwellian and relativistic kappa distributions shows good agreement with analytical and numerical spectra, confirming the method’s accuracy across relevant regimes. This approach facilitates forward modeling and Bayesian inference for non-Maxwellian distributions, with potential extensions to incident-spectrum and detector responses to support diagnostic design and inverse problems.

Abstract

We developed a Monte Carlo simulation method to calculate incoherent Thomson scattering spectra in high temperature plasmas. The basic idea is to treat the entire scattering process as the superposition of individual photon-electron interactions. We introduce macro-particles, referred from particle-in-cell simulations, to reduce the computational cost, and obtain scattered spectra within a reasonable computational time. Since the velocity of the interacting electron is randomly sampled from an electron distribution function, the method can be applied to arbitrary electron distribution functions provided an appropriate sampling scheme is available. We present simulation results for relativistic Maxwellian and kappa distribution functions, and compare them with both analytical and numerical spectra for validation. The simulated spectra show good agreement with both analytical and numerical results, demonstrating that the Monte Carlo simulation method can reliably reproduce incoherent Thomson scattering spectra.

Figures (6)

• Figure 1: The scattering geometry within the scattering plane.
• Figure 2: The flow chart of Monte Carlo simulation.
• Figure 3: (a) Scattered photon spectra from relativistic Maxwellian distribution function obtained by Monte Carlo simulation, numerical calculation of Eq. \ref{['eq:photon_spec_int']}, and approximate analytical model with the scattering angle of 163°. (b)--(d) Difference between numerical result and approximate model and Monte Carlo simulation at $T_e =1$, 10, and 100keV. The legends in (b)--(d) are the same.
• Figure 4: Signal-to-noise ratio and computational time as a function of number of macro-electrons at $T_e=10keV$. The red and blue markers indicate the signal-to-noise ratio and the computational time corresponding to the left and right axes, respectively.
• Figure 5: Scattered photon spectra from relativistic kappa distribution function with $T_e=1keV$ and $\kappa = 3.5$ obtained by Monte Carlo simulation and numerical calculation of Eq. \ref{['eq:photon_spec_int']} in (a) linear and (b) logarithmic scales. The legends in (a) and (b) are the same.