Bayesian inference of ion velocity distribution function from laser-induced fluorescence spectra

S Tokuda,H Arakawa,K Terasaka,S Inagaki,Y Kawachi,K Yamasaki,M Sasaki

doi:10.1038/s41598-021-00138-4

Abstract

The velocity distribution function is a statistical description that connects particle kinetics and macroscopic parameters in many-body systems. Laser-induced fluorescence (LIF) spectroscopy is utilized to measure the local velocity distribution function in spatially inhomogeneous plasmas. However, the analytic form of such a function for the system of interest is not always clear under the intricate factors in non-equilibrium states. Here, we propose a novel approach to select the valid form of the velocity distribution function based on Bayesian statistics. We formulate the Bayesian inference of ion velocity distribution function and apply it to LIF spectra locally observed at several positions in a linear magnetized plasma. We demonstrate evaluating the spatial inhomogeneity by verifying each analytic form of the local velocity distribution function. Our approach is widely applicable to experimentally establish the velocity distribution function in plasmas and fluids, including gases and liquids.

Highlights

The velocity distribution function is a statistical description that connects particle kinetics and macroscopic parameters in many-body systems
We propose a novel approach to evaluate which form of the velocity distribution function assumed for an observed spectrum is valid
We introduce our models while briefly reviewing the relationship between the velocity distribution function and their representation in the absorption frequency domain

Summary

Introduction

The velocity distribution function is a statistical description that connects particle kinetics and macroscopic parameters in many-body systems. Laser-induced fluorescence (LIF) spectroscopy is utilized to measure the local velocity distribution function in spatially inhomogeneous plasmas. We propose a novel approach to select the valid form of the velocity distribution function based on Bayesian statistics. We formulate the Bayesian inference of ion velocity distribution function and apply it to LIF spectra locally observed at several positions in a linear magnetized plasma. We demonstrate evaluating the spatial inhomogeneity by verifying each analytic form of the local velocity distribution function. Changes in internal degrees of freedom, such as the Zeeman and Stark effects, make it more challenging to identify the explicit expression of the velocity distribution function. We propose a novel approach to evaluate which form of the velocity distribution function assumed for an observed spectrum is valid. We successfully verify that each local ion velocity distribution function is Maxwellian rather than other candidates

Methods

Results

Conclusion