# A Lagrangian model for laser-induced fluorescence and its application to measurements of plasma ion temperature and electrostatic waves

## TL;DR

This paper develops a Lagrangian model for laser-induced fluorescence (LIF) to accurately measure plasma ion temperature and electrostatic waves, accounting for optical pumping effects and metastable ion production methods.

## Contribution

The paper introduces a numerical Lagrangian model for LIF that incorporates optical pumping effects and metastable production from neutrals, improving measurement accuracy in plasma diagnostics.

## Key findings

- Optical pumping broadening affects ion velocity distribution measurements.
- Ion temperature measurements require metastable ions to have longer lifetimes than ion-ion collision times.
- Wave detection accuracy depends on wave period being shorter than metastable ion lifetime.

## Abstract

Extensive information can be obtained on wave-particle interactions and wave fields by direct measurement of perturbed ion distribution functions using laser-induced fluorescence (LIF). For practical purposes, LIF is frequently performed on metastable states that are produced from neutral gas particles and ions in other electronic states. If the laser intensity is increased to obtain a better LIF signal, then optical pumping can produce systematic effects depending on the collision rates which control metastable population and lifetime. We numerically simulate the ion velocity distribution measurement and wave-detection process using a Lagrangian model for the LIF signal for the case where metastables are produced directly from neutrals. This case requires more strict precautions and is important for discharges with energetic primary electrons and a high density of neutrals. Some of the results also apply to metastables produced from pre-existing ions. The simulations show that optical pumping broadening affects the ion velocity distribution function (IVDF) $f_0(v)$ and its first-order perturbation $f_1(v,t)$ when laser intensity is increased above a certain level. The results also suggest that ion temperature measurements are only accurate when the metastable ions can live longer than the ion-ion collision mean free time. For the purposes of wave detection, the wave period has to be significantly shorter than the lifetime of metastable ions for a direct interpretation. It is more generally true that metastable ions may be viewed as test-particles. As long as an appropriate model is available, LIF can be extended to a range of environments.