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

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.

Determining Metastable Ion Lifetime and History through Wave-Particle Interaction

“…Furthermore, since this model does not impose constraints on the ion orbits, it can be applied to systems with complicated ion dynamics. A detailed description of the model and its application are presented in [12] and [13]. The simulation results for f 1-LIF and f 2-LIF demonstrate a good agreement with the theoretical predictions, as shown in Fig.…”

“…Previous experimental results [9,10] suggest that there are limitations of this laser diagnostic technique due to the finite lifetime of metastable ions. Simulations based on our newly developed Lagrangian model for LIF [11][12][13] show that under circumstances where the metastable ion population is produced from direct ionization of neutrals, the velocity distribution measured using LIF will only faithfully represent processes which act on the ion dynamics in a time shorter than the metastable lifetime. For instance in wave measurements [14,15], the perturbed distribution f 1 (v, t) on these metastables cannot be correct if the wave period is greater than the metastable lifetime.…”

Measurement of wave-particle interaction and metastable lifetime using laser-induced fluorescence

“…Numerical simulations based on our newly developed Lagrangian model for LIF [12][13][14] show that under circumstances where the metastable ion population is produced from direct ionization of neutral atoms, the velocity distribution measured using LIF will only faithfully represent processes which act on the ion dynamics in a time shorter than the metastable lifetime. For instance, the LIF measured ion temperature on these metastables is only accurate when they live longer than the ionion collision mean free time.…”

Laser-induced fluorescence saturation effects on ion velocity distribution functions in the vicinity of reflecting surfaces

“…While being well developed and mastered, some experimental artifacts exist and have to be cautiously considered like laser beam absorption, 11 spatially inhomogeneous laser intensity, 12 Stark shift, 13 ion metastable cross section dependence on electron temperature, 14 and optical pumping saturation. [15][16][17][18] The LIF diagnostic is well fitted for plasma sheath investigation. It has been successfully applied to sheaths facing metal samples 11,19 and gave quantitatively good agreements with theory and simulations.…”

“…In this regime, the signal intensity is no more proportional to the laser power density as no more ions/atoms may be excited. 18 High laser power density also leads to a broadening of the measured velocity distribution function, especially when the spectral width of the laser is close to the transition's one. Indeed, the laser emission ray is, in simple cases, a gaussian function with a finite spectral width.…”