# Time-Resolved Imaging of Femtosecond Laser-Induced Plasma Expansion in a Nitrogen Microjet
## 3 Study of the Plasma Expansion Dynamics  
The interaction of the gas sample with the femtosecond pulses leads to the generation of a population of high-energy electrons through multiphoton ionization and electron tunnel ionization [12]. The laser-induced ionization of the gas occurs on the time scale of the pulse duration, which is significantly shorter than the characteristic gas dynamic response of the neutrals and ions undergoing expansion (\(\geq\)10 ns). The kinetics of the plasma, thus, occurs under field-free conditions and involves different interaction channels among the gas species (neutrals, ions and electrons), including electron impact ionization, electron-ion recombination, and dissociative recombination [13]. In femtosecond laser filaments, the plasma decay by collisional mechanisms mainly depends on the gas density and composition; it is commonly on the scale of tens of nanoseconds [14]. In turn, the kinetics of a plasma population governs the radiative lifetime of the emitting species. In the specific case of the 391-nm N\({}_{2}\)\({}^{+}\) component, the lifetime in a filament driven by femtosecond pulses in vacuum ranges from a few nanoseconds up to tens of nanoseconds [15; 16]. In a 2D fluorescence image the information on the density distribution of the emitting species is not directly related to the intensity distribution of the fluorescence, due to the collective nature of the radiative process. Indeed, the decay of excited molecules is due to both radiative and non-radiative deactivation processes, such as collisions. In this sense, the rates of radiative (\(k_{r}\)) and non-radiative (\(k_{nr}\)) decay mechanisms determine the emission quantum yield \(\phi=k_{r}/(k_{r}+k_{nr})\), which, in turn, is strongly related to the fluorescence lifetime by \(\tau=\phi/k_{r}\)[17]. The collisional deactivation rates mainly depend on the gas density and the mean velocity of the interacting particles, namely, on the gas temperature [18; 19]. To evaluate the radiative behaviour of a plasma generated in a non-uniform gas medium, information on the electron/ion density and temperature distributions within the plasma is required. For this purpose, which is beyond the scope of our work, several techniques can be used in combination with 2D fluorescence imaging, including optical interferometry [20; 21], terahertz-based scattering [20], and pump-probe fluorescence spectroscopy [22]. To study the gas jet behavior, we traced the spatial distribution of the plasma produced by 25-femtoseconds laser pulses through the collision-mediated decay of nitrogen ions fluorescence at 391 nm. We imaged the temporal evolution of the gas excited by the 25-fs pulses, on the timescale of tens of nanoseconds, for various times after plasma onset by steps of 5 ns. Figure 3 reports the frames detected at selected delays from the laser arrival, showing the fluorescent spatial distribution of the nitrogen plasma in two different conditions, with and without the gas flux from the micronozzle. With the scope to separate the effect of vacuum environment gas diffusion from the expansion of gas jet, we preliminarily evaluated the fluorescence emitted in a \(2\times 10^{-1}\) mbar vacuum environment by detecting the whole filament emission intensity in vacuum (with no gas flux from the micronozzle) as a function of time. In our experimental conditions, we measured a radiative decay characterized by an intensity peak after 10 ns from the laser arrival, followed by an exponential decrease with a lifetime of 45 ns. The observation of an intensity peak delayed by 10 ns from the laser excitation suggests the early activation of non-radiative contribution and might be attributed to the effect of plasma growing under the excitation by secondary electrons. After 10 ns, the effect of secondary electrons extinguishes. In this pressure conditions, the mean free path of nitrogen molecules is estimated on the few hundreds of micrometers scale (\(\sim\)300 \(\upmu\)m).