# Time-Resolved Imaging of Femtosecond Laser-Induced Plasma Expansion in a Nitrogen Microjet
## 3 Study of the Plasma Expansion Dynamics
The gas flux is directed downwards according to the image orientation. The high nitrogen density in the focused jet produces a local increase of fluorescence intensity. At T = 5 ns, the signal intensity is enhanced by almost two orders of magnitude compared to the fluorescence of the filament in vacuum (Figure 3a). In particular, the intensity on the peak is higher by a factor of 76 as compared to the intensity along the plasma filament. In Figure 3d, the fluorescence emitted along the whole filament is not visible as in Figure 3a, since the camera gain was tuned for acquiring the bright emission form the gas-jet volume. The high local density in the region corresponding to the gas jet strongly influenced the spatial evolution of the plasma at later delays, as suggested by the 20 ns and 40 ns delayed frames. The gas flux at the exit of the nozzle modifies the isotropic gas expansion with the appearance of a high-intensity fluorescence pattern centered on the gas jet. We expect a non-uniform fluorescence lifetime depending on the local gas density and temperature along the filament. In particular, we predict a significantly high contribution of non-radiative decay channels in the gas-jet region. Due to the non-uniform fluorescence properties, the 2D fluorescence yield of a plasma in a gas jet does not provide direct information on the gas density. However, structural information on the evolution of the laser-induced plasma can be obtained from the morphology of the fluorescence distribution. In particular, the 2D maps indicate the formation of a shock wave, associated with the generation of spatial regions with lower and higher gas density. The density wave propagated from the bulk of the excited volume isotropically, as suggested by the spherical-like shape of the low-intensity zone. In Figure 3e,f, two bright lobes rise at the sides of the jet and undergo a rapid lateral displacement. These two lobes correspond to low-density regions, where the fluorescence lifetime was longer and the quantum yield higher than in the jet, thus, appearing brighter at longer delays. The plasma plume confined in the central region corresponding to the gas jet evolved under the combined effect of the internal force driving expansion and external gas flux. As time increased, the plume underwent both a spatial spreading and a splitting into two different front-waves, a brighter fluorescent feature downwards and a less intense feature closer to the nozzle (see Figure 4a). The bright peak moved onwards along the gas-jet axis. On the other hand, the second peak was initially propagating towards the nozzle position, and underwent a direction reversal after \(\sim\)40 ns, under the effects of the nitrogen flux from the nozzle. These two components follow different dynamics, both in terms of fluorescence decay and time-dependent propagation velocity. For sake of comparison, we report in Figure 4b the intensity profiles along the gas jet axis as a function of the distance from the nozzle output at different time delays. At early times, the intensity distribution is composed of one peak, spatially spreading while propagating away from the nozzle. For T \(\geq\) 15 ns, the two counter-propagating waves rise, associated with two well-defined intensity peaks. The fluorescence underwent a rapid decay, with a characteristic lifetime \(<\)5 ns, due to the shorter lifetime of excited nitrogen states upon the higher frequency of collisions in a dense gas jet. However, the difference between the intensity of the two wavefronts reduced in time, suggesting a faster radiative decay of the downwards component. To quantify the plume expansion dynamics, we determined the position of the two peaks from the intensity profiles and estimated the propagation velocity, as provided in Figure 4c,d. Both the two wavefronts experienced a fast transitory regime, during which the propagation velocity reached values up to 7 \(\times\) 10\({}^{3}\) m/s and 5 \(\times\) 10\({}^{3}\) m/s for the onwards and the backward components, respectively.