# Time-Resolved Imaging of Femtosecond Laser-Induced Plasma Expansion in a Nitrogen Microjet
## 3 Study of the Plasma Expansion Dynamics
The velocity peak ranged between 15 ns and 20 ns from the pulsed excitation. At longer delays, the velocity converges towards a steady value. Compared to the unperturbed filament (green curve in Figure 4c), plasma generation in a gas flux produced both faster expansion dynamics and higher propagation velocities. In this framework, we explored the dependence of both the onward and the backward shock wave components on the gas flux by changing the nitrogen backing pressure. Upon increasing the backing pressure, the onward component underwent an increase of the expansion velocity. On the other hand, the increasing directional force opposed by the gasjet on the propagation of the backward component produces a slower transitory response and a lower peak expansion velocity. This pressure dependence mainly affected the initial expansion dynamics by 40 ns, up to the dissipation of the thermodynamic forces driving the plasma expansion. Besides gas density, the plasma dynamics depend on the energy deposited in the ionized gas, which scales with the energy of the femtosecond laser pulses. Figure 5a,b provide the axial velocity of the two shock waves for different pulse energies (160 \(\upmu\)J, 300 \(\upmu\)J, 440 \(\upmu\)J) at a fixed backing pressure of 3 bar. The onward and backward waves depend monotonically on the amount of energy transferred by the laser pulses, displaying an increase of the expansion velocity upon increasing pulse energy. We also observed a non-linear dependence of the fluorescence yield with the pulse energy. Figure 5c,e show the fluorescence distribution for 440-\(\upmu\)J pulse energy at delays 5 and 10 ns, respectively; herein  
Figure 4: (**a**) 30-ns delayed frame showing the splitting between the onward and the backward wavefronts. (**b**) Fluorescence profiles along the jet axis at several delays up to 120 ns. The intensity of each curve is normalized to the peak value. (**c,d**) axial velocity evolution for the onward and backward components, respectively. The propagation velocity is evaluated at three different gas pressures (1 bar, 2 bar, 3 bar). For sake of comparison, the green line shows the radial expansion velocity of the filaments in the absence of gas flux. a counterintuitive spatial reshaping of the fluorescence distribution can be noticed, from an elongated to a more focused bright spot. For these two delays, in Figure 5d,f we report the intensity profiles along the x-direction at different pulse energies. At a 5-ns delay, the fluorescence emission consists of bell-like amplitude-scaled spatial profiles. By increasing the pulse energy from 160 to 300 uJ, the fluorescence yield scaled almost proportionally, while, from 300 to 440 uJ it exhibited a saturation associated with no remarkable increase in the measured intensity. Instead, at a 10-ns delay, different pulse energies produced a considerably different fluorescence yield, which increased by more than one order of magnitude from 160 to 300 uJ, and a spatial modulation of the fluorescence distribution, which led to a locally enhanced emission. In particular, the intensity profile along the laser propagation direction (\(x\)-axis) showed strong confinement resulting in the appearance of a narrow intensity peak at high pulse energies. Interestingly, we found a correlation between the narrow fluorescence peak, rising at high pulse energy and the gas density profile as resulting from numerical microfluidics calculations in unperturbed conditions, namely, those unaffected by the laser field. In particular, this peak was delayed with respect to the laser pulse and progressively matched the steady-state density profile as the pulse energy increased, thus, retaining information on the gas jet spatial properties preceding the plasma expansion. This behaviour suggests the activation of a different plasma decay regime depending on the energy deposited by the driving laser pulse. In a high-energy regime, Coulomb collisions among electrons start playing a crucial role due to the high density of electrons [24].