# Time-Resolved Imaging of Femtosecond Laser-Induced Plasma Expansion in a Nitrogen Microjet
## 3 Study of the Plasma Expansion Dynamics
Herein, collisional mechanisms play a minor role, and the characteristic fluorescence lifetime is attributed to a purely radiative decay. Figure 3a-c display the radial diffusion of a portion of the plasma filament (the field of view of the imaging system \(\sim\)500 \(\upmu\)m). The laser propagation direction is orthogonal to the camera position and the pulse arrival time is conventionally indicated as T = 0. After 5 ns from the pulse arrival, the fluorescence emission from the ionized molecules is strongly confined, approximately a cylinder with a diameter \(w\) = 21 \(\upmu\)m calculated as the full width at half-maximum of the Gaussian fit along the direction orthogonal to the laser propagation. Since in the first few nanoseconds after the laser arrival, the plasma kinetics can be assumed almost isochoric; the fluorescence emission at 5 ns delay provides a reasonable estimation of the initial dimension of the plasma, with \(w\) being approximately the radial extension of the gas volume ionized by the femtosecond pulses. At longer delays (\(\geq\)10 ns), the fluorescence signal spreads under the pressure increase inside the high-temperature conductive plasma. The radial diffusion is mainly related to the energy of the laser pulses and gas pressure [14]. Upon femtosecond laser excitation, the typical response of a low-pressure air filament is expected to produce a rapid growth of the plasma, associated with a radial increase of the nitrogen ions volume of a few microns on a time scale of a few nanoseconds. Monte Carlo simulations of nearly free molecular expansion of a hot gas column into the low-pressure cold nitrogen background, indicate that the observed time evolution of gas fluorescence is compatible with an initial gas temperature in the range of (5000-10000) K. The fluorescence propagation is dominated by individual molecule motion, the average advection velocity being much smaller than the molecular thermal speed. The expansion of the plasma generated in a gas jet was explored by using the same scheme. We positioned the glass nozzle in the laser focus at a distance \(d\) = 80 \(\upmu\)m from the laser beam (y-direction). The focal length of the focusing mirror provides a Rayleigh  
Figure 3: (**a–c**) show the expansion at different time delays of a plasma filament generated by femtosecond laser pulses in vacuum (2 \(\times\) 10\({}^{-1}\) mbar). 300 \(\upmu\) pulses with 25-fs duration were focused in the vacuum chamber by a 300-mm focal lens. (**d–f**) show the evolution of the plasma by adding a nitrogen flux through a micronozzle loaded with a backing pressure of 3 bar. The nozzle illustration is not to scale. Each frame is normalized to the peak intensity. For each delay, the camera gain is optimized for compensating to the decay of the fluorescence. range much longer than the radial size of the nozzle, thus, allowing for a uniform excitation of the gas jet along the beam propagation direction (x in Figure 2), inside the interaction region. The nozzle was loaded with a nitrogen backing pressure of 3 bar. Preliminary numerical microfluidic calculations, performed with Comsol Multiphysics(r) [23], indicate that, in steady conditions, the axial velocity of the gas jet produced by the glass nozzle ranged between 620 m/s and 730 m/s from the nozzle outlet to a 100 \(\upmu\)m distance, along the jet axis. Herein, the steady pressure ranged from 9 \(\times\) 10\({}^{2}\) mbar to 1.6 \(\times\) 10\({}^{2}\) mbar. Based on the nozzle geometry (circular throat and output with diameters respectively of 30 and 65 \(\upmu\)m), the gas jet is expected to have a circular section in the transversal plane. From the Comsol calculations, the diameter at a beam distance \(d\) will be 85 \(\upmu\)m, thus, exceeding the radial extension of the plasma volume (\(w\)-21 \(\upmu\)m). In this configuration, only a small portion of the gas jet is ionized by the ultrashort pulses. Figure 3d-f report time-delayed 2D maps of the nitrogen fluorescence by filamentation in the gas jet.