Revisiting argon cluster formation in a planar gas jet for high-intensity laser matter interaction

Abstract

We determine the size of argon clusters generated with a planar nozzle, based on the optical measurements in conjunction with theoretical modelling. Using a quasi-one dimensional model for the moments of the cluster size distribution, we determine the influence of critical physical assumptions. These refer to the surface tension depending on the presence of thermal equilibrium, the mass density of clusters, and different methods to model the growth rate of the cluster radius. We show that, despite strong variation in the predicted cluster size, 〈N〉, the liquid mass ratio, g, can be determined with high trustworthiness, because g is predicted as being almost independent of the specific model assumptions. Exploiting this observation, we use the calculated value for g to retrieve the cluster size from optical measurements, i.e., calibrated Rayleigh scattering and interferometry. Based on the measurements of the cluster size vs. the nozzle stagnation pressure, we provide a new power law for the prediction of the cluster size in experiments with higher values of the Hagena parameter (Γ*>104). This range is of relevance for experiments on high-intensity laser matter interactions.

Cluster size dependence of high-order harmonic generation

“…For most of the experiments mentioned above [15,16,18,19], the researchers interpret their results by choosing g=1 without further justification, namely, they assume that a pure cluster jet is generated and thereby the measured HH signals are entirely to be attributed to clusters. However, both our recent modeling of cluster formation [26] and other measurements [27,28] strongly indicate that g is not unity but dependent on both the stagnation pressure and reservoir temperature. For instance, for our slit nozzle, the value of g for argon clusters lies only at about 20% at room temperature over a broad range of stagnation pressures.…”

“…To determine the effect of absorption and phase matching on the HH yield when n a is increased, we plot the calculated absorption length [34] (L abs , red dashed curve) and the coherence length (L coh , blue dashed curve) in figure 4 versus the atomic number density together with the effective experimental interaction length (effective length of the medium, = L 0.65 mm med , pink dashed line as determined in [26]). The absorption length, starting with a rather big value, = L 6.5 mm abs , drops gradually with increasing n a .…”

“…As figure 5 shows an enhanced yield for the mixture of clusters and monomers when the average cluster size is in the range from ∼200 to ∼3000, we show in figure 6 the ratio as calculated using equation (4) for this range of average cluster sizes. The horizontal error bar is due to the estimated uncertainty in g, obtained from our model [26], while the vertical error bar is due to both the uncertainty in g and the experimentally measured yield of the 21st harmonic for the gas-cluster mixture. The latter has been experimentally determined for a few representative values of á ñ N .…”

“…Importantly, for disentangling the contribution to HHG from clusters and gas monomers, we perform experiments at two different reservoir temperatures in order to vary the liquid mass fraction, g, for the same range of cluster sizes. We determine the dependence of the liquid mass fraction, g, on both stagnation pressure and reservoir temperature with a high degree of reliability using our one-dimensional model [26]. We find that about a maximum of 20% of the gas atoms are converted into clusters under our experimental conditions.…”

Quasi-equilibrium phase separation in supercritical fluids

“…Fig.2a shows the sudden increase of the droplet density across the critical pressure, above which it is saturated. The argon gas is cumulatively compressed into the chamber through the check valve while creating LL droplets and clusters [20][21][22]. As the operating pressure of the check valve (300 bar) is fixed, the rate at which the droplets are generated decreases as the chamber pressure increases, and eventually, the droplet formation stops.…”