Effect of pulse duration on the x-ray emission from Ar clusters in intense laser fields

We study experimentally and theoretically the production of characteristic $K\alpha$ x-rays during the interaction of intense infrared laser pulse with large ($N\sim {10}^4–{10}^6$ atoms) argon clusters. We focus on the influence of laser intensity and pulse length on both the total x-ray yields and the charge-state distributions of the emitting cluster argon ions. An experimental optimization of the x-ray yield based on the setup geometry is presented and the role of the effective focal volume is investigated. Our theoretical model is based on a mean-field Monte-Carlo simulation and allows identifying the effective heating of a subensemble of electrons in strong fields as the origin of the observed x-ray emission. Well-controlled experimental conditions allow a quantitative bench marking of absolute x-ray yields as well as charge state distributions of ions having a $K$-shell vacancy. The presence of an optimum pulse duration that maximizes the x-ray yield at constant laser energy is found to be the result of the competition between the single cluster dynamics and the number of clusters participating in the emission.

Figure 1

(Color online) Absolute $3.1\mathrm{keV}$ photon yield as a function of the laser peak intensity for $\lambda =800\mathrm{nm}$, $\tau =60\mathrm{fs}$, and $⟨N⟩=5.1\times {10}^5$ argon atoms per cluster; full circle: data from the high resolution spectrometer, open circle: data from semiconductor detectors, dashed gray line: fit to the effective focal volume [Eq. (2)] with $I_{\mathrm{th}}=1.4\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$; square: ab initio simulation with a clustering fraction of 0.33 and a fluorescence yield of 0.25 (see text).

Figure 2

Dependence of the time-averaged effective focal volume on the beam waist for different laser energies. For an intensity threshold and pulse duration of $1.4\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$ and $60\mathrm{fs}$, respectively, each $V_{\mathrm{eff}\mathrm{foc}}$ displays a pronounced maximum.

Figure 3

(Color online) (a) Laser intensity dependence of the mean energy of $1s2pnl\to 1s^{2}nl$ transitions from irradiation of argon clusters for the same experimental conditions as presented in Fig. 1. Experimental spectra obtained at (b) $2.1\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$ and (c) in the intensity range $4\times {10}^{15}–3\times {10}^{16}\mathrm{W}∕{\mathrm{cm}}^2$.

Figure 4

Comparison of experimental and theoretical charge-state distributions obtained at $6\times {10}^{16}\mathrm{W}∕{\mathrm{cm}}^2$. The experimental distribution was obtained from the spectrum in Fig. 3b assuming mean fluorescence yields $⟨{\omega }_{12+}⟩=0.19$, $⟨{\omega }_{13+}⟩=0.24$, $⟨{\omega }_{14+}⟩=0.31$, $⟨{\omega }_{15+}⟩=0.49$, $⟨{\omega }_{16+}⟩=0.45$. Experimental data on charge states $\mathrm{q}<12+$ could not be extracted. Full lines are to guide the eye. Data are normalized to ${\mathrm{Ar}}^{14+}$.

Figure 5

(Color online) (a) Snapshot of the electric field $F_z\left(z\right)$ along the polarization axis at $t=86\mathrm{fs}$ where the laser field $F_L\left(t\right)=2.3\times {10}^{11}\mathrm{V}∕\mathrm{m}$ (dashed line). The dotted lines mark the original cluster borders at $t=0\mathrm{fs}$. (b) Snapshot of the charge density distribution (in units of ${10}^9\mathrm{C}∕{\mathrm{m}}^3$) at the same time. The circle marks the original cluster borders at $t=0\mathrm{fs}$. Note the sheath density near the pole on the right-hand side.

Figure 6

(Color online) Evolution of the projected electron phase space $(z,v_z)$ during half a laser cycle [(a)–(c): $t=86\mathrm{fs}$, $t=86.8\mathrm{fs}$, and $t=87.5\mathrm{fs}$]. Only electrons within $R<2.5\mathrm{nm}$ of the $z$ axis are represented. Gray: Slow electrons inside the cluster. Blue: Electrons outside the cluster and fast electrons inside the cluster. The light-blue traces mark the path of the electrons over the previous $0.04\mathrm{fs}$. The vertical lines show the original cluster borders. The production and evolution of fast electrons can be observed (arrows).

Figure 7

Time evolution of the maximum electron kinetic energy (gray) in the high density core of the cluster for three peak laser intensities, $I=7.2\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$ (upper curve), $I=1.4\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$ (center curve), and $I=4\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$ (lower curve) and pulse duration $\tau =60\mathrm{fs}$. The dashed horizontal line marks the neutral argon $K$-shell binding energy $E_K=3.2\mathrm{keV}$. Each curve is delimited below by the electrostatic potential $\Phi (r=0,t)$ at the center of the cluster and above by ${\tilde{E}}_{\max }\left(t\right)=\Phi (r=0,t)+F_{\mathrm{osc}}^2∕\left(2{\omega }^2\right)$ (see text).

Figure 8

(Color online) X-ray yield from argon clusters with $⟨N⟩\sim 3.7\times {10}^4$ atoms as a function of laser peak intensity at $800\mathrm{nm}$ for different pulse durations of $\tau =55$, 140, and $570\mathrm{fs}$. Gray dashed lines correspond to the fitted effective focal volume and full lines with squares to the simulation data.

Figure 9

Evolution of the $K$-shell ionization probability per atom as a function of the laser peak intensity for different pulse durations $\tau =55\mathrm{fs}$ (triangle), $140\mathrm{fs}$ (circle), and $210\mathrm{fs}$ (square) calculated with shielded ion dynamics (gray) and without ion shielding (black).

Figure 10

(Color online) Comparison between experimental and theoretical charge state distributions for different pulse durations (same experimental conditions as Fig. 8, $⟨N⟩=3.7\times {10}^4$ atoms/cluster), (a) $\tau =55\mathrm{fs}$, $I_{\text{peak}}=4.0\times {10}^{16}\mathrm{W}∕{\mathrm{cm}}^2$, (b) $\tau =140\mathrm{fs}$, $I_{\text{peak}}=1.6\times {10}^{16}\mathrm{W}∕{\mathrm{cm}}^2$, and (c) $\tau =570\mathrm{fs}$, $I_{\text{peak}}=4.0\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$. Black bars: simulation with shielding, green bars: simulation without shielding (full lines are plotted to guide eye), red bars: experimental data with error bars. All data are normalized to the lowest experimentally observed charge state $(12+)$.

Figure 11

Simulation of the $\tau$ dependence of x-ray yields $N_X\left(\tau \right)$ at fixed total $E=20\mathrm{mJ}$ for argon clusters with $N=3.7\times {10}^4$ atoms: (a) number of $K$-shell vacancies per cluster atom calculated without shielding, (b) effective focal volume deduced from the threshold intensities calculated with shielding, (c) qualitative estimate of the total x-ray yield $N_X$ by taking the product of (a) and (b).

Figure 12

Evolution of the measured absolute x-ray yield with the pulse duration at a constant energy per pulse of $20\mathrm{mJ}$ for different cluster sizes $⟨N⟩$. Bottom to top: $5.1\times {10}^5$ atoms/cluster, $1.1\times {10}^6$ atoms/cluster, and $1.8\times {10}^6$ atoms/cluster. For sake of clarity, experimental data for $1.8\times {10}^6$ atoms/cluster are multiplied by 1.5.

Figure 13

Evolution of the absolute x-ray yield with the pulse duration at a constant laser intensity of $8\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$ for a cluster size $⟨N⟩=1.1\times {10}^6$ atoms/cluster (full circle: data from the high resolution crystal spectrometer, open circle: data from semiconductor detectors) (lines to guide the eye).