Femtosecond X-ray Lasers at λ=32.8 and 44.4 nm in a Plasma Formed by Optical Field Ionization in a Krypton Cluster Jet

Due to high efficiency, X-ray lasers based on transitions of Ni-like krypton (Kr8+) are being actively studied. The main focus is on an X-ray laser based on the conventional 3d5/24d5/2 [J=0] – 3d3/24p1/2 [J=1] transition at λ=32.8 nm. Gaseous krypton targets or krypton cluster jets are used in various experiments. X-ray lasers at 32.8 nm in a plasma formed by optical field ionization in a krypton cluster jet are widely used for research of nanoobjects. In this article, the possibility of creating an efficient X-ray laser in Ni-like krypton based on a transition with optical self-pumping 3d3/24f5/2 [J=1] – 3d3/24d5/2 [J=1] at λ=44.4 nm is predicted for the first time. The plasma filament is excited upon interaction of a jet of krypton clusters with an intense pump laser pulse. Optimal conditions to achieve the duration tlas ≤300 fs of the X-ray laser radiation are determined. The optimal electron density is in a rather narrow interval in the range ne ~ 1021 - 2×1021 cm-3. The optimal electron temperature is several keV. It is likely that this explains the fact that no X-ray laser has been observed on this transition in Kr8+ so far. The conversion factor per pulse is found to be ~5×10-5. For an X-ray laser operating on the conventional transition 3d5/24d5/2 [J=0] – 3d3/24p1/2 [J=1] at λ=32.8 nm, tlas ≤ 300 fs can also be achieved; however, the conversion factor for this transition is times ~5 smaller than that for the former transition.


Introduction
X-ray free electron lasers (XFELs) with λ=1-10 nm and a pulse duration (t las ) of the order of a hundred of femtoseconds allow recording holographic images of intermediate states of nano-objects at times comparable to the times of atomic motions [1][2][3][4]. These works demonstrate the possibility of observing the dynamics of phase transitions in solids -the formation of cracks, the nucleation and separation of phases, and rapid fluctuations in liquids and biological cells. Intense X-ray lasers (XRLs) with sub picosecond t las can be used to diagnose very rapidly changing laser plasmas in the region of critical surface density.
In 2017, a new generation femtosecond XFEL came into commission in Hamburg [5]. The minimum t las reached 100 fs, the pulse repetition rate of the XFEL was 27000 s -1 , and the wavelength varied in the range 0.05 -6 nm. At present, intensive investigations are underway to determine the mechanisms of formation of toxic proteins responsible for the formation of diseases of various kinds.
Experiments [6][7][8][9] have demonstrated the fundamental advantage of using cluster jets as targets for creating high-temperature plasmas. The plasma is pumped by intense pulses of femtosecond lasers; the plasma formation mechanism is the optical field ionization (OFI). Let us list the main prerequisites for using the OFI method for cluster targets to create highly efficient X-ray lasers in cluster jets: (i) The target can absorb of up to ~ 90% of the pump energy due to weak reflection; in this case, the plasma does not contain any fragments and oxides. (ii) Electrons are capable of achieving energies on the order of tens and hundreds of thousands of keV. (iii) The plasma density is controlled by the size and number of clusters. (iv) The ionization balance is controlled by the pump intensity I pump ; if the intensity I pump is correct, immediately after the interaction of the pump pulse with the target, a plasma is formed in which ~90% of all ions are formed in the state of the working ion of an X-ray laser (XRL).
(v) A high degree of coherence of the output radiation of an XRL is possible if one uses a high-order harmonic with a wavelength close in value to λ of the XRL; a high-order harmonic is formed in the delay line and propagates simultaneously with the XRL pulse.
Ivanova [10,11] developed a theoretical model of a sub picosecond XRL formed in a jet of xenon clusters upon interaction with an intense pump laser, where the gain of spontaneous emission on the 4d5d [J=0] -4d5p [J=1] transition at λ=41.8 nm in Pd-like xenon (Xe 8+ ) was determined. It is important to note that the results of calculations of Ivanova [11] for low temperatures were confirmed by subsequent experimental results performed by Mocek et al [12].
In the work of Ivanova and Vinokhodov [13], a model of an X-ray laser based on the conventional 3d 5/2 4d 5/2 [J=0] -3d 3/2 4p 1/2 [J=1] transition with λ=32.8 nm in Ni-like krypton (Kr 8+ ) was calculated. In this work, the known experimental measurements of quantum yield of an XRL on this transition were interpreted. In various experiments, the plasma was pumped in gaseous krypton and in a jet of krypton clusters. For the jet of clusters, optimal conditions were found under which the saturation of the quantum efficiency along the plasma length was ~ 300 µm (that corresponds to the XRL pulse duration t las~ 1 ps). Under optimal conditions, the density of krypton atoms was n Kr ~ (4-9)×10 19 cm -3 and the electron temperature was T e ~ 5000 eV. The conversion factor was ~ 5×10 -3 of the pump pulse energy. Ivanova and Vinokhodov [13] proposed a detailed schematic diagram of the experimental setup of a highly efficient XRL formed in a jet of krypton clusters. A similar scheme was implemented in the experiment of Sebban et al [14], where a Ni-like krypton plasma was created by the method of OFI of krypton atoms. In this experiment, a circularly polarized pump laser beam was focused either into a cell with gaseous krypton or into a jet of gaseous krypton; the XRL on the conventional 3d 5/2 4d 5/2 [J=0] -3d 3/2 4p 1/2 [J=1] transition with λ=32.8 nm in (Kr 8+ ) was studied. In the experiment of Sebban et al [14] it was shown that the dynamics of the output XRL pulse can be controlled by using a pulse of a high-order harmonic that is focused into the gain medium; the high-order harmonic wavelength is close to the XRL wavelength. By stretching the time of the high-order harmonic pulse to the gain duration g(t), continuous and coherent XRL emission can be achieved. It was found [14] that, as the plasma electron density increased from n e =3×10 18 to n e =1.2×10 20 cm -3 , the XRL radiation duration t las decreased from 7 ps to 450 fs. The duration t las was defined as the full width at half maximum (FWHM) of the XRL radiation pulse intensity. Figure 1 shows the scheme of an XRL that operates on two conventional transitions 3d4d [J=0] -3d4p [J=1] in the Kr 8+ ion. The ground state of a Ni-like ion is a closed shell of the 3d 10 [J=0] core. The classification of levels is presented in the j-j coupling scheme of the angular momenta. An excited state of the ion is presented by the state of a vacancy in the core (3l j ) and by the state of an electron above the core (4l j ). The transition 3d 5/2 4d 5/2 [J=1] -3d 3/2 4p 1/2 [J=1] with λ=32.8 nm is strong. The XRL transition whose inversion is caused by the optical self-pumping (OSP) 3d 3/2 4f 5/2 [J=1] -3d 3/2 4d 5/2 [J=1] at λ=44.4 nm is also presented.

Formulation of the Problem
Physical principles of an XRL with OSP have been presented by Nilsen et al [15,16]. In fact, an XRL with OSP is an alternative approach to the conventional radiative collisional model. In the conventional model, the upper working level is populated from the ground level at a high rate due to its monopole excitation by electron impact, it radiatively decays only into lower working levels (radiative decay into the ground state is forbidden); the population inversion of the working levels occurs due to the rapid decay of the lower working level into the ground state (see Figure 1).
The inversion of XRL working levels under the OSP conditions is due to a high rate of population of the upper working level by means of dipole excitation by electron impact, as well as reabsorption of radiation from the upper working level 3d 3/2 4f 5/2 [J=1] to the ground state 3d 10 [J=0]. The reabsorption of radiation manifests itself in the fact that the effective radiative decay of the upper level into the ground state in an optically dense plasma is much smaller than in an isolated ion. In our model, the plasma appears to be stable and quasi-stationary, and mass transfer is not taken into account. In this case, the reabsorption of radiation can be taken into account by the Biberman-Holstein factor -the escape factor G, which determines the ratio of the effective rate of radiative decay of an ion in plasma (A eff j-0 ) to the rate of radiative decay of an isolated ion (A j-0 ): A eff j-0 =G·A j-0 (G <1). For an optically dense plasma, Fill [17] proposed the following form to calculate the escape factor G: where к 0 is the photon absorption coefficient, and d is the diameter of the cylindrical plasma.
A new class of XRLs based on OSP principles has been investigated experimentally by Nilsen et al [16] in Ni-like Zr 12+ , Nb 13+ , and Mo 14+ ions. In this experiment, solid targets were used. Plasma was pumped by means of two laser pulses: preliminary (1 J, 600 ps), which was used to create the plasma, then the main pulse (5 J, 1 ps), which heated the plasma. The interval between the pulses was 700 ps. The laser pumping beams were focused into a line into a target, whose length was varied from 0.4 to 1 cm. The emission XRL spectra are shown in Figure 2 from the reference [16], where one can see high-intensity XRL lines for the conventional and OSP transitions.
Progress in the study of XRLs based on the OSP mechanism was observed in a subsequent experiment performed by Kuba et al [18], where a sub picosecond heating pulse was used to pump plasma from a solid silver target. In this experiment, conditions for achieving a strong laser effect on an OSP transition in Ag 19+ were determined. In a recent experimental work of Siegrist et al [19], the OSP mechanism was investigated in Ni-like ions, such as Ru 16+ , Pd 18+ , and Ag 19+ . In this experiment, XRL lines based on the OSP mechanism were experimentally observed in Ne-like ions, such as V 13+ , Cr 14+ , Fe 16+ , and Co 17+ . Ivanova [20] presents results of calculations of the wavelengths of XRL transitions based on the OSP principles for Ni-like ions sequence with Z≤ 79. The calculations were performed using relativistic perturbation theory with a model potential of zero-approximation (RPTMP) by Ivanova [21].
Neither calculations of Ivanova [13] nor experiment of Sebban et al [14] have not considered the gain due to the OSP transition in Ni-like krypton at λ=44.4 nm. Below we will calculate a theoretical model of an XRL with λ=32.8 nm and λ=44.4 nm in a plasma formed upon interaction of a femtosecond pump laser with a jet of krypton clusters. The goal of the calculation is: (i) to determine plasma parameters, pumping conditions, and basic principles of an experiment to achieve the duration of the output XRL radiation ≤ 300 fs; (ii) for each transition, to calculate the dependences of energy yields of the XRL on the plasma density.

Evolution of the Gain of an XRL at λ=32.8 nm and λ=44.4 nm Under Optimal Conditions
Under the assumption that plasma is homogeneous and free of impurities, five parameters are sufficient to describe it: the temperatures and the densities of electrons and ions, T e , T i , n e , and n i , and the diameter of the plasma filament d. It was shown by Ivanova [10,13] that the shape of the T e distribution practically does not affect the calculation results. To calculate the gain g at the center of an XRL line, we will use the well-known expression proposed by Whitney et al [22]: g=A ul λ 2 (N up -(g up /g low )N low )/8π∆ν 0 (2) where A ul is the probability of a radiative transition from the upper to the lower working level, λ is the transition wavelength, N up and N low are the numbers of atoms per unit volume in the upper and lower working states, respectively, g up and g low are the statistical weights of the upper and lower working levels, respectively. The shape of the transition line is determined by the convolution of the intrinsic and Doppler contours. The intrinsic contour is determined by radiative transitions and collisional processes, which connect each of the levels with all other levels of the working ion, as well as with the levels of the ion of the adjacent stage of ionization. The line width at the center (Voigt profile) ∆ν 0 is determined by a simplified method, which was developed by Whitney et al [22]. The calculations will assume the following.
1) The plasma is formed in the shape of a cylinder with diameter d and length L as a result of propagation of a laser pumping pulse through a beam of clusters with thickness L.
2) The parameters of the pump pulse are such that, immediately after the end of the interaction of the optical field of the laser with clusters, the plasma is formed with an electron temperature T e , in which the Kr 8+ ions constitute ~90% and reside in the ground state. g. [23]). Such calculations are necessary to determine the saturation of g(t) along the plasma length L. In the case considered here (as well as in the overwhelming majority of experiments), the gain is observed in the ionization regime of the working ion in the state of a higher stage of ionization. In principle, the lifetime of the working ion in the plasma determines the value of L. 7) In the calculation, we will average the gain g(t) over the spatial and temporal coordinates. For this purpose, we will divide the target-cylinder into segments that are shorter than the length of the spatial scale of the pump pulse; then, elementary processes in each segment will proceed identically, but with some time delay. In this case, it is sufficient to perform only the time averaging for the function g(t). In addition to Figure 1, Table 1 presents spectroscopic characteristics (rate coefficients of kinetic equations) for two XRL transitions. The probabilities of radiative transitions (PRTs) in the table are given for an isolated ion. Figure 2 Optical Field Ionization in a Krypton Cluster Jet graphically shows the PRTs of two working levels: A eff low-0 for the lower working level of the conventional transition and A eff up-0 for the upper working level of the OSP transition to the ground state of the Kr 8+ ion in relation to the electron density. The calculation was carried out taking into account formula (1) at d=25 µm and T e =10000 eV. Figures 3a and 3b show the temperature dependences of the electron impact excitation rates of the upper and lower working levels of both transitions. The calculation was performed by the RPTMP method according to the formulas derived by Ivanov et al [24].
Below, we will explain why a significant inversion of the rapidly decaying upper level 3d 3/2 4f 5/2 [J=1] of the OSP transition is possible with respect to the 3d 3/2 4d 5/2 [J=1] lower level, which is practically stable against radiative decay (see Table 1). Figure 2 demonstrates that the rates of radiative decay of the lower working level of the conventional transition (A eff low-0 ) and the upper working level of the OSP transition (A eff up-0 ) to the ground state of the Kr 8+ ion significantly decrease with increasing density. At the optimal density n e =1.5×10 21 cm -3 (which will be defined below), A eff up-0 ~ 10 10 s -1 ; in this case, the population of the upper OSP level is P up =0.07. Radiation depletion of this level in kinetic equations is given by P up ×A eff up-0 =7×10 8 s -1 .  Designations: E (eV) -energy level above the closed shell 3d 10 ; λ (nm) -wavelength of the XRL transition; Etr (eV) -XRL transition energy; Alow-0 (s -1 ) -PRT of the low working level to the ground state; Aup-0 (s -1 ) -PRT of the upper working level to the ground state; Aup-low (s -1 ) -PRT of the upper working level to the low working level. PRT are given for the isolated level Kr 8+ . R up Col (cm -3 s -1 ), R low Col (cm -3 s -1 ) -electron impact excitation rates per unit volume of the upper and lower working levels, respectively; ∆ν0 (s -1 ) -Voight width at the center of the transition line -are calculated at Te=10000 eV, d=25 µм; for each transition, the value ∆ν0 is calculated at optimal ne. The rates of the electron impact excitation of levels from the ground state of the Kr 8+ ion, R col up and R col low , increase in proportion to the density. At optimal n e =1.5×10 21 cm -3 for the OSP transition, the population of the upper level by electron impact in the balance equations: R col up ×n e ×P 0 =10 -10 ×1.5× 10 21 ×0.55=8.3×10 10 s -1 , where P 0 =0.55 is the population of the ground level at the optimal n e . Therefore, due to the optical self-pumping (reabsorption) and a high rate of collisional population, the population of the upper level of the OSP transition is ~2 orders of magnitude higher than the radiative decay. Figure 3b shows that the population of the lower level of the OSP transition is 2.5 orders of magnitude smaller than the population of the upper level, which provides a large value of inversion of this transition at optimal n e . Because the lower working level is populated weakly, the inversion of the SPP transition takes place in the entire range of the considered densities. The kinetic equations take into account the states of two ions of adjacent ionization stages; all radiative-collisional processes coupling two adjacent ions are taken into account in the kinetic equations. These processes and methods for their calculation were presented by Ivanov et al [25]. In this approach, it is possible to calculate the evolution of the gain coefficient taking into account the ionization of the working ion. The ionization time actually determines the duration of the XRL pulse. Figure 4 shows the time dependence of the fraction of working ions Fr [Kr 8+ ] in the plasma for different n e .
For sub-picosecond XRLs to be efficient, it is necessary that the average value of the gain coefficient was g (t) ~ 1000 cm -1 . Preliminary calculations of Ivanova and Zinoviev [26] show that the value of g(t) with λ=32.8 nm and λ=44.4 nm in Ni-like krypton increases extremely rapidly with increasing electron temperature T e . Rapid growth takes place at relatively low T e ; see Figure 3a for the rates of excitation by electron impact.
A large number of parameters that characterize (a) plasma and its geometry; (b) nozzle, pressure in the gas reservoir, and size of clusters; and (c) laser pump pulse should be consistent with the theoretical model. Then the active medium, in principle, can be created using only one main pump pulse. This is possible if the model adequately reproduces the results of experiment. Ivanova and Vinokhodov [13] interpreted the experimental results on the observation of gain and quantum yield of XRL with λ=32.8 nm in gaseous krypton and in a jet of clusters; the comparison with them demonstrated the correctness of our model. First experiments on the creation of high-temperature plasmas upon interaction of an intense pump laser pulse with a jet of xenon clusters demonstrated the achievement of electron temperatures on the order of a few keV [27][28]. Ditmire et al demonstrated [29], that maximum ion temperatures in their experiment were T i max ≥ 1 MeV. In later works of Ditmire et al [30], it was shown that the size of the cluster is important for the formation of a high-temperature plasma upon interaction of an ultrashort pump pulse with a jet of clusters. The pedestal of the pulse is usually several nanoseconds; during the interaction of the pulse pedestal with the cluster, the cluster is heated, electrons escape from its surface, and the cluster expands.
The largest values of T e and T i are achieved when the electron density n e in the cluster nanoplasma is 3×n crit (n crit =πc 2 m e /e 2 λ 2 ): the laser frequency is equal to the plasma frequency; in this case, the laser energy is resonantly contributed to the plasma energy. To achieve the maximum energy contribution, the duration and intensity of the pedestal should correspond to the cluster size: if a cluster is too small (expands rapidly, reaching 3×n crit ), it collapses too quickly (prior to the arrival of the main intense pulse), and the plasma ͞ T e is not high. If a cluster is too large (it expands for too long), it collapses after the passage of the intense pulse, and T e of the plasma is also not high. A cluster of the correct size reaches n e =3×n crit at the moment of time of the arrival of the main femtosecond pump pulse; in this case, a maximum contribution of a pump pulse energy to the nanoplasma temperature becomes possible.
The sizes of clusters as functions of the pressure and temperature of the gas in the initial chamber, as well as of the geometry of the valve, have been well studied for cone-shaped valves with round holes, for which the number of atoms in noble gas clusters is usually determined by the Rayleigh scattering method using the empirical formula given by Hagena and Obert [31]. Chen et al [32] studied the dependences of the cluster sizes on gas pressure in the initial chamber for a slotted nozzle. In this experiment it was shown that a slotted supersonic nozzle provides a significantly higher number of atoms in a cluster as compared to a cone-shaped nozzle.
The dependences of the energies of electrons and ions in plasma on cluster size were studied in many experiments, e.g., by Shao et al [28] and by Springate et al [33]. In the experiment [28], a jet of xenon clusters was irradiated by a laser with a peak intensity of 2 × 10 16 W/cm 2 and with a pulse energy of 30 mJ; it was shown that the clustering of xenon atoms with increasing pressure in the initial chamber begins at a pressure of ~ 1 bar. With increasing pressure, the size of the cluster increases, which leads to a rapid increase in the electron temperature in the plasma (see Figure 2 in the reference [28]). The plot of the growth of T e with increasing density qualitatively coincides with the result obtained by Ivanova [10], which was shown in Figure 4 of that work. To continue this plot into the range of high plasma densities (n i ≥ 10 18 cm -3 , which corresponds to a cluster size of ≥ 10 3 atoms/cluster), we will use Figure 4 from the reference [10], as well as plots from the experiment [33]. The resulting plot of T e versus n i was shown in Figure 6 of the calculation [13]. The inset of Figure 6 of the calculation [13] shows the corresponding dependence of T e on the cluster size for Xe and Kr. We used this dependence to calculate the gain g(t) in the work [13].
As can be seen from the plots of Figure 6 from the calculation [13], for Kr clusters, T e drops at larger cluster sizes (larger values of n Kr ). As will be shown below in this work, to create XRLs of sub-picosecond duration, it is assumed that the pump pulse intensity is 5 × 10 17 W/cm 2 , while the pulse energy is 0.16 J. The corresponding T e values are at least one and a half orders of magnitude higher than those in the experiment [28]. Based on the convenience of focusing the pump pulse, we will assume that the diameter of the plasma filament is d=25 µm. The length L=100 µm was selected from the condition that the XRL pulse duration is t las ≤ 300 fs. Figures 5 and 6 show the evolution of the gain for the conventional transition at λ=32.8 nm and the transition with OSP at λ=44.4 nm, respectively. The plots demonstrate dependences g(t) at different plasma densities. The electron density of the plasma varies within 5×10 20 ≤ n e ≤5×10 21 cm -3 . In order not to clutter Figures 4-10, weak transitions are indicated by blank operators. Figures 7 and 8 show the dependences of the quantum yields of XRLs at the same plasma densities. The plot of Figure 7 shows that, for the conventional transition with λ=32.8 nm, the optimal density is n e =1.25× 10 21 cm -3 , and the density of krypton atoms ~ n Kr ~1.5× 10 20 cm -3 . The plot of Figure 8 shows that, for the transition with λ=44.4 nm, the optimal density is n e =1.5×10 21 cm -3 , while the density of krypton atoms n Kr ~ 1.9× 10 20 cm -3 .   The occurrence of maxima in the functions N out ph (n e ) at constant T e and d (see Figures 7,8) can be easily understood. At small n e , an increase in the density leads to an increase in g(t), since the number of working ions, ions with the population inversion of working levels, increases. With a further increase in n e , the collisional mixing of the level populations is enhanced, which leads to a decrease in the inversion. Therefore, for the XRL with λ=44.4 nm, optimal values of n e lie in a rather narrow interval in the range n e ~ 10 21 -2×10 21 cm -3 . It is likely that this explains the fact that no XRL has been observed on this transition so far. Let us calculate the intensity I pump and duration t pump of a pump laser of a cluster target with the volume V=5×10 -8 cm 3 and electron density in the plasma n e =1.5×10 21 cm -3 . The amount of the absorbed energy in the volume V is E pump~1 0 18 eV. Then, t pump =40 -50 fs, I pump =5×10 17 W/cm 2 . The energy output of an XRL pulse with λ=44.4 nm is E out =1.8×10 12 ×27.4=5×10 13 eV (see Figure 8). The energy output of an XRL pulse with λ=32.8 nm is E out =2.5×10 11 ×37.7=9.4×10 12 eV (see Figure 7); i.e., it is 5 times smaller than that on the OSP transition.
The XRL pulse width at half maximum for the transition with λ=32.8 nm is shown in Figure 9: FWHM=0.3 ps; for the transition with λ=44.4 nm, it is shown in Figure 10: FWHM=0.37 ps.

Conclusion
A comparison of the technical characteristics of an XRL in krypton cluster jet and a new generation free electron laser is presented in Table 2. In the model of a femtosecond XRL that was calculated here, it was proposed to use as a target a jet of krypton clusters emitted from a flat valve. The cluster size is ~ 50 nm. The pump laser intensity incident on the target is I pump ~5×10 17 W/cm 2 , E pump~1 0 18 eV, and t pump =40 -50 fs. The pedestal of the pump laser should be selected preliminarily in order to achieve a maximum energy deposition.
The model of a femtosecond XRL with λ=32.8 nm and λ=44.4 nm that was calculated here has conversion factors of ~10 -5 and 5×10 -5 , respectively. For an XRL with λ=44.4 nm, the number of emitted photons was found to be ~ 2 × 10 12 photons/pulse. This intensity of the XRL output radiation is, in principle, sufficient to achieve high quality single-pulse images of objects with sizes ≤100 nm [9]. At present, methods have been developed on the basis of works [6][7][8][9] for obtaining high-quality images of various nano-objects, although the XRL pulse duration there was tens of picosecond.
The duration of an XRL pulse can be made significantly shorter if optical shutters of the time-gating method proposed by Ivanova Vinokhodov [13] will be used; however, in this case, the efficiency will decrease. One of the advantages of an XRL in cluster jets is its high repetition rate of XRL pulse. In one of the first studies of plasma radiation produced upon interaction of an intense pump laser pulse with a jet of clusters performed by Ter-Avetisyan et al [34], a pulse repetition rate of 1.2 × 10 5 Hz was experimentally demonstrated. Due to the fast-pumping rate of the cluster jet, the repetition rate can be significantly increased. In this case, it is possible to achieve a rate of ≥10 6 , at which the energy yield will be ~ 10 W. In 2017, the first laser with a petawatt power (10 15 W) was brought into operation by Spinka and Haefner [35][36], which is located in the Czech Republic and which was created by specialists from the Laurence Livermore National Laboratory. The first of the four lines delivered pulses with an energy of 100 mJ and a duration of ~ 20 fs; the repetition rate in the first version was 1 kHz. By 2020, the pulse repetition rate was 10 kHz. At point, the system is being developed that will provide a repetition rate of the order of 100 kHz or higher.