This paper presents a brief review of the x-ray laser development at the Institute of Laser Engineering, Osaka University, implemented with worldwide collaboration. The scaling of the x-ray lasing toward shorter wavelengths has been investigated in the recombination-pumped (RP) and electron-collisional-excitation (CE) pumped x-ray lasers. Extension of the RP x-ray laser close to the water window is described. With the CE x-ray laser, intense lasing of the J = 0-1 line at 19.6 nm in the neon-like Ge ion and lasing over 14.3 – 4.5 nm with the nickel-like ions are reported. Spectroscopic studies of the x-ray lasers are described, including the first observation of polarization of the x-ray laser beam generated by amplified spontaneous emission. The perspective of the plasma-based x-ray lasers is also presented.
Hydrogen storage alloys become more and more important in the fields of electric energy production and stage and automobiles such as Ni-MH batteries. The vacancies introduced in hydrogen absorption alloy by charged particle beams were found to be positive effect on the increase in the initial hydrogen absorption reaction rate in the previous study. The initial reaction rates of hydrogen absorption and desorption of the alloy are one of the important performances to be improved. Here, we report on the characterization of the hydrogen absorption reaction rate directly illuminated by a femtosecond and nanosecond lasers instead of particle beam machines. A laser illuminates the whole surface sequentially on a tip of a few cm square LaNi4.6Al0.4 alloy resulting in significant improvement in the hydrogen absorption reaction rate. For characterization of the surface layer, we perform an x-ray diffraction experiment using a monochromatized intense x-ray beam from SPring-8 synchrotoron machine.
Metallic sodium (Na) was proposed as a transparent material in the vacuum ultra-violet (VUV) spectral range in 1930s
and in 1960s. However no clear transmission has ever been demonstrated. In this paper we describe firstly the direct
measurement of actual transmittance of a sodium samples in a spectral range longer than 115 nm which corresponds to
the shortest transmission wavelength of magnesium fluoride (MgF2) windows, resulting in several tens of %
transmittance of a 3 mm-thick solid sodium sample including MgF2 windows at the wavelength of ~120 nm. We also
find very weak temperature dependency of the transmittance up to 150 degrees centigrade where the solid sample is
melted at 97 degrees. The measured transmittance pushes us to make a simple imaging experiment illuminated by the
VUV light through a 2-mm thick sodium sample, resulting in obtaining a clear image composed of 100 μm diameter
tungsten mesh recorded on a two dimensional Charge Coupled Device detector. The result also opens a way to construct
an optical imaging device for objects inside or through a solid or a liquid sodium medium. According to the present
experiment, we can make a continuous real time transmission imaging for a liquid sodium sample if we use proper
optical setup including an intense continuous VUV source or high repetition rated intense coherent source for
holographic data acquisition. Such an experiment opens up a way to perform transmission imaging through or inside a
sodium medium for characterization of hydrodynamic and material properties.
We present experimental results, theory, and simulations demonstrating two novel sources of coherent X-ray radiation
generated in the relativistic laser (>1018W/cm2) interaction with easily accessible, repetitive, and debris-free gas jet
targets. The first source is based on a relativistic mirror reflecting a counter-propagating laser pulse. A strongly nonlinear
breaking wake wave driven by an intense laser pulse can act as a semi-transparent relativistic flying mirror. Such a
mirror directly converts counter-propagating laser light into a high-frequency (XUV or X-ray) ultrashort pulse due to the
double Doppler effect. In the experimental demonstration with the 9 TW J-KAREN laser, the flying mirror generated in
a He gas jet partially reflected a 1 TW pulse, providing up to ~1010 photons, 60 nJ (~1012 photons/sr) in the XUV range
(12.8-22 nm). The second source is demonstrated with the laser power ranging from 9 to 170 TW in experiments with
the J-KAREN and Astra Gemini lasers. The odd and even order harmonics generated by linearly as well as circularly
polarized pulses are emitted forward out of the gas jet. The 120 TW laser pulses produce harmonics with ~3×1013photons/sr (~600 μJ/sr) in the 120±5 eV spectral range. The observed harmonics cannot be explained by previously
known mechanisms (atomic harmonics, betatron radiation, nonlinear Thomson scattering, etc.). We introduce a novel
mechanism of harmonic generation based on the relativistic laser-plasma phenomena (self-focusing, cavity evacuation,
bow wave generation), mathematical catastrophe theory which explains the formation of structurally stable electron
density singularities, spikes, and collective radiation of a compact charge driven by a relativistic laser.
This paper gives an overview of recent progress of laser-driven plasma x-ray lasers in Japan Atomic Energy Agency (JAEA). Fully spatial coherent plasma x-ray laser (XRL) at 13.9 nm with 0.1 Hz repetition rate has been developed using new driver laser system TOPAZ, and the succeeding optimization of the pumping condition has realized more efficient generation of the coherent x-ray pulse. The 0.1 Hz XRL is now routinely used in the wide variety of the
application experiments: The highlights of these applications are the study of fluctuation in the atomic structure of ferroelectric substances under the phase transition using the double XRL probe beam technique and the construction of new x-ray laser interferometer to observe nano-scale dynamics of materials.
Electromagnetic wave generation in the extreme ultraviolet (XUV) and infrared (IR) wavelength range occurs
during the interaction of intense short laser pulses with underdense plasmas. XUV pulses are generated through
laser light reflection from relativistically moving electron dense shells (flying mirrors). A proof-of-principle and
an advanced experiment on flying mirrors are presented. Both of the experiments demonstrated light reflection
and frequency upshift to the XUV wavelength range (14-20 nm). The advanced experiment with a head-on
collision of two laser pulses exhibited the high reflected photon number. IR radiation, which is observed in the
forward direction, has the wavelength of 5 μm and dominantly the same polarization as the driving laser. The
source of the IR radiation is attributed to emission from relativistic solitons formed in the underdense plasma.
We present the theory of the attosecond pulse generation by a relativistically intense few-cycle laser pulse interacting
with a thin plasma slab. In the limit of high plasma density or in the case of two identical pulses irradiating plasma from
opposite sides, the electron displacement in the direction perpendicular to the plasma slab is negligible. Electrons
moving along the plasma slab form the sliding mirror. The relativistic dynamics of the electrons result in the generation
of the phase-locked high order harmonics. After spectral filtering, isolated attosecond pulses with the duration less than
200 as can be obtained. We also find a very efficient regime of the attosecond pulse train generation without any
spectral filtering with the energy conversion efficiency into the main peak of about 3%.
We review our recent progress in the development of transient x-ray lasers and of their application to plasma diagnostic. The first observation of C-ray laser emission at the new PHELIX-GSI facility is reported. This TCE X-ray laser will be a promising tool for heavy-ion spectroscopy. We then present the main results obtained at the LULU-CPA facility with a compact high-resolution X-UV imaging device. This device was used to investigate the spatial source structure of the Ni-like silver transient X-ray laser under different pumping conditions. The key-role of the width of the background laser pulse on the shape of the emitting aperture is demonstrated. Finally the imaging device was used as an interference microscope for interferometry probing of a laser-produced plasma. We describe this experiment performed at APRC-JAERI.
We started a project to develop a very compact accelerator for cancer therapy. To reduce the size of the system, we adopted a laser plasma ion source using a compact ultra-high intensity laser. We have performed ion generation experiments in which the laser parameters were as follows: The wave length and the pulse duration were 800 nm and 50 fs, respectively. Peak power was 4 - 5TW. The laser pulse with normal incidence angle to the target was focused onto the target with 15 μm diameter giving power density of 3 - 4x1018W/cm2. The thin foil metals (Ti, Al) and plastics (polypropylene, polyethylene) with the thicknesses of 4 - 100 μm were used for targets. We found that the angular distribution of ions with an energy of ~0.1 MeV had a significant peak in the backward and forward in respect to the laser incidence direction.
The soft x-ray emission from He-like and H-like were obtained by using the double nozzle gas-puff (Nitrogen, and Oxygen) target irradiated by the laser which delivered a laser energy of 50 mJ in 400 ps pulse width. Efficient absorption of the incident laser energy into the double gas-puff target was demonstrated experimentally such as 15%, and 29% for Nitrogen and Oxygen, respectively. The sub keV x-ray emission from He-β(1s2-1s2p, 1s2-1s3p, and 1s2-1s4p) lines are observed around the 0.4 nm wavelength region by using the double nozzle Argon gas-puff target irradiated by a 5 J, 1 ns, 1 μm laser. Using the gas-puff target irradiated by a femto-second laser pulse, highly ionized ions of Cr-, Fe- and Ni-like Kr at the 5 - 20 nm wavelength region have been observed in a laser produced plasma. However, the intensity of the x-ray emissions from double nozzle gas-puff target are lower than that from the single nozzle gas-puff targets, using the Krypton gas. Using xenon gas, the intensity of the x-ray emissions from double nozzle gas-puff target is equivalent to that from the single nozzle target.
We proposed a method to generate highly spatial coherent x-ray laser, in which high order harmonics was used as a seed light of a laser-produced x-ray amplifier. In this case, the intensity and the spatial coherence of the output x-ray depended on the harmonic conversion efficiency and the spectral and spatial coupling efficiencies between the harmonics and the lasing line. Based on the present x-ray lasers using a transient collisional-excitation (TCE) scheme, we investigated the values of these efficiencies, which were needed to realize a high spatial coherence. For this purpose we constructed a Ti:Sapphire laser system in which the central wavelength and the spectral bandwidth were tunable, and we conducted a preliminary experiment. The neon-like Ti x-ray laser at a wavelength of 32.4 nm was taken as an example, and harmonics at the same wavelength was generated using Ar gas target under the conditions that the central wavelength of 810 nm and the pulse duration of 1 ps. The experimental result showed that the characteristics of the harmonics were good enough to use as a seed light of x-ray lasers.
We have observed lasing on Ne-like 3s-3p line from titanium (32.4 nm), Ni-like 4p-4d line from silver (13.9 nm) and tin (11.9 nm) with the transient collisional excitation (TCE) scheme that uses combinations of a long pre-pulse (approximately ns) and a short main pulse (approximately ps) or a short pre-pulse (approximately ps) and a short main pulse (approximately ps). A gain coefficient of 24cm-1 have been measured for plasma length up to 4mm with silver slab targets and 14cm-1 up to 6 mm with tin slab targets. We have installed a step mirror in the focusing system to generate traveling wave on the target. The traveling speed on the target is measured to be 3.08 cm/s and very close to the traveling speed of light. The traveling wave system improves the gain coefficient to 35cm-1 from 24cm-1 for Ni-like Ag and to 30cm-1 from 14cm-1 for Ni-like Sn. The strong gain saturation has been observed for the Ni-like Ag and Ni-like Sn. The output energy of the N-like Sn x-ray laser is 20 (mu) J. Spatial beam profiles of propagating x-ray lasers through gain plasma have been measured and are indicating localization of very high gain area and x-ray laser refraction.
We present a review of new progress performed in several laboratories (Laboratoire pour l'Utilisation des lasers Intenses, Rutherford Appleton Laboratory, Prague Asterix Laser System, Institute of Laser Engineering, Laboratoire d'Optique Appliquee). Concerning the realization of x-ray lasers sources, using different laser pumping techniques (600 ps, 100 ps, ns/ps, OFI) and the optimization of their optical properties, using curved and plane half-cavity mirrors. In parallel of these developments, we present the main results obtained with x-ray laser in interferometry applications. These studies concern on the one hand the Michelson interferometry with an x-ray laser emitting at 13.9 nm (recently realized at LULI), and on the other hand the Fresnel bi-mirror with an x-ray laser emitting at 21.2 nm (recently realized at PALS).
This paper summarizes our recent progress achieved in the characterization and understanding of the Ni-like Ag transient x-ray laser pumped under traveling wave irradiation. At the Rutherford Laboratory CPA laser facility, we measured the temporal history of the 13.9 nm laser pulse with a high-resolution streak camera. A very short, approximately 2 ps x-ray laser pulse was directly demonstrated for the first time. More recently we carried out an experiment at the LULI CPA laser facility. Several diagnostics that recorded the plasma emission at the XRL wavelength or in the keV range indicate the presence of small-scale spatial structures in the emitting XRL source. Single-shot Fresnel interferograms at 13.9 nm were successfully obtained with a good fringe visibility. Strong lasing was also observed on the Ni-like 4f-4d line at 16 nm.
Generation of x-ray and extreme ultraviolet (EUV) radiation from laser-produced source with a new double-stream gas puff target has been investigated. The target was formed by pulsed injection of heavy gas (argon, or xenon) into a hollow gas stream from helium by using a double-nozzle setup. This new approach allows to form a high-density gaseous target at a relatively large distance from the nozzle output. X-ray emission was produced by irradiation of the argon/helium target with pulses of 1 ns time duration with energy up to 20 J from a Nd:glass laser. Strong x-ray emission at the wavelength near 0.4 nm from the argon target, similar to the emission from the solid sulphur target irradiated in the same conditions, have been observed. These new results may be useful to develop a laser-produced radiation source for x-ray lithography. To generate EUV radiation the xenon/helium target was irradiated using a Nd:YAG laser producing pulses of 10 ns and 0.7 J or energy. Efficient production near 11 nm from the xenon target exceeding emissions from solid targets was observed that should be useful for EUV lithography.
A double stream gas puff was proposed as a target for a laser pulse in a soft x-ray source, to overcome a problem of 3D gas flow outside the sonic nozzle. In a case of the sonic nozzle the gas density drops dramatically with a distance from the nozzle outlet. The double stream gas puff target is created by an injection of high Z gas into a hollow stream of low Z gas. Such a solution allows to decrease an x-ray absorption in cold gas and to keep the inner gas at a relatively high density on a distance up to 2mm from the nozzle outlet. Also in this case plasma emitting soft x-rays created by the laser pulse on the distance over 1mm from the nozzle outlet would not destroy it.
X-ray spectroscopy is one of the most important diagnostics of laser-produced plasmas, finding application in diverse areas such as laser fusion, x-ray lasers, and novel experiments using shot-pulse lasers to probe chemical and biological phenomena on the femtosecond timescale. Depending on the aims of these experiments, either high resolution spectra combined with either spatial or time resolution, or monochromatic x-ray spectrometer was also used here in x-ray diagnostics of 4f yields 3d transitions in Nickel-like transitions of elements with atomic numbers between 70 and 74. The dependence of this x-ray emission on laser energy, spot size, and target materials provides information about ionization degree, electron temperature and density - important parameters for the population inversion of a Ni- like x-ray laser in the water window.
To obtain high gain saturated amplification soft x-ray lasing output, uniform and long amplification medium must be created by focusing and target set-up technology. We report on the cylindrical lens array and multi target coupling system for creating uniform line focus. Through these methods, serial x-ray lasing with the wavelength towards the wavelength of water window are obtained on the GekkoXII Nd glass laser facility in ILE, Osaka, University.
We characterize a laser produced gas puff plasma for soft x- ray generation. Strong emissions at 11.4 nm wavelength region was observed, using krypton and xenon gas puff targets irradiated by a 0.7J/8ns Nd:YAG laser. Space resolved x-ray spectra measurement indicated that the source size depends on the Rayleigh length and the gas density profile. A channeling effect for larger tare size which is connected with the thermal focusing has been observed.
Soft x-ray emission from plasmas produced using a laser- irradiated gas puff target have been investigated. The use of the gas puff targets, created by pulsed injection of high- density gas from a solenoid valve through a nozzle, eliminates the production of debris associated with solid targets. To improve the gas puff target two approaches have been used: (1) cooling of the valve with liquid nitrogen to increase condensation of gas and (2) formation of the target by injection of gas in gas surrounding the nozzle output using the double nozzle setup. The gas puff targets created with these two approaches were characterized with x-ray backlighting method using laser-produced x-ray source. Laser pulses of 1 ns time duration with energy up to 10 J from a Nd:glass laser and of either 0.9 ns or 10 ns time duration with energies up to 0.7 J from a Nd:YAG laser were used to produce plasmas. Emissions in the soft x-ray range from laser- produced gas puff plasmas were studied for various gases. Significant improvement of x-ray production from the double stream gas puff target has been observed.
We report experimental results on Ni-like x-ray laser at the wavelength as short as 4.4 nm. The performance of x-ray lasing pumped by various types of pulse trains which were composed of 100 ps pulses was investigated with a double slab targets which were placed in series to double the gain length. Two opposing laser beams irradiated the double targets with a suitable time difference for quasi traveling wave pumping. The well collimated double target amplification was successfully demonstrated with two beam irradiation for Yb and Hf lasing at 5.0 nm and 4.7 nm whose gain length products were 11 and 6, respectively. The Ni- like lasing line of Ta have been observed at 4.5 nm. Based on these results, we will report the suitable pumping condition for the saturated water window x-ray lasers.
Annie Klisnick, Antoine Carillon, Gerard Jamelot, Pierre Jaegle, David Ros, Philippe Zeitoun, F. Albert, P. Fourcade, Jaroslav Kuba, Jean-Luc Miquel, Nathalie Blanchot, J. Wyart, Pierre Agostini, P. Breger, David Garzella, Heimo Mueller-Seelich, Denis Joyeux, Daniel Phalippou, E. Bechir, S. Hubert, G. De Lacheze-Murel, Hiroyuki Daido
We present new progress in the optimization and understanding of the transient collisional pumping scheme using an ultra-short sub-ps heating pulse. The effect of traveling-wave irradiation in enhancing the lasing output of the 4d-4p Ni-like Ag line is studied in detail. A new irradiation scheme using a frequency-doubled 600 ps pulse to preform a plasma is tested. Strong lasing is also obtained on a new line at 16.05 nm that we identify to a 4f-4d transition in Ni-like Ag. Finally we review our recent work in the development of applications of the 21.2 nm zinc laser for imaging or exciting matter. New experiments include the probing of a plasma by imaging Fresnel interferometry and a first attempts to demonstrate two-photon ionization in a xenon gas.
Soft x-ray and extreme-UV emissions form plasmas produced using a gas puff target irradiated with a Nd:YAG laser has been investigated. The use of the gas puff targets, create by pulsed injection of high-density gas through a nozzle, eliminates the production of debris associated with solid targets. Laser pulses of either 0.9 ns or 10 ns time duration with energies up to 0.7 J were used to produce plasmas. Emissions in the 1-22 nm wavelength range from laser-produced gas puff plasma were characterized for various gases. The spectral measurements were performed with the use of grating spectrographs equipped with the back- illuminated CCD camera. The source sizes was measured using the Fresnel zone plate imaging system and the grating spectrograph equipped with a slit placed perpendicularly to the dispersion direction. The obtained results would allow to develop an efficient and debrisless laser-produced radiation source for applications in proximity x-ray lithography and extreme UV lithography technologies.
Results of the joint experiment between ILE Japan and NLHPLP/IAPCM China are reported. New optics for improved line focusing, a cylindrical lens array and a deformable mirror, were used in irradiation of x-ray laser targets. Double-pass amplification at 7.9 nm has been demonstrated. Strong lasing at 7.9 nm with approximately 100 (mu) J output energy has been obtained in Ni-like Nd ions by quasi-traveling wave pumping of double targets.
The physics of laser-plasma interaction and x-ray generation by laser have been extensively investigated as close relevance laser fusion. Efficient conversion to x-rays and controllability of wavelength, pulse width, and geometrical size have given us the high potentiality of applications to wide scientific and technical fields. An efficient high average power laser with a good beam quality is also under development as the key technology for the applications.
A high aspect ratio line focus on a target for the x-ray laser experiments is required for obtaining a high gain-length product. A new line focus system is developed to generate a uniform line focus. The system consists of a deformable mirror of a continuous faceplate type which provides an appropriate wavefront distribution for compensating an aberration of a line focus optic. The width and intensity distribution of 18.2 mm long line focus has been improved on 2 times diffraction limit. In another application, a rectangular beam shaping from a circular defocused beam is investigated by the experiment and the diffraction calculation. The controllability of intensity distribution of laser beam by deformable mirror has been demonstrated.
Experimental progress in Ne-like Ge x-ray lasers (19.6 nm and 23.6 nm) has been made by using a curved target and multiple-short pulse. The curved target was introduced to compensate x-ray laser beam refraction in a laser produced plasma. The pulse shape of the pumping laser was varied in search for the improvement in the pumping efficiency. For generation of shorter wavelength lasers, the scheme using a curved target pumped with a multiple-short pulse laser was extended to the amplification studies in Ni-like lanthanide elements (Nd, Sm, Gd, Tb and Dy) corresponding to the spectral range of 6 nm to 8 nm.
X-ray emission spectra in the wavelength range of 2 - 13 nm from 21 kinds of material (carbon through tin) irradiated either by a 4 J/35 ns slab Nd:glass laser or by a 0.5 J/8 ns Nd:YAG laser were recorded with a grazing incidence spectrometer equipped with a microchannel plate detector. The absolute photon intensities of these spectra were determined by simultaneous measurement of the emission from a molybdenum plasma with the grazing incidence spectrometer and a transmission grating spectrometer. For the carbon plasma, the electron temperature and density are derived from the spectrum and the conditions for intense Lyman (alpha) line are discussed. Finally, we describe the application to an x-ray microscope with the laser-produced carbon plasma.
I. C. Edmond Turcu, Ian Ross, P. Trenda, C. Wharton, R. Meldrum, Hiroyuki Daido, M. Schulz, P. Fluck, Alan Michette, A. Juna, Juan Maldonado, Harry Shields, Gregory Tallents, L. Dwivedi, J. Krishnan, D. Stevens, T. Jenner, Dimitri Batani, H. Goodson
At Rutherford Appleton Laboratory we developed a high repetition rate, picosecond, excimer laser system which generates a high temperature and density plasma source emitting approximately 200 mW (78 mW/sr) x ray average power at h(nu) approximately 1.2 KeV or 0.28 KeV < h(nu) < 0.53 KeV (the `water window'). At 3.37 nm wavelength the spectral brightness of the source is approximately 9 X 1011 photons/s/mm2/mrad2/0.1% bandwidth. The x-ray source serves a large user community for applications such as: scanning and holographic microscopy, the study of the biochemistry of DNA damage and repair, microlithography and spectroscopy.
It is shown that curved slab targets are effective in compensating x-ray refraction due to electron density gradient in the expanding plasma. Significant improvement in the beam divergence and laser intensity has been observed. Soft x-ray laser of 1 mrad divergence has been generated in double- pass amplification of a collisionally-excited Ne-like Ge laser with the curved target. Generation of a polarized beam with a polarizing half cavity is described. Initial results of in-line holography as well as Fourier transform holography using the Ge laser as the light source are also presented.
In x-ray microscopy applications of CCDs in the water window region, radiation damage in the MOS structure due to x rays is a problem. The backside illuminated CCD is one of the possibilities to solve the problem. This paper reports about a CCD imaging system for x-ray microscopy applications using a backside illuminated CCD (EEV Ltd., CCD 02-06). The system is used for a zone plate x-ray microscope using a laser plasma source. It is effective to take an image with a single x-ray pulse. The dark noise is 1 electron/s/pixel (r.m.s.) at a temperature of -53 degree(s)C. The quantum efficiency is measured between the wavelength of 2.25 - 8 nm.
An imaging x-ray microscope using an incoherent laser plasma source and zone plates is reported. The He-like line of 4.03 nm (1 X 1014 photons/sr/pulse) from a carbon plasma produced by a compact glass laser is used as a source. The x-ray source is monochromatized by a condenser zone plate and a pinhole. As an x-ray image detector, a Kodak 101-07 film and an MCP or a cooled backside illuminated CCD are used. An image of the #1000 copper mesh is obtained by a single x-ray pulse at a magnification of 10 by the CCD. In the case of a singe pulse, the magnification is limited so that enough photons are incident on a pixel of the CCD. Thus, the spatial resolution is limited. Further improvement such as an ellipsoidal mirror with multilayer coating is considered to improve the resolution.
We have successfully demonstrated double pass enhancement of amplified spontaneous emission of soft x rays, 23.2 and 23.6 nm of 3p - 3s transitions in Ne-like Ge, using an x-ray multilayer mirror. In this paper, we report on the fabrication of the mirror and analysis of its damage suffered during the experiments. The mirror used was a Mo-Si multilayer mirror with the reflectivity of 35% at the wavelength of 23.6 nm, deposited by an rf-sputtering system. In the damaged area of the mirror, only the multilayer was locally evaporated and the bare substrate underneath appeared. The size of the damaged area corresponded to the aperture size. We carried out the simulation on the spatial and temporal distribution of the mirror temperature during the experiment. Assuming that thermal x rays enter the mirror with the largest amount of energy among all the fluxes at the early stage of the enhancement, the result of the simulation can explain the damage feature and the temporal profile of the intensity of the amplified spontaneous emissions.
Basic characteristics of soft x-ray lasers generated as amplified spontaneous emission are described. Experimental results on soft x-ray amplification in neon-like germanium ions, obtained recently at the Institute of Laser Engineering, are reported. By comparing the experimental results with a simplified model on amplified spontaneous emission, basic parameters such as coherence and brightness of the Ge soft x-ray laser are evaluated.
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