High Power Optical Sources of Femtosecond Pulses

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TW and PW optical sources of femtosecond pulses on the base of the hybrid ... amplifiers, an optical compressor and an optical generator of third harmonic). This.

High Power Optical Sources of Femtosecond Pulses on the Base of Hybrid Laser Systems with Wide-Aperture Gas Laser Amplifiers A.A.Ionin, A.V.Konyashchenko, B.M.Koval’chuk*, O.N.Krokhin, V.F. Losev*, G.A.Mesyats, L.D.Mikheev, A.G.Molchanov, Yu.N.Novoselov, L.V.Seleznev, D.V.Sinitsyn, A.N.Starodub, V.F.Tarasenko*, S.I.Yakovlenko**, and V.D.Zvorykin Lebedev Physical Institute, 53 Leninsky prosp., 119991, Moscow, Russia Fax/phone: 7(495)132 0425, e-mail: [email protected] *Institute of High-Current Electronics of Siberian Branch of Russian Academy of Sciences, Akademicheskii pr. 2/3, 634055 Tomsk, Russia **General Physics Institute of Russian Academy of Sciences, 38 Vavilov st., 119991 Moscow, Russia ABSTRACT The multi-stage hybrid laser system producing ultrashort pulses of radiation with peak power ~1014 - 1015 W now under developing at the Lebedev Physical Institute of the Russian Academy of Sciences is discussed. The distinctive feature of the laser system is direct amplification of ultrashort pulses produced by solid state laser system, first going through a prism stretcher with negative dispersion, in gas active medium without using a rather expensive and complicated grating compressor of laser pulses. Two hybrid schemes are being developed now based on the amplification of femtosecond pulses of the third harmonic of Ti:Sapphire laser at the wavelength 248 nm in the active medium of KrF laser amplifier, and on the amplification of the second harmonic of Ti:Sa laser at the wavelength 480 nm in the active medium of photochemical XeF(C-А)-laser excited by VUV radiation of an e-beam pumped Xe2 lamp. The final stage of the laser system is supposed to be an e-beam pumped facility with a laser chamber of 60 cm in diameter and 200 cm long in the case of KrF laser, and with another laser chamber of 30-40 cm in diameter put into the former one in the case of XeF(CA) laser. The parameters of such e-beam facility are close to those of previously developed at the Institute of HighCurrent Electronics: electron energy ~600 keV, specific input power ~ 300-500 kW/cm3, e-beam pulse duration ~ 100200 ns. A possibility of using Kr2F as an active medium with saturation energy 0.2 J/cm2 for amplification of ultrashort laser pulses is also under consideration. There was theoretically demonstrated that the energy of a laser pulse at the exit of the final stage of the laser system could come up to ~ 17 J with pulse duration ~50 fs in the case of KrF laser, and ~75 J with pulse duration of 25 fs in the case of XeF laser. Two Ti:Sa laser systems producing ~50 fs pulses with energy ~0.5 mJ at the wavelength 248 nm and ~5 mJ at the wavelength 480 nm have been already developed and are being now installed at the Lebedev Institute. Preliminary experiments on amplification of UV femtosecond pulses were carried out with electric discharge KrF laser amplifier. Keywords: femtosecond pulse, terawatt power, petawatt power, gas laser amplifier, wide-aperture gas lasers, KrF laser, XeF (C-A) laser 1. INTRODUCTION Nowadays, for getting terawatt and petawatt laser pulses, quite expensive solid-state master oscillator (MO) - power amplifier (MOPA) systems are generally being employed. However, the potential of high-power hybrid MOPA laser systems, in which a solid state MO lasing femtosecond pulses and a number of solid state laser preamplifiers referred below as to a starting laser facility are combined with a set of gas laser preamplifiers and final wide-aperture amplifier(s), has not been entirely used yet. The distinctive feature of the hybrid laser system is direct amplification of ultra-short femtosecond pulses produced by a solid state starting laser facility, first going through a prism stretcher with negative dispersion, in gas active medium without using a rather complicated and expensive grating compressor of laser pulses. The cost of such a laser system seems to be less than that of a solid state one with the same output power. Moreover, the technology of high-power wide aperture e-beam pumped gas lasers, which might be employed as final stage amplifiers, has been extensively developed1-21. The experience in such a technology acquired at the Lebedev Institute and the Institute of High Current Electronics in Russia looks very attractive for its using in the development of TW and PW optical sources of femtosecond pulses on the base of the hybrid systems. Two hybrid schemes based on the amplification of femtosecond pulses of the third harmonic of Ti:Sapphire laser at the wavelength 248 nm in active medium of KrF laser amplifier, and on the amplification of femtosecond pulses of the second harmonic of Ti:Sa laser at the wavelength 480 nm in active medium of photochemical XeF(C-А)-laser excited by VUV radiation of an e-beam pumped Xe2 lamp, which are being developed now at the Lebedev Institute together with the Institute of High Current Electronics, are discussed in the paper. International Conference on Lasers, Applications, and Technologies 2007: High-Power Lasers and Applications, edited by Vladislav Panchenko, Vladimir Golubev, Andrey Ionin, Alexander Chumakov, Proc. of SPIE Vol. 6735, 67350K, (2007) · 0277-786X/07/$18 · doi: 10.1117/12.753227 Proc. of SPIE Vol. 6735 67350K-1 Downloaded From: http://spiedigitallibrary.org/ on 10/22/2013 Terms of Use: http://spiedl.org/terms

2.

HYBRID FEMTOSECOND KrF LASER SYSTEM

Experimental facility. The KrF laser system is supposed to consist of a solid state starting laser facility producing femtosecond pulses, several KrF laser preamplifiers and final amplifier. Starting laser facility. The solid state starting laser facility producing UV femtosecond pulses was manufactured by the Russian company “Avesta Project” together with the Lebedev Institute. The facility presented in Fig.1 consists of a master oscillator (Ti:Sapphire laser, laser wavelength ~744 nm, pulse duration ~30 fs), an optical stretcher, a regenerative amplifier, multipass amplifiers, an optical compressor and an optical generator of third harmonic). This laser facility produces ~60 fs pulses of the third harmonic of Ti:Sa laser radiation at the wavelength 248 nm with output energy ~0.5 mJ at repetition rate 10 Hz. The laser beam diameter is 8 mm. The optical scheme of the starting laser facility is presented in Fig.2. The laser facility comprises also pump lasers "Finesse" for the master oscillator, and “Lotis TII” for the laser amplifiers, temperature stabilization system for active crystals, electronic system for controlling and synchronization, apparatuses for measuring and controlling of laser parameters (Spectrometer “ASP” for wavelengths 700-800 nm and 200-300 nm, and calorimeters “OPHIR”.

Fig.1. Starting laser facility at the wavelength 248 nm

10 Hz 532 nm 15 ns

,

EnerLPower meterl

Spectrograph

\

ASP-250

0.5 mJ 248

Fig.2 Functional diagram of the starting laser facility at the wavelength 248 nm. KrF laser preamplifiers. Preliminary experiments on amplification of UV femtosecond pulses were carried out with electric discharge industrial KrF laser “Lambda Physik” operating as a laser preamplifier. Two-pass amplification was used. The experimental conditions were as follows: repetition rate 10 Hz, pulse duration at the entrance of the

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preamplifier ~60 fs, single pulse energy 0.5 mJ. When synchronizing the input laser pulse with the moment of maximum inversion population in the preamplifier, the output energy reached 6 mJ, i.e. the full gain came up to ~6. It should be pointed out that the output energy density exceeded the saturation energy 2 mJ cm-2 for KrF laser. One of the preamplifiers called “Berdysh” (Fig.3) has an active volume 10x10x100cm3 and pumped by e-beam with current density up to 40 A cm-2, pulse duration ~80 ns, and total energy 900 J. The e-beam is stabilized by pulsed magnetic field. The e-gun producing the e-beam is fed by a double forming line connected with a Marx generator with energy storage 3.6 kJ. Another KrF preamplifier “Garpun”9,15 (Fig.4) with active volume 16x18x100 cm3 is pumped by two counterpropagated e-beams with current density 50 A cm-2. The e-beams are produced by two e-guns and are directed into the laser chamber of 19x33x140 cm3 volume through the Ti-foil on Hibachi structure. Pulsed magnetic field with magnetic induction 0.8 kG and half width pulse duration 250 ms is employed for stabilizing the two e-beams. The e-guns are fed by 350 kV pulses of ~100 ns pulse duration produced by four double forming lines resonantly charged from the 7-stage Marks generator with output voltage ~500 kV and storage energy ~14 kJ. The total energy loaded into the active volume and specific input power are 2 kJ and 0.8 MW cm-3, respectively, the nonuniformity of input power being less than 20% at gas pressure 1.5-1.75 atm of gas mixture Ar/Kr/F2.

Fig.3. KrF laser preamplifier “Berdysh”

Fig.4. KrF laser preamplifier “Garpun”

Final KrF laser amplifier. The final KrF laser amplifier is supposed to be designed following the experience obtained in designing the DM laser facility21 pumped by radial convergent e-beams and manufactured at the Institute of High Current Electronics, however the power supply being a linear transformer20,22 instead of Marx generator. The parameters

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of the final amplifier (Fig.5) looks like the follows: energy of electrons after a foil ~500 –600 keV, specific input power ~0.3-0.5 MW cm-3, e-beam pulse duration ~100 ns, optical diameter ~40-60 cm, active length 200 cm, gas medium Ar/Kr/F2, gas pressure 1-3 atm. The final amplifier will be below referred to as DM.

Fig.5. The final KrF laser amplifier

Theoretical calculations. Amplification of ultrashort fs pulses. Parameters of KrF (B-X) transition are as follows: wavelength 248 nm; spectral width ~10 nm; spectrally limited time ~20 fs; radiative lifetime 6 ns; stimulated emission cross section 2.6×10-16 cm-2; saturation energy 2 mJ cm-2. The amplification of ultrashort laser pulses in the active medium of KrF laser at the wavelength 248 nm has been well studied. The specific of ultrashort laser pulses amplification is relatively low saturation energy 2 mJ cm-2. This fact results in necessity of using wide-aperture amplifiers. The amplification of 60 fs laser pulses at the wavelength 248 nm was obtained in Ref.23. Output peak power 4TW with output energy density 5 mJ cm-2 for subpicosecond pulses was obtained24. These results enable one to hope to get output energy ~15 J and peak power of ~1 PW for MOPA KrF laser system with final amplifier with aperture of 3000 cm2 emitting spectrally limited optical pulses ~20 fs long. So, for the amplification of ultrashort (femtosecond and picosecond) pulses in KrF laser amplifier at the wavelength 248 nm one can expect the output energy density to be hardly higher than ~10 mJ cm-2. Therefore, the maximal attainable energy of a single ultrashort laser pulse is first of all determined by an output aperture of KrF – amplifier. DM

GARPUN

KrF amplifiers: Berdysh

FM

FM

Ti:Sa front-end

Compressor

80 mJ

0.1 mJ

V=7x7x100 cm3 Wb=O.6 MW/cm3

1.6 J

V=16x16x100 cm3 Wb=O.6 MW/cm3

17 J

Fig.6 Schematicic of amplification of single ultrashort pulse in the cascade of KrF amplifiers. The size, specific pump power, and output energy are indicated for each amplifier.

V=53x53x200 cm3 Wb=O.3 MW/cm

Ar/Kr/F3=59.85/40/O.15, P=1.2 atm

In the experiments the 0.1 mJ energy ~ 50 fs single pulse of the third harmonic of the starting Ti:Sa laser facility, preliminarily time-broadened in a negative-dispersion stretcher, is supposed to be directed into the cascade of two-pass KrF-laser amplifiers “Berdysh”, “GARPUN”, and “DM” (Fig.6). It is assumed that after the negative-dispersion, the

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stretcher transforms the ~50 fs laser pulse into a comparatively long pulse of 0.3-1 ps duration. By passing successively through the active medium of above amplifiers and positive-dispersion output windows of each of the amplifiers, the pulse is amplified and compressed. It is also necessary to put an extra plane-parallel plate with positive dispersion as a time-compressor at the output of the amplification cascades. By selecting the plate thickness one can compensate the negative chirping of the amplified pulse that is set in it at the beginning of the cascade of amplification. The final pulse duration can be determined only experimentally. Numerical calculations of the wide-aperture KrF-amplifiers for ultrashort pulses were implemented on the basis of theory developed in Ref. 25. For the gain in the active medium of KrF laser is high, it is sufficient to use a two-pass geometry of amplification with one reflecting mirror. The calculation results can be represented in the form of dependences of the output energy density on the input energy density in respect to the saturated pulse energy Qs , which weakly depends on the pulse duration and varies from 2 to 3 mJ cm-2 at pulse duration changing from 10 ps to 50 fs. An example of the calculations for the final KrF amplifier at the wavelength of 248 nm is shown in Fig. 7. (left). The right part of the figure demonstrates the dependence of specific output energy on the relative length of amplification. DM

DM

(two-aass awalitiert

(two-pass amplifier)

Ar/Kr/F2(59.85/40/O. 15)

W53x53x200 cm3 P1.2 atm, W50.28 MW/cm°

V=53x53x200 cm3

Output pulse: 17 J

Input pulse: 1.5 J

Ar/Kr/F2(59.85/40/O. 15) P=1 .2 atm, Wb=0.28 MW/cm3

'1E-3

0,01

0,1

1

XIL

Q. IQ

Fig.7. The output characteristics and the energy density behavior of ultrashort pulse inside the final “DM” amplifier with the active volume 53x53x200 сm3. The arrow (left) shows the value of the input pulse energy of the previous preamplifier. L is the length of the active medium.. The theoretical calculations demonstrate (Figs. 6 and 7) that the output energy of a single ultrashort pulse at the exits of KrF preamplifier “Berdysh”, preamplifier “Garpun” and final amplifier “DM” can come up to 80 mJ, 1.5 J and ~17 J. Therefore one can expect ~ 350 TW peak power at the exit of the cascade of amplification provided by the final pulse duration is ~50 fs. The first experiments are supposed to be carried out with the starting facility and two preamplifiers, which can produce 1.6 J output energy and ~30 TW peak power. It should be pointed out, that the two preamplifiers are considered as prototypes for preamplifiers, which can be used for the laser cascade with the final KrF laser amplifier. Simultaneous amplification of ultrashort and long pulses in e-beam-pumped KrF amplifiers. As calculations demonstrate, KrF laser has a unique possibility to simultaneously amplify both ultrashort and long laser pulses, which can be used for fast ignition ICF concept with KrF laser drivers26,27, long pulses being used for pellet compression and ultrashort pulses for ignition. In fact, the gain in KrF medium is recovered very fast in about ~ 2 ns after a passage of a ultrashort pulse, which duration is far less than a lifetime of the upper laser level of B→X transition of KrF molecule. To match pumping time of high-power e-beam-pumped KrF laser, which for technical reasons is about a hundred nanoseconds, with required duration of long pulses ~ 5 ns to be longer than the recovery time, angular multiplexing scheme should be used28. Amplification of a train of long pulses in such a scheme is scarcely affected by a passage of ultrashort pulses. On the contrary, amplification of long pulses has an additional advantage of depleting a population inversion and thus controlling the amplified spontaneous emission (ASE), which due to a short radiation lifetime 6 ns results in low contrast of ultrashort pulses. The numerical simulations of output parameters for such a laser system were carried out27 using a quasistationary KrF laser code based on generalized “forward–back” multidirectional approximation for radiation transfer of both ASE and long laser pulses29. While the output energy for a single ultrashort pulse is ~17 J, about 4.0 kJ is available for a 250-ns train of long nanosecond pulses. In principle, the amplification of a train of ultrashort fs pulses in active medium of KrF laser amplifier, which results in an enhancement of output energy

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and output power, is possible in the same way of multiplication as for the long ones. However, the technical problems of delivery of radiation emitting by such a laser system onto the target look quite complicated at the moment. Amplification on Kr2F laser transition. The other approach of amplification of ultrashort fs pulses in active medium of KrF laser amplifier considers Kr2F(42Г→1,22Г) transition27, which has significant advantages in a better storage of population inversion because of longer lifetime and higher saturation energy density extracted by an ultrashort pulse. Parameters of Kr2F(42Г→1,22Г) transition are as follows: wavelength 420 nm; spectral width 80 nm; spectrally limited time ~7 fs; radiative lifetime 180 ns; stimulated emission cross section 2.3×10-18 cm-2; saturation energy 200 mJ cm-2. One can see that its bandwidth does not restrict a duration of injected second harmonic of Ti:Sa pulse. Excited triatomic molecules Kr2F are formed in kinetic processes under e-beam pumping of typical KrF laser gas mixture in amounts comparable with usual diatomic KrF molecules. It means that they can, in principle, amplify femtosecond pulses on a par with amplification of long pulses at KrF(B→X) transition. Although free-running oscillations were already obtained30 on Kr2F(4 2Г→1,2 2Г) transition, the main problems to be overcome are low small signal gain for this transition (due to large bandwidth), which makes necessary multi-pass amplification scheme, and transient absorption by atomic and molecular species produced during e-beam pumping. The latter should be reduced in optimization studies of pumping of laser gas mixture. In this case output energy for a single ultrashort laser pulse obtained in numerical simulations reaches 500 J (Fig. 8). Therefore, output power of several PW can be, in principle, obtained. DM

GARPUN

Kr2F amplifiers: Berdysh

Ti: Sa front-end

Compressor

1J

lmJ V=7x7x100 cm3 Wb=O.6 MW/cm3

20J V=16x16x100 cm3 Wb=O.6 MW/cm3

ArJKrJF2=59.8514010. 15,

500J

Fig.8. Schematic of amplification of single ultrashort pulse on Kr2F (4 2 Г→1,2 2Г) transition in the cascade of KrF amplifiers. The size, specific pump power, and output energy are indicated for each amplifier.

V=53x53x200 cm3 Wb=O.3 MW/cm

P=1.2 atm

3. HYBRID FEMTOSECOND PHOTOCHEMICALLY-PUMPED XeF(C→A) LASER SYSTEM Behind the principle of operation of photochemically driven active media are numerous mechanisms of the broadband optical excitation of dense gases, the main mechanisms being photolysis31 resulting in electronically excited atoms or radicals, direct excitation of molecules into a bound state, and secondary photochemical reactions of excited species produced in above photoprocesses. These active media are pumped by UV-VUV radiation from flash-lamps (including e-beam excited excimer lamps), open radiating discharges or strong shock waves in rare gases. This pumping technique along with gaseous nature of these active media enables a photochemical laser to be scalable up to very high output energy32,33. Among variety of media lasing due to optical excitation, the broadband active media XeF(C-A) being the most widely studied in the free-running lasing mode upon optical pumping31 is extremely attractive for the amplification of femtosecond optical pulses up to ultrahigh peak powers34. Parameters of XeF(C-A) transition are as follows: wavelength 480 nm; spectral width about 60 nm; radiative lifetime 100 ns; stimulated emission cross section 10-17 cm-2; saturation energy 50 mJcm-2. Therefore, this active media characterized by broad gain bandwidth allows one to support 10 fsec pulses and is centered in the blue-green region spectrally matching to the second harmonic of a Ti:Sa laser. A nonlinear frequency conversion to the second harmonic provides pulse temporal cleaning and along with low ASE (< 1 Wcm-2) in the photochemically driven active media promises 1010 temporal contrast to be achieved in a hybrid (solid/gas) ultra-high power MOPA laser systems. Relatively high saturation energy density due to long spontaneous lifetime promises obtaining peak power density, I, of several TW/cm2 and along with scalability to a very high volume

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makes it feasible to design a MOPA laser systems with multipetawatt output peak-power. The low nonlinear index of refraction and high breakdown threshold for the active medium allows one to directly amplify high peak-power fs pulses and thereby not to use an expensive vacuum grating compressor at the exit of the laser system. Starting laser facility. As in the case of KrF laser, the solid state starting laser facility producing femtosecond pulses was manufactured by Russian company “Avesta Project” together with the Lebedev Institute (Fig.9). The facility consists of Ti:Sapphire laser, amplifiers, and frequency converter, and produces ~50 fs pulses of the second harmonic of Ti:Sa laser radiation at the wavelength 480 nm with output energy ~5 mJ.



k11ift

Regenerative amlifier

1

Optical strether

Pump laser

____

Generator second harmonic

of

Fig.9 Starting laser facility at the wavelength 248 nm. XeF(C-A) laser preamplifier. To demonstrate experimentally fruitfulness and advantages of the new concept of the direct amplification of fs optical pulses in photochemically driven active media, the photochemically driven XeF(C-A) amplifier was built at the Lebedev Institute with aperture 3×11 cm2 and pump energy 2.9 kJ of electrical energy stored in a capacitor bank (Fig.10). The pumping source is based on the multi-channel surface discharges initiated along the walls of rectangular dielectric chamber half a meter long filled with a mixture of XeF2 vapor, argon and nitrogen at gas pressure 1 atm. Behind the principle of photochemical XeF(C-A) gain medium pumping is the formation of excited XeF(B) molecules as a result of XeF2 vapor photodissociation under VUV (120-185 nm) radiation from the multichannel surface discharge, which is followed by collision relaxation into the XeF(C) state within an environment of buffer gas (Ar, N2). The pumping scheme, in which two analogous planar sources pump an active medium placed between them, provides spatially homogenous excitation of the medium. Numerical simulations35 showed that a spatially homogenous amplification of laser beams having cross-section of several cm in diameter is possible with the gain uniformity better than 1%. Rectangular aperture of the designed amplifier offers a simple approach to the development of a multipass optical scheme for energy extraction from active medium 50 cm long. In a multipass scheme of the “wedge-trap configuration” a seed pulse runs between two tilted mirrors. This optical arrangement allows up to 45 double passes through the active medium to be implemented.

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Fig 10. Photochemical XeF(C– A) preamplifier of fs optical pulses built at the Lebedev Institute (a) and the view through its front window while the multi-channel surface discharge is initiated in the chamber (b).

a

b

It should be pointed out that pilot experiments was recently performed with a photochemically driven XeF(C-A) amplifier using 55 and 150 fs seed pulses at 475 and 483 nm36-39 . The best results demonstrated an amplification of the femtosecond pulse energy by a factor of 102 corresponding to a small-signal gain of 2×10−3 cm−1 at the wavelength 480 nm. Final XeF(C-A) amplifier. Another promising technique for pumping XeF(C-A) amplifier is the e-beam excited Xe2 VUV radiation at 172 nm. This technique was used in Ref. 2 to pump XeF(C-A) laser with 5.8 J output energy. An advantage of this pumping source is higher efficiency allowing a more compact fs XeF(C-A) amplifier to be designed with output power well beyond 10 TW. Taking into account energy balance in the pumping source and active media thoroughly studied2, it is possible to analyze prospects of applying this technique for the multi-petawatt system design. Let us consider a design of the XeF(C-A) amplifier pumped by Xe2 VUV radiation from an e-beam driven converter 60 cm in diameter filled with Xe at 2-3 atm pressure (Fig. 11). . Vacuum

Vacuum chainhar

T

Xe

Xe cflamber Marx aenerator

-\\\-Foi1 11(11/\ fV\N

Cathode

\7 )&

J//

Jaser ceii ..'-I-'.-. Ir')

Lj—i---JH

Fig.11. A cross-section of the final XeF(C-A) laser Fig.12. Schematic of the XeF(C-A) laser amplifier amplifier with e-beam driven converter. A photolytical cell containing XeF2-N2 mixture at pressure 1 atm is a hexahedral tube with rectangular CaF2 windows, which is housed into the converter driven by six e-beams. The xenon pressure is chosen to assure that electrons are decelerated in the gas layer between an e-gun foil and CaF2 windows. The design of the final amplifier is close to the

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one applied for the KrF final laser amplifier DM (Fig.5, see also the information above), except for the photolytical cell should be put inside. It should be pointed out that the design of the final laser amplifier enables us to use it as KrF laser amplifier and XeF(C-A) one. The maximum total power, W, of the e-beams loaded into Xe in the converter of 60 cm in diameter and 200 cm long is supposed to be ~ 250 GW. According to results obtained2 the overall efficiency, η, of the XeF(C) state excitation related to the e-beam energy is about 1%. Due to quenching of XeF(C) state, its real lifetime, τ, is about 70 ns. Thus, one can estimate the total energy which can be extracted in a short pulse to be Wητ = 175 J. At 25 fs pulse-width of an amplified pulse this energy corresponds to the peak power of ~ 7 PW. Taking into account the active medium volume of 250 l and stimulated emission cross-section of 10-17 cm2, one can estimate the small-signal gain to be 1.7×10-2 cm-1. As an intermediate phase, another final XeF(C-A) laser amplifier is under design now (Fig.12) at the Institute of High Current Electronics. It includes a Marx generator, a vacuum diode, a Xe filled chamber-converter, and a laser cell. The Marx generator is placed into a box filled with the dry air/SF6 mixture and is connected to the vacuum diode with the vacuum isolation of high voltage parts. This design allows us to minimize the inductance of the supply circuit and weight of the accelerator. The vacuum diode forms four 120 cm long × 15 cm wide e-beams, which are injected into the Xe converter. The 7.5 cm distance between Ti foil and CaF2 windows was chosen to assure electron deceleration in the converter at xenon pressure 3atm. The aperture of the 128 cm long laser cell is 12x12 cm. The laser cell is filled with XeF2/N2 mixture at pressure 1-2atm.The parameters of the e-beam in the vacuum diode are as follows: total current 80 kA, peak voltage 420 kV, current pulse duration ~400 ns (FWHM). The total peak power of the electrons coming through the foil into the Xe cell is expected to be 16 GW for the 210 ns pulse (FWHM). Simulation of gain and stored energy. To simplify numerical modeling, the square laser cell was replaced with the tube of circular section with the same perimeter. According to the data presented in Ref.2, the fluorescence efficiency of ebeam pumped xenon was taken to be equal to ηpumpXe = 30% and the VUV coupling efficiency, which is the product of CaF2 windows transmission and the solid angle factor, was estimated to be ηcyl = 15%. In this case, the VUV photon flux density at the internal surface of CaF2 windows was calculated to be FR = ηpumpXe⋅ηcyl⋅(PpumpXe /S)/ ћω= 1.0⋅1023 cm2 sec-1, where S is the area of the laser-cell side-face. The average cross section of XeF2 photoabsorption at 172 nm weighted by the xenon intensity distribution is equal to2 σ(XeF2) = 1.6⋅10-17 cm2. Calculation of the spatial distributions of the photon flux density F(r) and XeF(С) concentration is based on the solution of the non-stationary equations of the radiation transport in the cylindrical geometry along with the simplified kinetic model for the XeF(С) state. The results obtained for the small signal gain and the energy on the C-A transition, which is stored in the active volume, are presented in Figs. 13 and 14. The moment t = 170 ns corresponds to the maximum of the small signal gain. A rather uniform gain distribution in the active medium could be obtained at [XeF2] = 1⋅1016⋅cm-3 at t=170 ns, with the g value being about 0.005 cm-1 and the energy stored in the active medium being Est = 6 J. According to the numerical modeling of the XeF(C-A) laser amplifier one can expect up to 100 TW peak power in a 30 fs laser pulse.

g , c m -1 0.025

0.02

0.015

[ X e F 2 ] = 3 .2 ⋅1 0 1 6 ⋅c m - 3 [ X e F 2 ] = 2 ⋅1 0

16

⋅c m

E s t, J

-3

[ X e F 2 ] = 1 ⋅1 0 1 6 ⋅c m - 3

0.01 0

0.005

C 2.1016

4.1016

6.1016

8.1016

1.1017

[ X e F 2 ] , c m -3

0o

r, cm Fig. 13. Gain distribution against radius at various XeF2 concentration at the time moment t = 170 ns.

Fig.14. The energy stored in active volume at the time moment t = 170 ns

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4. CONCLUSIONS The multi-stage hybrid (solid state/gas) laser system producing ultrashort pulses of radiation with peak power ~1014 1015 W is now being developed at the Lebedev Physical Institute together with the Institute of High Current Electronics. The distinctive feature of the laser system is direct amplification of femtosecond pulses produced by a solid state laser system, first going through a prism stretcher with negative dispersion, in gas active medium without using a rather expensive and complicated compressor of laser pulses. Two hybrid schemes are being developed now based on the amplification of femtosecond pulses of the third harmonic of Ti:Sapphire laser at the wavelength 248 nm in the active medium of KrF laser amplifier, and on the amplification of the second harmonic of Ti:Sa laser at the wavelength 480 nm in the active medium of photochemical XeF(C-А)-laser excited by VUV radiation of an e-beam pumped Xe2 lamp. Preliminary experiments on amplification of UV femtosecond pulses were carried out with electric discharge KrF laser amplifier The final stage of the laser system is supposed to be an e-beam pumped facility with a laser chamber of 60 cm in diameter and 200 cm long in the case of KrF laser, and with another laser chamber of 30-40 cm in diameter put into the former one in the case of XeF(C-A) laser. 5. ACKNOWLEDGMENTS This research was implemented within the Programs of the Russian Academy of Sciences “Fundamental problems of relativistic pulsed and stationary high-power electronics” and “Femtosecond optics and new optical materials”, and with financial support of the Russian Ministry of Science and Education. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39.

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