High-density lithium plasma columns generated by intense subpicosecond KrF laser pulses

15 April 1998

Optics Communications 149 Ž1998. 289–295

High-density lithium plasma columns generated by intense subpicosecond KrF laser pulses W. Theobald

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2 , C. Wulker , J. Jasny 3, J.S. Bakos 4 , J. Jethwa, F.P. Schafer ¨ ¨

Max-Planck-Institut fur Germany ¨ biophysikalische Chemie, Abteilung Laserphysik, Postfach 2841, 37018 Gottingen, ¨

Abstract Subpicosecond KrF laser pulses were focused with an intensity of 2 = 10 15 Wrcm2 to a traveling-wave line-focus on solid lithium targets to create a 3 mm wide plasma column of up to 800 mm length. The soft X-ray emission between 1 nm and 15 nm of the laser produced plasma was measured in both longitudinal and transversal directions to the plasma axis with two single-shot spectrographs. An almost linear increase of the Li III Lya- and Lyb -line intensity with growing plasma length was observed. An average electron temperature of 35 eV and an electron density of about 1 = 10 21 cmy3 could be inferred from the lithium spectra. q 1998 Elsevier Science B.V. PACS: 52.40.Nk; 52.25.Nr; 42.55.Vc

1. Introduction Since the first demonstration of soft X-ray amplification in 1984 w1,2x a wealth of new laser schemes have appeared. This development is pushed forward by the huge potential of applications for X-ray lasers in biology, atomic and molecular physics, chemistry and, last but not least in industry and material science w3x. The most important requirement to open the doors for such devices in various fields is the design of small scale X-ray lasers of reduced cost, improved repetition rate and, of course, high laser power. Apart from collision and recombination pumped

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E-mail: [email protected] Present address: Institut fur ¨ Optik und Quantenelektronik, Universitat ¨ Jena, Max-Wien-Platz 1, D-07743 Jena, Germany. 2 Permanent address: OMICRON Vakuumphysik GmbH, Idsteiner Strasse 78, D-65232 Taunusstein, Germany. 3 Permanent address: Institute of Physical Chemistry of the Polish Academy of Sciences, ul. Kasprzka 44r52, 01-224 Warsaw, Poland. 4 Permanent address: Department of Plasma Physics, Research Institute for Particle and Nuclear Physics, P.O. Box 49, H-1525 Budapest, Hungary. 1

X-ray lasers using small scale ultrashort-pulse length lasers as drivers w4–10x, discharge pumped soft X-ray lasers are also now available w11x. The so-called water window between the K-absorption edge of oxygen at 2.32 nm and carbon at 4.36 nm is of special interest since X-ray microscopy can use the one order of magnitude difference in the absorption coefficients to provide a natural contrast for biological samples in their aqueous environment. The use of femtosecond high intensity lasers has opened up new promising routes in the development of compact X-ray laser sources. High intensity subpicosecond laser pulses are capable of producing plasmas with electron densities exceeding 10 23 cmy3 w12–16x and they are promising tools for the realization of recombination pumped X-ray laser schemes in the water window range employing a traveling-wave excitation w17–20x. Population inversion by recombination of optical-field ionized ŽOFI. plasmas in the wake of high intensity femtosecond laser pulses renewed the interest in achieving high gains w5–8,21x. High inversion density is achieved due to strong three body recombination in a fully ionized but relatively cold plasma. In the conventional OFI-recombination scheme the generation is collinear to the direction of the incident excitation femtosecond laser pulse and there are severe problems to provide long enough plasma

0030-4018r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 3 0 - 4 0 1 8 Ž 9 8 . 0 0 0 3 0 - 3

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channels for large gain–length products. A solution to this problem could be to implement the so-called ‘‘plasma channeling’’ technique which was introduced by Milchberg et al. w22x and provides optical guiding of an intense focused laser beam for up to 70 Rayleigh lengths. Another promising technique to avoid defocusing seems to be the use of micro-capillaries. Suckewer et al. w23x recently demonstrated lasing on the Li III 2p–1s transition at 13.5 nm up to a gain length of 5 mm and a gain–length product of 5.5 was reported. Up to now it is difficult to realize an OFI-scheme for wavelengths shorter than the 13.5 nm lithium-laser since higher Z-target materials and drastically increased driver intensities are required. A transversal arrangement with a line-focus geometry together with a traveling-wave excitation allows one to work with high densities and circumvent some of the above mentioned problems. Adiabatic expansion is usually applied for cooling in the recombination pumped X-ray laser schemes w24x. This mechanism seems to be too slow to produce transient population inversions in near solidstate laser-produced plasmas w25x. A much faster cooling mechanism occurring on a subpicosecond time scale is thermal heat conduction in the electron gas providing rapid heat transport to cooler parts of the plasma. This cooling process can be applied by using slab targets in which case the proper plasma density scale length and the optimum target design is very important. For the experiments presented here, we have chosen to use lithium as the target material because it can be fully ionized by a subpicosecond laser pulse with an intensity of ; 10 15 Wrcm2 which is readily available in our line-focus geometry. In contrast to the OFI-experiments performed with underdense lithium gas targets where intensities of 10 17 Wrcm2 are needed to fully ionize the medium, the solid-target-interaction has the advantage of efficient energy absorption achieving higher ionization stages with a laser of several orders of magnitude lower intensity.

2. Experiment The experimental set-up shown in Fig. 1 includes a hybrid dye-KrF short-pulse laser system ŽSPL. w26x and an X-ray preionized final KrF-amplifier ŽAM. pumped by a fast discharge w27x. The beam is first expanded by a negative lens and then a prism tilts the pulse front with respect to the phase front by an angle of 458 which is required for the traveling-wave excitation at the speed of light in the line-focus w28,17x. A spherical mirror ŽSM 1 . then focuses the beam in a vacuum tube to an intermediate line-focus ŽLF. of 30 mm length and 65 mm width. The beam is collimated by a plano-convex lens after double pass amplification in the module ŽAM. and then focused on the target by means of a Maksutov-optics comprising a spherical mirror ŽSM 2 . and a meniscus for correction of the spherical aberration w29x. In fact, the intermediate focus

Fig. 1. Experimental set-up for the traveling-wave line-focus measurement described in the text. Subpicosecond laser pulses are generated in a short pulse laser system ŽSPL. and are then further amplified in a KrF-module ŽAM.. A Maksutov-system comprising a meniscus and a spherical mirror ŽSM 2 . demagnifies 25-fold an intermediate line-focus ŽLF. onto a target producing a plasma column. Two single-shot soft X-ray spectrographs are used to measure the plasma emission along the plasma column axis ŽSP1 . and transversal to it ŽSP2 .. A back reflection is used to measure the pulse energy of each shot with a calibrated energy meter ŽEM.. A small fraction of the beam is coupled out by a planeparallel CaF2 -plate ŽPP. and is focused onto a CCD-camera to monitor the focused intensity.

ŽLF. is demagnified 25-fold onto the target resulting in a line-focus of 1.2 mm length and 3 mm width. The size of the focused beam was directly measured by imaging the spot of the strongly attenuated laser beam with a microscope objective with 40 times magnification onto a CCDcamera. The outer parts of the beam with lower intensity were blocked by an aperture to make sure that a constant intensity distribution along the line-focus was present. Therefore, only a maximum length of 800 mm was available. CaF2 material was used for the complete refractive optics to avoid two photon absorption and other nonlinear effects. All optical components were carefully designed to avoid prolongation of the laser pulse in the optical elements. Laser pulses of energy up to 200 mJ with a pulse duration of 0.7 ps, measured with an autocorrelation method and assuming a Gaussian pulse profile, were available at a repetition rate of 0.1 Hz. The contrast ratio, which is defined as the ratio of peak pulse power to that of the pedestal before the main pulse, was measured to be about 10 6 for fresh gas fillings in the KrF-amplifiers. In order to increase the contrast ratio, the first few shots with the worst contrast ratio were not used and to minimize fluctuations of the laser system, an average energy of up to 100 mJ was used. This results in an intensity of about 2 = 10 15 Wrcm2 on target taking into account that about 50% of the total energy was concentrated in the central line-focus while the rest was distributed over a larger area. The back reflection from the collimating lens after the

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final amplification stage was used to measure the energy of each shot with a calibrated calorimeter. In addition, the quality of the focused beam was monitored by coupling out a small fraction of the beam with a plane parallel plate ŽPP. and focusing it onto a CCD-camera. For the data evaluation, only events with monitor values in the interval of " 20% around the average were considered. The target, an optically polished glass rod of 5.7 mm diameter covered with a pure lithium coating, was located in the middle of a vacuum chamber Žbackground pressure of 5 = 10y6 mbar.. The incident laser light was p-polarized with respect to the plane of incidence and it was focused onto the upper side of the rod under an angle of incidence of 458 to the surface normal Žsee side view in Fig. 1.. Two identically built single-shot soft X-ray spectrographs w30x ŽSP1 and SP2 . with electronic data acquisition and spectral coverage between 1 nm and 15 nm were used for the line-focus measurements. One spectrograph collected the radiation emitted along the plasma axis while the other one was aligned transversal to the plasma column. A cross-calibration of the spectrographs was carefully performed and it revealed that the transversal spectrograph is less sensitive by a factor of about 20. At a wavelength of l s 4.03 nm ŽCV Hea-line., a sensitivity difference of 19.2 " 0.3 units and in the spectral range between 9 nm and 15 nm an average value of 23.6 " 3.0 units was measured. The difference is due to poor sensitivity of the microchannel plate ŽMCP. detector of the transversal spectrograph.

3. Results and discussion Figs. 2Ža. –2Žd. show single shot lithium spectra for various line-focus lengths between 100 mm and 800 mm. The measurement was performed by shifting the target in direction of the plasma axis and controlling the length of the plasma column with the sharply cut end of the target rod. Therefore, the intensity and the focusing conditions were always kept same during the whole experiment. The target was rotated after each shot to present a fresh surface. The longitudinal spectra were recorded by SP1 while the transversal ones were recorded by SP2 . Both spectra in each figure belong to the same laser shot and can be compared because the scaling of the left and right ordinate take the sensitivity difference of both spectrographs into account. The longitudinal spectrum in Fig. 2Ža. clearly shows the Lya-line at 13.5 nm and Lyb at 11.4 nm of the hydrogen like Li III together with a strong continuum emission. In contrast, the transversal spectrum in Fig. 2Ža. just lies above the noise level and only a week Lya-line is visible. Similar spectra were observed with increasing plasma column length while Lya and Lyb become more visible with increasing length in the transversal direction wsee Figs. 2Žc., 2Žd.x. The Lya-radiation emitted in direction of the plasma axis is 6 times stronger than in transver-

Fig. 2. Li III spectra for various plasma lengths Ža. 100 mm, Žb. 200 mm, Žc. 400 mm, and Žd. 800 mm. The plasmas were created by 0.7 ps KrF-laser pulses at an intensity of 2=10 15 Wrcm2 . The solid curve shows the measured X-ray emission along the plasma column axis Žlongitudinal. and the dotted curve the emission transversal to it. Notice the different vertical scales for each figure.

sal direction in case of the 100 mm length, but this ratio drops down to about 2 for the length of 800 mm. A careful interpretation is required to discuss this radiation anisotropy. By itself, the anisotropy cannot be taken as evidence for stimulated emission since the soft X-ray radiation observed in transversal direction probably suffered absorption in a surrounding cold preplasma produced by a prepulse. The amplified spontaneous emission ŽASE. intensity was in the range of 10 8 –10 9 Wrcm2 and it is expected that a cloud of neutral and singly ionized lithium atoms is produced blowing away from the surface many nanoseconds before the main short pulse impinges on the target. For a further analysis, Fig. 3 shows the line intensities of the Lya- and Lyb -line as a function of the length. For each length, 3 to 4 spectra were recorded and the strength of the line was inferred from each spectrum and finally averaged. The error bars represent the weighted average of the errors obtained from each fit. The transversal signal in

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Fig. 3. Ža., Žb. Measured line strengths of Lya and Lyb , respectively, as a function of the plasma length Žlongitudinal: solid square symbols and transversal: open circle symbols.. All measurements were performed under the same conditions as in Fig. 2.

Fig. 3Ža. increases linearly with the column length as one would expect it to do. In contrast, the Lya signal increases in the longitudinal direction almost linearly until 400 mm but then slightly bends off. For the Lyb-line intensity, a linear increase with the column length is observed wsee Fig. 3Žb.x. The measurements show that the Lya emission intensity is only slightly decreased while traveling through the elongated plasma. This can be caused by absorption in the plasma itself or is due to refraction in a steep density gradient of the plasma. If only absorption in a homogeneous elongated plasma slab is assumed, a simple fit of the signal versus plasma length L with the function f Ž L. s const w 1 y exp Ž ya L . x yields an absorption coefficient of a s 7 cmy1 while for Lyb the absorption is almost zero. A time- and space-integrated electron temperature of the recombining plasma can be inferred from the slope of the Lyman continuum w31x. The frequency dependence of the Lyman continuum for energies above the ionization potential is proportional to expŽyhnrk BTe . assuming a Maxwellian velocity distribution in the electron gas. Continuum emission originates from free-bound and free-free transitions with a similar frequency dependence. The electron temperature can then be directly obtained from the inverse of the slope by a straight-line fit. For the different plasma lengths an averaged electron temperature of 35.4 " 0.4 eV is deduced from the longitudinal spectra, and from the transversal spectra, an averaged temperature of 32.2 " 0.4 eV is extracted. The spatially and temporally integrated electron density n e can be estimated by the evaluation of the large spectral line-broadening observed in Fig. 2. The broadening of

hydrogenic spectral lines in dense plasmas is mainly due to linear Stark effect in the fields of electrons and ions w32x. The spectral profile is described by a Holtzmark distribution, but for a rough estimate only a Lorentz fit is taken here. This gives for Lya in Fig. 2Ža. Ž L s 100 mm. a spectral half width of 0.23 nm. A Stark broadening of about 0.13 nm is estimated taking the instrumental width of 0.15 nm with a Gaussian instrumental profile into account. The broadening for Lya and Lyb measured from the spectra for various plasma lengths are 0.13 " 0.02 nm and 0.28 " 0.05 nm, respectively. This results in an electron density of n e f 6 = 10 20 cmy3 for a fully ionized plasma. A rough estimate for the electron density can be also obtained from the Inglis-Teller limit. The last well-resolved line in the spectrum is Lyb wsee Fig. 2x while all other lines with higher principal quantum number of the upper level merge in the continuum Žonly Lyg with n s 4 might be present in Figs. 2Žc. and 2Žd... An electron density of 9.6 = 10 21 cmy3 is calculated for n s 3 as the series limit, while n s 4 would yield a density of n e f 1.1 = 10 21 cmy3 which is a factor 1.7 higher than for the previous estimation. For increasing quantum number, the lines become more and more indistinguishable from the continuum, since the spectral-widths of a ground state transition increases approximately with the square of the principal quantum number of the upper level. Considering both estimates obtained from line-broadening and from the Inglis-Teller limit, the electron density is on the order of 1 = 10 21 cmy3. If it is assumed that Lya and Lyb are emitted from a plasma volume with the same electron density, the ratio of the widths D v 3y1rD v 2y1 should be 8r3 f 2.7. The measured ratio lies between 1.6 and 2.5 which is a little lower than expected. Hence, the assumption of equal densities is not well justified and the emission of Lya and Lyb seems to originate from different volumes and stages in the plasma evolution. For the interpretation of the measurement it is assumed that the plasma is in local thermodynamic equilibrium ŽLTE. which is valid when the electron density is larger than n e ) 5 = 10 17ŽTereV.1r2 Ž Z ) . 6 cmy3 for a given electron temperature w33x. An electron density of 2 = 10 21 cmy3 is obtained for Te s 35 eV which is close to the measured value and hence LTE might be used here. The Saha equation yields for hydrogen-like lithium ions under the present plasma conditions Ž n e f 1 = 10 21 cmy3 , Te f 35 eV. a ratio of LiIVrLiIII f 18.9 which means that the concentration of hydrogen-like ions is approximately 19 times lower than the concentration of fully ionized lithium. Most of the laser energy of the p-polarized beam with an angle of incidence of 458 is deposited around critical density where the electron-ion collision frequency is maximum w14x. Here heating is most efficient and the hottest part of the plasma leads to an almost fully ionized lithium plasma. If the plasma undergoes an adiabatic expansion after the laser pulse has ceased, the density and electron

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Fig. 4. Ža. Calculation of the Lya absorption coefficient versus time assuming a planar adiabatic expansion of the plasma. Žb. Calculation of the number of spontaneously emitted Lya-photons per second along a plasma column of 800 mm length in an expanding plasma.

temperature at later times are determined by the equation .gy1 s TecrrTe for a planar target geometry neŽ n cr e rn e glecting any density and temperature gradients. Here, n cr e and Tecr are the initial electron density and temperature respectively and g s 5r3 is the adiabatic coefficient of the plasma. As initial density we take the critical density, which is indicated by the index ‘‘cr’’ in the equation. An initial temperature of 240 eV is calculated which results in a concentration ratio of even LiIVrLiIII f 374.3. The absorption coefficients of the H-like ion resonance lines can now be calculated as a function of time using the Boltzmann distribution for evaluation of the level populations and the Saha equation for the degree of ionization. Fig. 4Ža. shows a calculation for the Lya-absorption coefficient a 12Ž t . which increases rapidly during the plasma expansion. For times longer than 20 ps, the medium becomes optical thick for the radiation, and therefore, only the first 20 ps contribute substantially to the measured time-integrated signal. The measurable Lya-intensity in the spectrograph SP1 is related to the time-averaged photon flux that has traveled through a plasma column with length L supposing that the soft X-ray radiation is suffering absorption. If stimulated emission is neglected, the number of photons NphŽ t . emerging per second at the front side of the column into the solid angle D V solid of the detector Ž D V solid s 5.9 = 10y4 ster. is given by the spontaneous radiation in the direction of the plasma column: Nph Ž t . f F Ž t . N2 Ž t . A 21 =

Ž D V solid . rster 4p

1 y exp Ž ya 12 Ž t . L .

a 12 Ž t .

,

Ž1.

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where F Ž t . is the transversal cross-section of the plasma column increasing linearly in time in the case of a planar expansion of the plasma with approximately the ion sound velocity. N2 Ž t . is the population density of the upper level and A 21 is the spontaneous emission rate which is A 21 s 3.8 = 10 10 sy1 for the Li III 2p–1s transition w34x. The calculated number NphŽ t . for the Lya -radiation versus time is shown in Fig. 4Žb. for a plasma length of L s 800 mm. The intensity NphŽ t . first increases because the product N2 Ž t . = F Ž t . which is equal to the number of emitters per column length increases steadily in the first 40 ps. It can be seen in Fig. 4Ža. that the opacity for a column length of 800 mm is weak for times less than 7 ps. At about 10 ps, the absorption coefficient a 12 has become large enough so that a considerable reabsorption balances the enlargement of N2 Ž t . = F Ž t . and the Lya -intensity detected by SP1 peaks and then decreases. The corresponding electron density and absorption coefficient at the peak intensity at 10.5 ps are n e s 1.6 = 10 21 cmy3 and a s 16 cmy1 respectively which are close to the temporally and spatially integrated measured values n e s 1 = 10 21 cmy3 and a s 7 cmy1. At later times, the ground state population-density increases quicker than the population of the upper level resulting in an increased opacity and an eventual decrease of the emission intensity. For example, the absorption coefficient reaches a value of 50 cmy1 at 16 ps with a characteristic optical thickness of only 80 mm. The simple model used here does not take any density and temperature gradients into account and it is assumed that the plasma evolution is determined by adiabatic expansion neglecting any thermal heat conduction. A more detailed analysis would need calculations with a time-dependent collisional-radiative computer code which is beyond the scope of this paper. Nevertheless, the simple model presented here seems to give a good qualitative agreement with the obtained results. It is well known from soft X-ray laser experiments that substantial refraction of the X-rays occur in a plasma with steep transverse electron density gradients. The resulting gradients in the refractive index tends to bend the soft X-ray radiation out of the gain region. Therefore, the electron density distribution must be kept as uniform as possible in the active medium. Curved targets can provide a significant enhancement in the output intensity and an improved beam quality due to compensation of refraction in the density gradient plasma w35x. The plasmas produced by femtosecond laser-solid interaction result in severe refraction effects since the density scale lengths are very short. The radius of curvature of the rays is approximately proportional to the scale length. The scale length L at a time t after the short laser pulse has ceased can be estimated by L s cs = t where cs is the ion sound speed. A scale length of 1 mm is obtained for t s 10 ps and cs s 10 7 cmrs which is calculated for an initial electron temperature of 240 eV for a fully ionized Li-plasma. A radius of curvature of about 1.2 cm is obtained for the

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Lya-radiation emitted parallel to the target surface at an electron density of 1 = 10 21 cmy3. The rays are refracted after a length of approximately 100 mm at an angle of 8 mrad with respect to the target surface, which is still within the acceptance angle of the spectrograph. Rays that are traveling longer distances are refracted out of the solid angle and can not be detected any more. This has to be taken into account for line-focus measurements and even in case of inversion, the usual detected exponential behavior can be suppressed due to the additional radiation loss. Since it is not possible to distinguish between the effects of refraction and absorption, the question as to whether the plasma has undergone a condition favorable for inversion can not be clearly answered. A spatially and temporally resolved measurement is required for further investigations.

w2x w3x w4x

w5x w6x w7x w8x w9x

4. Conclusion

w10x

We have performed, to our knowledge for the first time, measurements with high intensity subpicosecond KrF laser pulses focused to a traveling-wave line-focus on solid lithium targets. The soft X-ray emission of the plasma was measured in both longitudinal and transversal directions to the plasma column. For increasing plasma lengths, the emission of the hydrogen-like lithium Lya-radiation in the longitudinal direction increased slightly less than linear. A linear behavior was observed for Lyb . If only absorption of the Lya-radiation in a homogenous plasma slab is assumed, an absorption coefficient of 7 cmy1 can be inferred. An additional loss of radiation in the longitudinal direction is expected due to strong refraction in steep density gradients which are present in subpicosecond laser produced plasmas. From the lithium spectra, an average electron temperature of 35 eV and an electron density of about 1 = 10 21 cmy3 could be extracted. Further investigations are needed to clarify which scale lengths and target geometries exploit most efficiently a fast thermal heat conduction providing a high gain of the soft X-ray radiation in combination with less refraction.

w11x w12x w13x

w14x w15x w16x w17x

w18x w19x w20x

w21x

Acknowledgements The authors would like to thank B.N. Chichkov and S. Szatmari ´ for valuable discussions. We are grateful to D. Ouw and J. Bergmann for technical assistance.

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