review of soft x-ray laser researches and developments

7/30/2019 Review of soft x-ray laser researches and developments

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INSTITUTE OF PHYSICS PUBLISHING REPORTS ON PROGRESS IN PHYSICS

Rep. Prog. Phys. 65 (2002) 15131576 PII: S0034-4885(02)07827-2

Review of soft x-ray laser researches and developments

Hiroyuki Daido

Advanced Photon Research Center, Kansai Research Establishment, JapanAtomic Energy Research Institute, 8-1 Umemidai, Kizu-cho, Soraku-gun, Kyoto 619-0215,Japan

E-mail: [email protected]

Received 1 November 2001, in final form 12 April 2002Published 18 September 2002

Online at stacks.iop.org/RoPP/65/1513

Abstract

In this paper, the author reviews the plasma-based x-ray lasers which we have alreadydemonstrated saturated amplification whose wavelengths are between 50 and 6 nm.

Section 1 describes the motivation of this review paper which includes basic ideas,developments and their applications of x-ray lasers. In section 2, the author describes the earlyx-ray laser researches on the recombination and the electron collisional excitation schemesincluding the hydrogen-like and lithium-like ion recombination schemes and the electroncollisional excitation scheme. Section 3 describes the first demonstration of significant lasing

at Livermore for the electron collisional excitation scheme of neon-like selenium ions at awavelength of 20.6 and 20.9 nm and Princeton for the recombination scheme of hydrogen-like carbon ions at a wavelength of 18.2 nm. In section 4, the author describes the electroncollisional excitation type soft x-ray lasers which are at present the most successful x-raylasers. The subjects with which the author deals are saturated amplification neon-like softx-ray lasers, improvement of neon-like soft x-ray laser performance using multi-layer mirrors,atomic physics issues of the neon-like soft x-ray lasers, gain guiding of the x-ray laserbeam propagation, discharge-pumped compact repetitive neon-like ion soft x-ray lasers, thecollisional excitation nickel-like ion soft x-ray lasers, high gain and saturated amplificationnickel-like soft x-ray lasers at wavelengths as short as 7 nm, the short wavelength nickel-likex-ray lasers whose wavelengths are close to the longest wavelength edge the water window of4.4 nm, transient collisional excitation scheme which is currently the most popular soft x-raylasers pumped by short-pulse compact lasers with a laser energy of a few J to a few tens of J.

In section 5, the author describes various plasma-based x-ray laser schemes other than therecombination and the collisional schemes, such as the optical field ionization schemes andinner-shell ionization schemes. Section 6 includes soft x-ray laser applications such as softx-ray holography, soft x-ray interferometers, soft x-ray microscopy and other applications. Insection 7, the author summarizes this review paper and he proposes a future direction for x-raylaser researches.

0034-4885/02/101513+64$90.00 2002 IOP Publishing Ltd Printed in the UK 1513
http://stacks.iop.org/rp/65/1513


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Contents

Page1. Introduction 15152. Early x-ray laser researches on therecombination andtheelectron collisional excitation

schemes 15172.1. Introduction 15172.2. Hydrogen-like ion recombination scheme 15182.3. Lithium-like ion recombination scheme 15202.4. Electron collisional excitation scheme 1523

3. First demonstration of significant lasing at Livermore and Princeton 1525

3.1. An electron collisional excitation soft x-ray laser at LLNL 15253.2. A recombination-pumped soft x-ray laser at Princeton University 1526

4. Electron collisional excitation soft x-ray lasers 15274.1. Introduction 15274.2. Saturated amplification neon-like soft x-ray lasers 15314.3. Improvement of neon-likesoft x-ray laser performance using multi-layer mirrors15314.4. Atomic physics issues of the neon-like soft x-ray lasers 15324.5. Gain guiding of the x-ray laser beam propagation 15344.6. Discharge-pumped neon-like ion soft x-ray lasers 15344.7. The collisional excitation nickel-like ion soft x-ray lasers 15374.8. High gain and saturated amplification nickel-like soft x-ray lasers 15384.9. The short wavelength nickel-like x-ray lasers 1543

4.10. Transient collisional excitation scheme 15444.11. Summary 15485. Various plasma-based x-ray laser schemes other than the recombination and

the electron collisional excitation schemes 15485.1. Introduction 15485.2. Various optical field ionization schemes 15495.3. X-ray lasers produced by inner-shell excitation and ionization processes 15525.4. Summary 1556

6. Soft x-ray laser application experiments 15566.1. Introduction 15566.2. Coherence property of the x-ray lasers 15576.3. Soft x-ray holography 15596.4. Soft x-ray laser interferometers 1562

6.5. Soft x-ray laser radiography 15666.6. Soft x-ray laser microscopy 15686.7. Other applications 15686.8. Summary and future directions 1570

7. Conclusion 1570Acknowledgments 1571References 1571


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Soft x-ray laser 1515

1. Introduction

Currently, x-ray lasers based on the laser-produced plasmas have been developed worldwide.Since the first demonstration of a ruby laser at a wavelength of 694.3 nm (Maiman 1960), the

laser scientists have pursued to make shorter and shorter wavelength laser actions. At present,a lot of papers have claimed that they have observed x-ray lasing signals. For readers, first ofall, the author should define the term of x-ray laser. The x-ray laser is the laser which deliversthe quasi-monochromatic, partially coherent photons in the spectral range shorter than a fewtens of nm. The x-ray laser action is realized in highly ionized plasmas or free electron lasers.In this paper, the author is restricted to describe the plasma-based x-ray lasers. Next, whatare the x-ray laser wavelengths which should be achieved? The wavelength of the x-ray isoverlapped with the shortest wavelength edge of the ultraviolet light. The boundary maynot be clear. According to the books which describe x-ray sciences (Elton 1990, Michette1993, Attwood 1999), the spectral range of the soft x-ray is between a few tens of nm and0.2 nm. In this spectral range, we have very good x-ray optics of multi-layer structures atthe spectral range longer than the silicon L-edge at 12.5 nm. The maximum reflectivity of

the molybdenum silicon mirrors is 70% at the wavelength of13.5nm. Soft x-ray (extremeultraviolet) projection lithography using a laser-plasma source is very promising technologyfor making next generation large-scale integrated circuit whose resolution is 7030nm. In thiscase, at-wavelength testing of opticsusing a coherent soft x-ray source is necessary. A compacthigh-coherence soft x-ray laser with a high repetition rate operation is one of the promisingcandidates for this purpose.

The next attractive spectral region is the so-called water window which is placed betweenthe carbon and oxygen K-edges (wavelength: 4.42.2nm), where the high resolution and highcontrast ratio images of live, biological specimen in water can be seen. This kind of effortwhich will be described in the latter section, has been made by many scientists. This is stillone of the very important milestones for the development of the short wavelength x-ray lasers.The strong x-ray lasers around 4 nm have been demonstrated (MacGowan et al 1990, Daidoet al 1999) using large-scale laser-fusion drivers.

The x-ray wavelength of less than 1nm is called x-ray or kilovolt x-ray where thephoton energy is beyond 1 keV. The relationship between the wavelength and the photonenergy h is as follows: h (eV) = 1200/ (nm), where h and are the Planck constantand frequency, respectively. For x-ray beyond 3 keV photon energy, the air of atmosphericpressure is almost transparent (Waynant and Elton 1976). In this case, x-ray laser beamcan be handled under the atmospheric pressure to perform high-precision holographic micro-fabrication, non-destructive testing with phase-sensitive projection imaging (Fitzgerald 2000),three-dimensional holographic recording of a random medium and so on. These wavelengthsare big milestones for developing the x-ray lasers in the near future. The x-ray laser in the hardx-ray regime or gamma-ray regime which is more than 10 keV photon energy is also attractivefor many applications. However, as far as the author knows, only the ideas have been proposedfor this spectral range (Korobkin and Romanovsky 1998).

The stage of the x-ray laser development includes spectroscopic regime where the lasingsignal is relatively high compared with other non-lasing lines. The second stage is that thelasing line dominates in the spectrum. The third includes the saturated amplification regimewhere the significant part of the population inversion is converted into the lasing signals. Thegain-length product gL for these stages corresponds to less than 5, less than 15 and beyond 15,respectively. For application of x-raylasers, the saturatedamplification is extremelyimportant,because theeffective intensityof the laser beam at this regime is 104 times higher than that fromthe Plankian thermal x-ray source having a radiation temperature of 150 eV (Key et al 1995).


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Note that the effective intensity means the intensity in the bandwidth of the x-ray mirror whichis0.05 (reflective bandwidth/central wavelength). The bandwidth of an x-ray laser is104,while the thermal source emits almost flat profile over the mirror bandwidth.

Thebrightness of variousx-ray sources is summarized in figure 1. At present, thesaturated

x-ray laser delivers extremely high brightness that is 5 or 6 orders of magnitude higher thanthe high-brightness synchrotron machines (Lee 1995).

A typical arrangement of the experimental setup of the x-ray lasers is shown in figure 2which corresponds to the most popular electron collisional excitation type laser which willbe described later. Either single- or double-slab targets have been used in the experiment.The amplifying medium is created by a line-focused laser beam on the target. The focusingoptics is composed of an aspherical lens and a cylindrical lens. The pumping laser pulsestypically consisted of a sequence of 2 or 3 short laser pulses. Then the population inversionis produced in an elongated plasma column. Spontaneous emission is amplified through theplasmacolumn, resulting in a narrow divergencemonochromatic x-ray beam which propagatesfrom both ends of the target to the other ends.

Thex-raylaseremissionis measuredusingon-axis grazing incidencespectrometersplaced

on either side of the plasma column as shown in figure 2. As for the detector of the on-axis

Figure 1. Peak brightness of the present x-ray sources as a function of the photon energy in keV(x-ray wavelength in nm). Soft x-ray lasers in the saturated amplification regime such as LLNL,Rutherford Lab, University of Paris-Sud and ILE are the world highest brightness source in thesespectral ranges. Undulators deliver high brightness x-ray in the wide spectral range shown in thefigure such as SPring 8 and Lawrence Berkeley Labs. Laser-plasma sources are the compact costeffective x-ray source.


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XRS1200l/mm

XRS1200l/mm

Pumping pulses140J in 100ps

Ag glass coated

targets

X-UV CCD

Angle

3ns3ns

Pumping pulses140J in 100ps

Figure 2. Typical experimental setup of a laser pumped soft x-ray laser including line-focusingpumping system, x-ray laser targets, thex-raylaserbeamand x-ray laser plasmadiagnosticssystem.

spectrometer, a back-side illumination type soft x-ray charge coupled device (CCD) providestime-integratedand angular-resolved spectra. A streak camera as a detector of the spectrometerprovides time-resolvedmeasurement of the angular intensitydistribution of the lasing line. Thegain coefficient is oftenmeasuredchanging thelength of a homogenous plasmacolumn withoutchanging other plasma characteristics by using the Linford formula made by Linford 1974.With g as the gain coefficient, L as the length of the plasma column, and S = j/g as thesource function, where j is the coefficient of spontaneous emission, the intensity emitted in aunit solid angle along the axis of the plasma column can be written as

IL =S(exp(gL) 1)3/2

(gL exp(gL))1/2.

If we change L such as L1, L2, L3 and so on, we can plot the intensity as a function of theplasmacolumn length. Then we can determine the gain coefficient which best fits the equationlisted above. If the x-ray laser beam is strong and stableenough, an on-axis beam-line is usefulfor x-ray laser application where multi-layer x-ray mirrors are used for beam handling.

Several diagnostic instruments are installed in the vacuum chamber to analyse the plasmaconditions. A filtered (for example, 20 m thick Al and 40 m thick beryllium) crossed-slitcamera coupled to a front-illumination type CCD detector providing the time-integrated x-rayimage of the plasma in the kiloelectronvolt region as shown schematically in figure 3, has beenimplemented in the horizontal plane close to each target to monitor the irradiation uniformity.A filtered x-ray pinhole camera coupled to an x-ray CCD camera looking at the plasma fromthe top is used to observe the expansion of the hot plasma, perpendicular to the target surface.In order to investigate the ionization balance, an appropriate spectrometer is installed in thechamber. The spectra are recorded with either a CCD detector or a streak camera to providethe time-integrated or time-resolved data, respectively.

2. Early x-ray laser researches on the recombination and the electron collisional

excitation schemes

2.1. Introduction

After demonstration of a ruby laser action by Maiman (1960), lasing in recombining plasmashave been proposed by Soviet scientists (Gudzenko and Shelepin 1965). They thought that the


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Figure 3. Schematic view of the x-ray crossed-slit camera to see an x-ray laser plasma producedby a line-focused laser.

short wavelength lasers in the soft x-ray region which need large energy gap was expected tobe realized in highly ionized ions. The systematic study was made on laserplasma interactionand atomic processes in a laser-produced plasma.

2.2. Hydrogen-like ion recombination scheme

In 1970s, English scientists (Irons and Peacock 1974, Dewhurst et al 1976) have performedspectroscopic experiments to find out the population inversion in hydrogen-like carbon ions.The simplified energy level diagram is shown in figure 4. The idea of making populationinversion is as follows: initially, fully stripped ions go into the recombination phase underthe rapid expansion cooling, strong three-body recombination occurs. Then the electrons areinitially trapped in the highly excited states following cascade decay to the lower excited statesand the ground states. The non-radiative decay rate is smaller if the energy gap is larger; on theother hand, the radiative decay is larger if the energy gap of an allowed transition is smaller. Atthe specific density and temperature, the population is fed into the specific level from higherlevels and decay of the population is minimum from the level. Then the population inversionoccurs at the specific energy levels such as the principal quantum number between 3 and 2 inthe hydrogen-like ions which is called Balmer- line.

Dewhurst claimed the population inversion of Balmer- transition (n = 32 transition,where n is the principal quantum number) in a rapidly expanding carbon plasma by measuringthe inverted intensity distribution of Lyman series lines (n = 21, 31, 41 and so on).

An extensive theoretical model for the recombination lasers in rapidly expanding cylindricalplasmas has been developed by Pert (1976). By separately analysing the initial burn forheating the plasma to fully-stripped ionic state and following adiabatic expansion to producegain, optimal conditions for themassandthermal energyof theheatedplasmaweredetermined.Once thedesired condition forsome specific ions such as carbonis obtained, therecombinationscheme can be extended to the shorter wavelengths by considering similar forms for thecollisional radiative rate equations for the hydrogen-like ions of charge Z. This leads toZ-dependence of the transition wavelength as Z2, the electron temperature T Z2,


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Figure 4. The simplified energy level diagram of the recombination-pumped soft x-ray laserscheme of hydrogen-like ions.

Figure 5. Schematic diagram of the explosive thin fibre target.

the electron density ne Z7, the timescale t Z4 and the gain coefficient g Z7.5

for a Doppler-broadened line. When the recombination laser is scaled to shorter wavelengths,rapid temperature decrease due to adiabaticexpansion becomes less effectiveandother coolingmechanismssuchasthermalconductiontothecolderregionoftheplasmaandradiationcoolingbecomes increasingly important. Trapping of Lyman- radiation has been considered to bea major limitation to the Balmer- gain. However, the trapping is still not well understoodtheoretically. EnglishFrench joint research group has performed the hydrogen-like carbonsoft x-ray lasing experiment at Rutherford Appleton Laboratory using VULCUN laser. Theyhave mainly used fibre targets which expanded cylindrically to rapidly cool the lasing plasma

and to reduce Lyman- line trapping due to the large velocity gradient. Figure 5 shows theschematic diagram of the fibre target. As a result, they have achieved a gain coefficient of4.1cm1 and the gain-length product of 3.3 (Chenais-Popovics et al 1987). Finally high-intensity carbon x-ray laser pumped by a 2 ps, 20 J, 1 m wavelength laser using a 7 mdiameter carbon fibre as an x-ray laser target was demonstrated by the English group (Zhanget al 1995). The intensity on the target was 6 1015 W cm2. The gain coefficient was12.5cm1 and the gain-length product was 6 which was the largest value in the recombinationschemes. Figure 6 shows the on-axis spectra for a 1.1 mm long carbon fibre plasma (lower


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Figure 6. On-axis spectra for a 1.1mm long carbon fibre plasma (lower spectrum) and a 5.0 mmlong plasma (upper spectrum).

Figure 7. Intensity of Balmer- and Balmer- lines as a function of the plasma length. Solid dotsare data for Balmer- and solid triangles the data for Balmer- (Zhang et al 1995).

spectrum) and a 5.0mm long plasma (upper spectrum). The line intensities of hydrogen-like

ion Balmer- and Balmer- lines as a function of plasma length are shown in figure 7. Theexponential growth of the Balmer- line is visible. The estimated power density of the x-raylaser source was 1.4 105 W cm2.

2.3. Lithium-like ion recombination scheme

Jaegle and his group 1978 have found population inversion in a recombining aluminiumplasma which was later identified as 3d4f and 3d5f transitions in lithium-like ions


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Figure 8. The simplified energy level diagram of the recombination-pumped soft x-ray laserscheme of lithium-like ions. The wavelengths correspond to aluminium.

(Jaegle et al 1987). The simplified energy level diagram is sown in figure 8. According to thepaper by Jamelot (1990), the interesting aspects of this scheme are

(a) the source of population inversion is the ground state of the closed-shell helium-like ions,

which are abundant in a large range of plasma densities and temperatures; it then canproduce a large population of lithium-like ions;

(b) contrary to thehydrogen-like case, this parent helium-like ions emit an intense resonanceline which could contribute to the plasma cooling;

(c) the radiative decay of 1s23d to 1s22p levels of the lithium-like electronic structure isvery fast due to the large overlap of the corresponding radial wave functions. Hence, thepopulation of the lower level 3d of the lasing transitions can be very low;

(d) the ionization potential of the amplifying ion is lower for the lithium-like scheme than forany other, relatively to the energy of the lasing transition. As a consequence, the lithium-like scheme requires a lower plasma temperature and hence a lower pumping power suchas 1012 W cm2 for 10 nm lasing transition.

The expected scenario of the lasing action is similar to the hydrogen-like recombination

scheme. In the intermediate density plasma such as 1019 cm

3, the electron temperaturewhich can be controlled by laser heating should be adjusted for producing helium-like ionsas much as posssible. When the pumping laser turns off, the temperature falls rapidly andthree-body recombination populates the higher excited levels of the recombining lithium-likeions. Recombination is followed by a radiative collisional cascade to intermediate levels ofn = 4, 5. At the same time, fast radiative decay from the levels in n = 3 to the ground statereduces the levels ofn = 3, where n is the principal quantum number. These processes resultin the population inversion between the levels of 3d and 4f or 5f.


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The French group have performed experiments on the population inversion of lithium-like 5f3d and 4f3d transitions in an aluminium recombining plasma. The measuredgain coefficients were 12 cm1 (Jamelot 1990). During the early phase of spectroscopicexperiments, theresults encouraged topromote thenext stagecompactx-raylaser development.

On the other hand, the Riken group in Japan has proposed the lithium-like soft x-ray laser as acompact table-top x-ray laser (Hara 1989). Successively, Kawachi et al (1997) performed thelasing experiment. An aluminium slab target was irradiated by 1.5 1012 W cm2 glass laserlight. The irradiation laser light consisted of 16 pulses, each of which was 80ps duration full-width at half maximum, and separated by 100 ps. The schematic diagram of the experimentalsetup is shown in figure 9. Amplification of soft x-ray light in the lithium-like aluminiumrecombining plasma was observed as shown in figure 10. The gain-length products of 4.2for the 15.4 nm line (3d5f transition) and 4.5 for the 10.5nm line (3d4f transition) wereobtained for a 3.0 cm long target. The beam divergence was 10mrad for a 2.5cm longtarget. Kawachi et al (1997) have also demonstrated the enhancement of the 15.4 nm line ofaluminium recombining plasmausing a half cavity in which a multi-layer soft x-ray mirror wasplaced at one of the ends of the x-ray lasing medium. Using a molybdenum/silicon multi-layer

mirror, the x-ray laser intensity became 1.8 times larger than that without the mirror.Although the recombination schemes inherently have significant advantages such as highpumping efficiency, no satisfactory lasing has been demonstrated. From the point of viewof the soft x-ray sources for applications, the recombination schemes should be developed toachieve at least the saturated amplification. Further investigation should be needed.

Figure 9. Schematic diagram of the experimental setup including line-focusing pumping system,x-ray laser targets, the x-ray laser beam and x-ray laser plasma diagnostics system (Kawachi et al1997a).


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Figure 10. Time-integrated spectra from the aluminium plasma for various target lengths. Thechannel number of the CCD camera is a function of the wavelength. The lengths of the target are(a) 0.3cm, (b) 1.2cm, (c) 2.5cm and (d) 3.0 cm. Arrows mark the 3d4f (wavelength= 15.4nm),3d5f (10.6nm), 3p4d (15.1nm) and 3p5d (10.4 nm) lines of the lithium-like aluminium ionsand the 3d4f line (17.7nm) of the bellium-like ions. A fluorine-like aluminium ion line, whichcorresponds to the transition of the 2p52p43s (11.8 nm) is also marked (Kawachi et al 1997a).

2.4. Electron collisional excitation scheme

In the equilibrium plasma, ions having specific number of electrons such as 2 (helium-like),

10 (neon-like), 28 (nickel-like) and46 (palladium-like)are relatively stable. Theseionssurvivein the wide range of temperature and density. Figure 11 shows the ion abundance as a functionof temperature. higher abundance of neon-like and nickel-like ions can be seen in figure 11where the collisional radiative equilibrium is assumed for a tin plasma at the electron densityof 1020 cm3. In such relatively stable plasmas, the electron collisional excitation creates thepopulation inversion.

Zherikhin et al (1976) first described a mechanism for obtaining an inversion between2p53pand2p53s levels in neon-like ions. Vinogradovetal (1977)have subsequently published


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a series of papers about theoretical description. To produce the inversion, the n = 3 excitedlevels are populated by electron impact excitation from the ground (2p6) state of the neon-likeion which is produced in the plasma heated by the pumping laser. The population inversionbetween 2p53p and 2p53s levels develops because of the large difference between the radiative

decay rates. Figure 12 shows the simplified energy level diagram of neon-like and nickel-likeion scheme. The nickel-like scheme, proposed firstly by Maxon et al (1985) has proven tobe successful for short wavelengthamplificationbelow10 nm (MacGowan etal 1987, 1990)attheLawrenceLivermore NationalLaboratory(LLNL). With thisscheme, thepumping intensitycan be reduced significantly, since the quantum efficiency (the laser transition energy/the exci-tation energy) of the nickel-like system is much higher than that of the neon-likesystem. How-ever, wehaveto also realize maximizing thenickel-likeabundanceaswell asefficientmonopole

Figure 11. Ion abundance as a function of the electron temperature for tin plasma.

Figure 12. Schematic diagram of the electron collisional excitation, neon- and nickel-like ionschemes.


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excitation from the nickel-like ground state to the upper lasing levels. For this requirement,the plasma profile control in time and space for generating population inversion is essential.

3. First demonstration of significant lasing at Livermore and Princeton

3.1. An electron collisional excitation soft x-ray laser at LLNL

In 1985, Matthews et al at the LLNL in the United States published on the first demonstrationof a soft x-ray lasing at wavelengths in the range of 20.63 and 20.96 nm from the neon-likeselenium plasma. The schematic diagram of the experimental setup is shown in figure 13.The x-ray lasing experiments were performed at the Novette laser-target irradiation facilitywhich was mainly used for the Inertial Confinement Fusion research. Typically, the targetwas composed of 75 nm layer of selenium, vapour deposited on one side of a 150 nm thickformvar substrate. The foil was normally 1.1 cm long and was illuminated by green laser light(wavelength= 532nm)alongalinefocuswithdimensionsof0.02cm1.12 cm. Thenominalpulse length was 450ps, and the typical incident intensity was 5 1013 W cm2. The targetswere irradiated in two different geometries: single-sided in which a given segment of the foilwas hit by only one laser beam and double-sided in which opposing laser beams irradiated acommontarget area. Figure 14 shows the evidenceof exponential growthof the line intensities

Figure 13. Experimental setup of the first soft x-ray lasing experiment (Matthews et al 1985).

Figure 14. Integrated line intensity ofJ = 21 transitions vs amplifier length for double sidedlaser irradiation conditions (Matthews et al 1985).


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which come from the axial grazing incidence spectrometer (GIS) and are integrated over theline widths. The output intensity emitted by a one-dimensional homogeneous gain mediumof length L under steady-state conditions scales is exp(gL)L1/2, where g is the line centregain coefficient. Fitting the data from double-sided shots with this expression yields a gain

coefficient of 5.51.0 cm1 for both 20.63 and 20.96 nm lines. The width of the 20.63 nm lineis assumed to be 0.004 nm (Doppler broadening), then the equivalent brightness temperatureis 40 keV. In contrast, the brightness temperature inferred from the sodium-like emission at20.11nm is 100 eV.

3.2. A recombination-pumped soft x-ray laser at Princeton University

The first clear demonstration of recombination type soft x-ray lasing pumped by a CO2 laserwaspublished in 1985 (Suckewer 1985). The recombination-pumped soft x-ray lasing schemewas originally based on the rapid cooling of the medium by free expansion which also causedrapid decrease of the electron density. The free expansion scheme also causes the difficulty ofobtaininga relatively long anduniformplasma column, andcontrol of thecooling rate. Inorder

to avoid these problems, Suckewer and Fishman (1980) proposed to create a plasma columnin a strong solenoidal magnetic field and cool it by radiation losses. They have shown themeasurements of enhancement of up to 100 of stimulated emission over spontaneous emissionfor the hydrogen-like carbon 18.2nm line (n = 32, where n is the principal quantum number)in a recombining plasma column, confined by a magnetic field of 9 T. The lasing plasmawas created by an irradiation of a 75 ns (full width at half maximum (FWHM)), 300 J, CO2laser with a solid carbon target as shown in figure 15. The emission in the axial directionwas measured by a soft x-ray grazing-incidence monochromator equipped with a 16-stageelectron multiplier, and emission in the transverse direction was measured by a soft x-raygrazing incidence duochromator equipped with two-channel electron multipliers. The role ofthe carbon blade was to create a more uniform plasma in the axial direction and to provideadditional cooling by heat transport from the plasma to the blade. Figure 16 shows an exampleof the experimental results of the time-evolution of the hydrogen-like carbon 18.2 nm line and13.5 nm line intensities in the axial and transverse directions. Intensities in the axial directionare presented in the same units as intensities in the transverse direction, obtained by use ofthe relative sensitivity of the axial and transverse instruments and a geometrical factor. Theenhancementof95whichcorrespondedtothegain-lengthproductof6.5forthecarbon18.2nmline was obtained. Additionalconfirmation of the stimulated emission wasobtained with a soft

Figure 15. Schematicviewof thecarbon-disktarget with a thin carbonblade,and laser illuminationand observation geometries (Suckewer et al 1985).


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Figure 16. Time evolution of hydrogen-like carbon (n = 32) 18.2nm line and (n = 42) 13.5nmline intensities measured with axial and transverse instruments for two discharges with the sameplasma conditions (Suckewer et al 1985).

x-ray mirror; with 12% reflectivity of the mirror, a 120% increase in intensity of the 18.2 nmline in the axial direction was observed. In spite of the clear lasing signals, the mechanism ofcreating the population inversion was still not so clear (Kim et al 1989). Anyway, the resulthas strongly encouraged people who were interested in x-ray laser studies.

4. Electron collisional excitation soft x-ray lasers

4.1. Introduction

Since the first demonstration of neon-like selenium soft x-ray laser in 1984, successful resultson soft x-ray amplification in a laser-produced plasma have been reported with the electroncollisional excitation schemes including neon-like (Matthews et al 1985, Rosen et al 1985,Lee et al 1987) and nickel-like iso-electronic ions (MacGowan et al 1987, 1990). In theneon-like ions, soft x-ray lasing have been observed with silicon (Z = 14) (Li et al 1997) tosilver (Z = 47) (Fields et al 1992) at the wavelengths between 87 and 8 nm. Table 1 showsthe wavelengths from the nickel-like and neon-like soft x-ray lasers which were observedexperimentally. With the neon-like scheme, however, the required pumping laser intensityincreases rapidly as the wavelength becomes shorter towards the water window spectral range(4.42.3 nm). The required pumping intensity for short wavelength extension of the neon-like

x-ray laser is very high, i.e. 1016 W cm

2 for gadolinium at 4 nm (Rosen et al 1988).Thefirst demonstration ofneon-likeseleniumsoft x-raylasingwas made with anexplodingfoil targettechnique using a large scale glass laser systemwhichcould deliver severalkJ energy.Many peoplewould like to achieve lasingusing a smaller pumping laser system. Amplificationof soft x-ray laser in neon-like germanium was firstly demonstrated by Lee et al (1987) usinga 600 J in 2 ns glass laser which irradiated solid slab targets at the Naval Research Laboratory.Due to the relatively low irradiance required to obtain lasing, the germanium laser coupledwith the solid slab target technique became popular worldwide. For example, the group at


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Table 1. Wavelengths of the electron collisional excitation soft x-ray lasers in nickel (Ni)-like andneon (Ne)-like ions which have been demonstrated experimentally.

Atomic numberand symbol of theElement Wavelengths (nm) Scheme Reference

79Au 3.56 Ni-like MacGowan et al 1992

74W 4.32 Ni-like MacGowan et al 1992

73Ta 4.48 Ni-like MacGowan et al 1992

72Hf 4.65 Ni-like Daido et al 1999b

70Yb 5.609, 5.026 Ni-like MacGowan et al 1988

67Ho 5.63, 6.20 Ni-like Daido et al 1999b

66Dy 5.85, 6.41 Ni-like Daido et al 1999b

65Tb 5.9, 6.7 Ni-like Daido et al 1997

64Gd 6.33, 6.86 Ni-like Daido et al 1999b

63Eu 6.583, 7.100 Ni-like MacGowan et al 1987a

62Sm 7.36, 6.85 Ni-like Daido et al 1999b

60Nd 7.92 Ni-like Daido et al 1999b

59Pr 8.2 Ni-like Daido et al 1997

58Ce 8.6 Ni-like Daido et al 199757La 8.9 Ni-like Daido et al 1997

54Xe 9.64, 9.98 Ni-like Lu et al 2002

52Te 11.1 Ni-like Daido et al 1997

50Sn 11.97 Ni-like Lin et al 1998

49In 12.58 Ni-like Lin et al 1998

48Cd 13.17 Ni-like Li et al 1998

47Ag 13.89 Ni-like Li et al 1998

46Pd 14.68 Ni-like Li et al 1998

42Mo 18.90 Ni-like Li et al 1998

41Nb 20.33 Ni-like Li et al 1998

40Zr 22.02 Ni-like Li et al 1998

39Y 24.01 Ni-like Li et al 1998

36Kr 32.8 Ni-like Sebban et al 2001b

47Ag 9.9365, 10.0377 Ne-like Fields et al 199242Mo 10.64, 13.10, 13.27 Ne-like MacGowan et al 1987b

41Nb 13.86, 14.04, 14.59 Ne-like Nilsen et al 1993a

40Zr 15.04 Ne-like Nilsen et al 1993a

39Y 15.5 Ne-like Da Silva et al 1993

38Sr 15.98, 16.41, 16.65, Ne-like Keane et al 1990

37Rb 16.50, 17.35, 17.61 Ne-like Nilsen et al 1992

34Se 18.2, 20.6, 20.9 Ne-like Nilsen et al 1995b

33As 21.884, 22.256 Ne-like McLean et al 1992

32Ge 19.6, 23.2, 23.6 Ne-like Daido et al 1995b

31Ga 24.670, 25.111 Ne-like McLean et al 1992

30Zn 21.2, 26.2, 26.7 Ne-like Rus et al 1997

29Cu 22.11, 27.93, 28.47 Ne-like Lee et al 1987

28Ni 23.1 Ne-like Li et al 1995b

26Fe 25.49 Ne-like Nilsen et al 1993b

25Mn 22.1, 26.9 Ne-like Li et al 1996a

24Cr 28.55, 40.22 Ne-like Nilsen et al 1993b

23V 26.1, 30.4 Ne-like Li et al 1995a

22Ti 32.63 Ne-like Nilsen et al 1993b

21Sc 31.2, 35.2 Ne-like Li et al 1995c

20Ca 38.3 Ne-like Li et al 1995c

19K 42.1 Ne-like Li et al 1995c

18Ar 46.875 Ne-like Rocca et al 1994


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Table 1. (Continued)

Atomic numberand symbol of theElement Wavelengths (nm) Scheme Reference

17Cl 52.9 Ne-like Li et al 1995c16S 60.1, 60.8 Ne-like Li et al 1997

14Si 87.4 Ne-like Li et al 1997

Simplified energy level diagram can be seen in figure 12. Note that the wavelengths listed in thetable have not been judged as the most accurate numbers or as the first demonstrations. They arelisted simply for readers convenience.

Figure 17. Time-integrated spectra of the neon-like germanium x-ray laser with curved slab targetpumped by a 1ns single glass laser pulse (Daido et al 2000).

Osaka University has tried to obtain lasing signals from neon-like germanium. Five lasinglines including the strongest two J = 21 lines at wavelengths of 23.2 and 23.6nm and theother 19.6, 24.7 and 28.6nm lines have been clearly observed. The x-ray laser was pumpedby a 1 ns, 1.1 kJ laser pulse at the wavelength of 1 m with a cylindrical lens coupled with anaspheric lens to make a 6 cm long line focus, giving an average intensity of 2 1013 W cm2

on the target (Murai et al 1994). A typical spectrum is shown in figure 17.A single flat slab target has a limitation in the gain length due to x-ray refraction caused

by electron density gradient in an x-ray laser plasma. Actually, the experimental results haveshown clearly the limit of intensity far below the level of real saturated amplification. Inorder to compensate the refraction de-coupling, the group at Osaka University in collaborationwith the Irish group has tested curved slab targets as shown schematically in figure 18 andcurved cylindrical targets which were originally proposed by Lunny (1986). The x-ray laser

beam can propagate along the gain region over a long distance when the target is bent at acurvature which is matched to the ray trajectory. They have obtained a very intense and verysmall divergence (1 mrad) soft x-ray laser beam using a curved slab target (Kodama et al1994). The intensity ofJ = 01 line at 19.6 nm with a curved slab target was 10 times moreintense than that with a flat slab target. The beam divergence along the vertical direction aswell as the horizontal direction decreased (Daido et al 1996). These results clearly show theeffectiveness in refraction compensation for controlling x-ray laser beam propagation in theamplifyingmedium. Usingthe curved slabtarget scheme, theyhave performedthe double-pass


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amplificationusingan x-raymirror(Kato etal 1993). Furthermore,theyhave tested thedouble-pass amplification with a polarizer made of multi-layer optics to obtain a polarized x-ray beamidentified by a streak camera coupled with a spectrometer (Murai et al 1994). They haveidentified the x-ray laser pulse reflected back from the polarizer. They have also measured the

real line widths of the germanium lasing lines using a high-resolution spectrometer having aresolving power of 16 000 (Yuan et al 1995). The narrowed line width of2 pm FWHM withVoigt profile was observed.

Further improvement has been achieved using a curved slab target which was irradiatedby two laser pulses of 100 ps duration separated by 300 ps with a total energy of 200300 Jon target. The average pumping intensity on target was 2.6 1013 W cm2. If we comparethe x-ray laser intensity with that obtained by 1 ns single pulse pumping with 1.1 kJ energy,the J = 01 line has 10 times higher peak intensity with a small beam divergence of12 mrad, corresponding to a factor of20 improvement in brightness. Figure 19 shows the

Figure 18. Schematic diagram of the curved slab target. The notation t and m are the bend angleof the target and setting angle of the x-ray mirror which are defined in the figure.

Figure 19. Time-integrated spectra with 100 ps double pulse pumping with a pulse to pulseseparation of 300ps. Very intense J = 01 lasing line can be seen (Daido et al 2000).


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time-integrated spectrum which was obtained with 100ps double-pulse pumping. If a readercompares figure 19 with figure 17, the J = 01 line increases significantly in the double-pulsepumping which is originally predicted theoretically (Rosen et al 1985). The multiple laserpulse pumping has provided us multiple x-ray laser pulses. The first pumping pulse creates

the pre-formed plasma and no lasing occurs. After the second pulse, clear lasing occurssuccessively up to four pumping pulses. Details have been described elsewhere (Daido et al2000).

4.2. Saturated amplification neon-like soft x-ray lasers

First saturatedamplification neon-likesoftx-ray laser in a selenium plasmaat thewavelengthof20.6 nm was demonstrated with an exploding foil target pumped by a 530 nm laser (Matthewset al 1987). Subsequently, the saturated amplification soft x-ray laser in a germanium plasmaat a wavelength of 23.6nm was demonstrated using a double plasma with a double-passamplification configuration with a multi-layer x-ray mirror as a reflector by EnglishFrenchcollaboration team performed at Rutherford Appleton Laboratory (Carillon et al 1992). Ultra-intense yttrium (Z = 39) soft x-ray laser at a wavelength of 15.5 nm has been demonstrated(Da Silva etal 1993). Thelaser wasgenerated by irradiating a 3.8cm long, 100nm thickplasticfoil coated with 90nm of yttrium with two cylindrically focused 530nm laser beams fromNOVA laser at LLNL. The total small signal gain is20 which is beyond the level of saturatedamplification of16. The total irradiation intensity on the target was 1.5 1014 W cm2

for a duration of 500 ps. The measured soft x-ray laser beam divergence was 10 mrad. Theycarefully measured the power of the x-ray laser using two multi-layer mirrors coupled with afiltered x-ray diode both of which were calibrated as shown schematically in figure 20. Themeasured pulse width was 200 ps and the measured peak x-ray laser output power was 32MW,and the total output energy was 7 mJ which was the worlds highest energy x-ray laser to theauthors knowledge. Subsequently, Da Silva et al (1994) have produced 45 ps output pulsesin neon-like yttrium x-ray laser pulse using a series of 100 ps 530 nm pump pulses separatedby 300 ps. In this experiment they also pointed out the importance of the travelling wave

pumping. The peak output power was 30 MW. Although the pumping energy is huge, i.e.3 kJ, the output power is quite attractivewhich is a unique source for probing the laser-fusionplasmas which emit intense black-body-like radiation. Using this laser, they have performedmany probing experiments which will be described later (see section 6.4 and 6.5).

4.3. Improvement of neon-like soft x-ray laser performance using multi-layer mirrors

The x-ray laser performance is significantly improved if we use a soft x-ray mirror as areflector for double-pass amplification. The first demonstration of half cavity (double-passamplification) and a full cavity operation was performed by Ceglio et al (1988a, b). For the

Figure 20. Experimental setup for x-ray laser power measurement (Da Silva et al 1993).


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full cavity operation, the most crucial optical element wasa half mirror (a beam splitter) whichwas extremely hard to make and support during the experiment. Actually the expensive softx-ray optics was broken at each shooting.

French group has developed a practical x-ray laser with double-pass amplification for

neon-like zinc soft x-ray laser at 21.2 nm pumped by a 1 m, 600ps, 350J laser (Rus et al1997). They term it as a half cavity operation. The gain-length product of the 17 wasachieved. An output energy of 400 J and power of5 MW was demonstrated. During anx-ray laser experiment, they placed the cover plate with a few mm diameter hole to exposea fresh surface as a reflector for the desired area at each shot and rotate the mirror after thepumping laser shooting. The beam divergence of the neon-like zinc soft x-ray laser at 21.2nmwas less than 2mrad which was 3 times better collimation than that without a mirror. Usingthis laser, they have also performed unique application experiments.

4.4. Atomic physics issues of the neon-like soft x-ray lasers

Atomic physics has generally contributed to the x-ray laser study as a basic science. Once

lasingoccurs, thex-ray lasingphenomenais a very good tool for very fineatomicspectroscopy,especially for the highly ionized ion spectroscopy. The lasing lines originate from a well-defined atomic configuration of a well-defined ionization stage. The plasma parameter spacefor creating population inversion is much narrower than that of spontaneous emission lines thatoverlap significantly with many lines from various ionization stages and from a wide rangeof density and the temperature regions. Therefore, it is very difficult to distinguish individualspontaneous emission lines in the high atomic number plasmas. Here, the author introduces afew examples of the x-ray laser studies which contribute to atomic physics.

According to the atomic constant, the gain of the J = 01 transition is much higher thanthat of the J = 21 transitions (Rosen et al 1985). However, early experiments show thereverse (Matthews et al 1985). Later, shorter pulse pumping with a slab target provides strongJ = 01 line (Daido et al 1995, Nilsen et al 1995). The desired plasma condition for theselines is different, i.e. higher density for J = 01. The controlled pre-pulse for producingpre-formed plasma makes it possible to enhance the J = 01 line (Nilsen et al 1993).

The second topic includes the high-resolution spectroscopy of the laser transitions. Kochet al (1992, 1994) have successfully observed the line width of the 20.638 nm neon-likeselenium laser. The results indicate un-amplified width of 50 m (equal to 5 pm) and gainnarrowingto10masshowninfigure21. Theresultalsoshowsnosignificantre-broadeninginsaturated amplifiers. The measured gain coefficient was6 cm1. The saturated amplificationstarts at the gain length of2.5 cm. The un-amplified width is 1.4 times the expected Dopplerwidth, and the lack of re-broadening leads to speculation that collisional effects may play asignificant role in determining the line profile.

The third topic is the hyper-fine splitting of the laser transition which describes the poorperformance of the odd atomic number neon-like ion lasers. Since elements with odd atomicnumber have nuclear spin and nuclear moment and those with even number tend to have no

nuclear spin, one possible explanation for this anomalous behaviour is that hyperfine splittingplaysan importantrole in thegain of neon-likelaserlines forelements with oddatomic number.The hyperfine splitting can affect the gain of the laser line by effectively increasing the linewidth. Since the gain is inversely proportional to the line width, the gain will decrease if thewidth increases. If the splitting is large enough, a single line may be split into several weakerlines. Investigating the various laser transitions which are observed, the hyperfine splitting islargest for the 2p1/23p1/2(J = 0) 2p1/22s1/2(J = 1) line where the under bars over the2p state indicates a vacancy in the closed L shell. This J = 01 transition is split into three


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components by the hyperfine effect, assuming I > 1/2. For a nucleus with nuclear spin I,the total spin F ranges from I + J to |I J|. For the J = 01 transition, this becomes thethree transitions, F = I F = I + 1, I, and I 1. The total radiative rate for the J = 01transition is split into three components, each of which are weighted by 2F + 1. Nilsen et al

(1993) have performed experiments on the high-resolution spectrum of the lasing lines. Themeasured high-resolution spectra are shown in figure 22. Measured J = 01 transition ofneon-like zirconium (Z = 40) is shown in figure 22(a) where Z is the atomic number. Itreveals a single narrow line which appears to be slightly gain narrowed. On the other hand,figure 22(b) shows the measured neon-like niobium (Z = 41) lasing line. Two componentsare clearly visible with a separation of 28 m which is very close to the 32 m predictiongiven by the 7m resolution spectrometer. The zirconium lasing line is 2 orders of magnitudebrighter than the niobium line, indicating that the gain is much higher. The result shows thefirst clear demonstration of hyperfine splitting in the x-ray regime.

The fourth topic is the spontaneous polarization ofJ = 01 lasing line which has beenobserved for the first time (Kawachi et al 1995). The opacity of the transition between thelower lasing level and the ground state of the neon-like germanium ions are not isotropic

because of the quasi-one-dimensional plasma flow. Even though the anisotropy is small but

Figure 21. Measured and reduced line widths as a function of target length. The error bars for theshortest target are due to background level uncertainties; for the others, they represent the spread inreduced widths obtained using different fitting functions. Also shown is the expected target-lengthscaling for inhomogeneous saturation (- - - -) and homogeneous saturation () with a 50mintrinsic width (Koch et al 1992).

Figure 22. Measured spectra around the line centre for the J = 01 laser line in neon-likezirconium in (a) at 15.04nm and niobium at 14.59 nm. A 28 m splitting of the F = 11/2 and9/2 components is observed in niobium lasing line (Nilsen et al 1993a).


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it is amplified exponentially due to the population inversion and finally polarization can beobserved. However, Benredjem et al (1997) claimed that selective trapping of the resonanceline was theoretically shown to be negligible especially when elastic electronion collisionswere taken into account. Anyway, this subject should be studied further both experimentally

and theoretically to reach definite conclusion.

4.5. Gain guiding of the x-ray laser beam propagation

In x-ray laser experiments, defocusing or deflection effects due to the refraction index of theplasma are cancelled by bending a slab target (Lunny 1986, Kodama et al 1994) or by using acylinder target (Daido et al 1996) where the deflection of a ray is geometrically compensatedaccording to the index n ofn = (1ne/nc)1/2 1 ne/2nc. Here ne and nc are the electrondensity and the critical electron density of the soft x-ray lasing wavelength such as nc = 1.110132, where nc isincm3 and in cm. Forexample, if theelectron density falls off linearly,ne = n

0e (1r/r0), the ray trajectory becomes a parabola. For n

0e = 510

20 cm3, = 10nmand a density scale length r0 of 100 m, offset of the x-ray is 25 m at a propagation distanceof 1 cm. However, without these compensations, the defocusing effects due to the refractive

index are eliminated by the gain profile transverse to the direction of the beam propagation.Figure 23 illustrates the physical picture of the gain guiding. Fill (1988) has calculated thatthe beam is efficiently guided by the gain distribution and gain guiding by far dominates theweak defocusing by the refractive index profile. Fill considered a Gaussian beam propagatingin a medium with quadratic gain and index profiles transverse to the propagation directionsuch as = 1/20 (2r

2)and = 1/20 (2r2) (Kogelnik 1965). The medium is characterized

by its complex propagation constant k = + i , where and are real quantities related tothe gain and the refractive index, respectively by a n = (/2 ), and g = 2 where g is theintensitygaincoefficientincm1. After thecalculation, oneobtainsnetamplitude gain n ofthestationarybeam n = 01/Rm . Note that by comparing this refractive index changewith therefractiveindexduetothefreeelectrongas,oneseesthatthegainlinecancontributeanequalorhigher amount to the refractive index only ifne/g0 < 8.75 1011 cm1. If = 10nm, ne =

51020

cm3

, g0 = 5 cm1

, therefractive index is dominatedby thefree electron contribution.If = 10nm, g = 5 cm1, n0e = 5 1020 cm3, and the gain falls to zero at a distance

of 100 m from the axis and the refractive index acquires the vacuum value of 1 at the samedistance, one obtains 2 = 5 104 cm3 and 2 = 2.86 106 cm3. For the parameters ofthe stationary beam one obtains Rm = 1.48 cm and Wm = 7.35 103 cm, where Wm is theradius of the beam. Figure 23(b) shows the beam approaches their steady state value underthe assumption of initial condition such as (a) the initial beam radius is 10 times its limitingvalue Wm and (b) the initial radius is 1/50 ofWm. In both cases the initial radius of the wavefront is 100 cm. In case (a), the behaviour of the beam is dominated by gain guiding and thebeam approaches its limiting value. In case (b), the beam has an initial diameter which issmall compared to the scale lengths of the gain and index profiles. The diffraction spreadingis dominant before 2cm as shown in figure 23(b). Under the appropriate conditions, the beamshould be guided by the gain profile and the increase in refractive index from the axis shouldnot lead to defocusing. The effective gain coefficient of the gain-guided beam is somewhatlower than the gain coefficient at the centre of the gain profile.

4.6. Discharge-pumped neon-like ion soft x-ray lasers

The most significant advantage of the discharge-pumped soft x-ray laser is that the wall-plug efficiency should be high. The group at Colorado State University has developed a fastdischargemachine which candeliver a good vacuum ultraviolet or soft x-ray laser beam (Rocca


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Figure 23. (a) Schematic diagram of the gain guiding in the lasing medium. At the same timediffraction anti-guiding and refraction occur in the medium. (b) Normalized beam radius andwavefront radius versus propagation distance. Dashed lines are the normalized beam radius withindex profile alone. The two pairs of curves correspond to two different initial conditions at a:W/ Wm= 10, b: W/ Wm= 1/50. R1 = 100 cm in both cases (Fill et al 1988).

Figure 24. Schematic illustration of the fast capillary discharge setup (Rocca et al 1993).

1993). High temperature (>150 eV), small-diameter (200 m) plasma column have beenefficiently generated by very fast pulsed discharge excitation of capillary channels filled withpre-ionized gas. The schematic diagram of the discharge machine is shown in figure 24. Thecapillaries were excited by discharging the Marx generator through a low-inductance circuit


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which includes the capillary and a spark gap switch. Rocca and his group (1994) were the firstto demonstrate the discharge-pumped ultraviolet laser at 46.9nm. A fast capillary dischargehaving a 1090% current rise-time of 20ns, 40 kA was used to excite plasma columns up to12 cm in length in 4mm channels, producing population inversion in the J = 01 of neon-like

argon and resulting in a gain of 0.6 cm1 at 46.9nm wavelength. The beam diameter wasmeasured to be 25 which shows the

saturated amplification clearly (Rocca et al 1996). Benware et al (1998) have also achieved7 Hz operation. Using this laser, they have performed the measurement of spatial coherencebuildup (Marconi 1997) and soft x-ray interferometry of a pinch discharge (Moreno 1999).

Figure 25. Variation of the intensity of the spectral lines in the neighbourhood of 48 nm as afunction of capillary length (Rocca et al 1994).


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4.7. The collisional excitation nickel-like ion soft x-ray lasers

The nickel-like ion soft x-ray laser scheme was firstly proposed by Maxon (1985) and firstlydemonstrated experimentally by MacGowan et al (1987). Subsequently, they made water

window x-ray lasers using a several kJ laser. After the successful demonstration by the largestlaser fusion system, people would like to reduce the pumping energy. The group at OsakaUniversity has developed multiple pulse-pumping techniques for this purpose (Daido et al1995, 1996). Clear lasing line has been observed in the Ni-like ions of silver (Z = 47),tellurium (Z = 52), lanthanum (Z = 57), cerium (Z = 58), praseodymium (Z = 59),neodymium (Z = 60), samarium (Z = 62), gadolinium (Z = 64), terbium (Z = 65) anddysprosium (Z = 66) at wavelengths of 614nm, where Z is the atomic number (Daidoet al 1995, 1996). A curved slab target was pumped with either double, triple or quadruple1.053 m laser pulses with the total energy of 200500 J which is an order of magnitudeless than those used in the previous exploding foil target experiments at LLNL (MacGowanet al 1987, 1990). A gain coefficient of3 cm1 and a gain-length product of8 have beenobserved with neodymium (Z = 60) at 7.9nm. The streak records of the Ni-like neodymiumx-ray laser is shown in figure 26. The lasing occurs at the rising part of each pumping pulse

except for the first pumping pulse which creates a pre-formed plasma. Lasing in the nickel-like neodymium and tin (Z = 50) ions has been also reported by the groups at LLNL and theMax Planck Institute for Quantum Optics using curved slab targets pumped by 0.5 m laser or1.3 m laser with the multiple pulse or the pre-pulse pumping technique (Nilsen and Moreno1995, Li et al 1996) resulting in the gain coefficients of1 cm1. The evidence for nickel-likexenon (Z = 54) lasing has also been observed using a gas-puff target irradiated by a singlelaserpulse (Fiedorowicz etal 1996) at the MaxPlanckInstitute in collaboration with thegroupat the Institute of Opto-electronics, Military University of Technology in Warsaw.

The group at Osaka University in collaboration with a group at National Laboratoryon High Power Laser and Physics in Shanghai has performed an experiment on an intenseneodymium x-ray laser using a double-curved slab target configuration (Wang et al 1998).The focusing optics was composed of an aspherical lens and four convex cylindrical lenses

which produce a line focus of 50 10 m width and 23mm length with the irradiation uni-formity better than 5%. They have also tested a deformable mirror to make better illumina-tion uniformity along the line focus, resulting in better neodymium x-ray laser performance(Yoon et al 1998). They have obtained an order of magnitude higher output for the travelling

Figure 26. A typical x-ray streak record of the Ni-like neodymium x-ray laser.


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Figure 27. Spectra of the nickel-like ion x-ray laser at the wavelength of 7.9nm. The arrows with1st, 2nd and 3rd corresponds to the lasing line of these diffraction orders, respectively. The linesfromthelithium-likeoxygenionsindicatedas(1)to(4)canbeclearlyseenduetotheoxidationofthetarget surface. If the intensity of these lines increases, the x-ray laser intensity drops significantly.

wave direction compared with that at the opposite direction. With the calibrated x-ray CCDandthecalibrated soft x-ray spectrometer, thex-ray laser energy is estimated to be40 J.Themeasuredlasingpulsewidthwith anx-raystreakcamera (Hamamatsu PhotonicsModelC2590)is approximately 4050 ps. Thus, the peak power is1 MW. It should also be pointed out thatthe relative merit of the curved target decreases if the plasma density scale length increases bythemultiple pulse pumping with a longerpulse to pulse separation (Nilsen et al 1994). The las-ing materials whose atomic number is between 56 and 70 belong to the lanthanide group whichareeasilyoxidized. Example of theoxidization is shown in figure 27. If the intensityof oxygenlines increases, the lasing signal tends to be weaker probably because of the dilution effect.

4.8. High gain and saturated amplification nickel-like soft x-ray lasers

In 1997, the British group published two papers on the saturated amplification nickel-like softx-ray lasers including samarium at 7.3 nm and silver at 14 nm (Zhang et al 1997a,b). Theexperimental setup is shown in figure 28. Three beams of the Nd : glass laser at 1.05 m witha 75ps duration were used in an off-axis focus geometry (Ross etal 1987), which provide a linefocus with 25mm length and 100m width, giving an irradiance of41013 W cm2. They

have studied a plenty of pumping pulse conditions as shown in figure 29. The correspondingx-ray laser intensities are also shown in figure 29 in arbitrary unit (Zhang et al 1997). Asa result, a low-intensity (1030% of the total energy) laser pulse was used to create a pre-formed plasmawith a lowerionization before themain pumping pulse arrived. Thepre-formedplasma was allowed to cool down for a much longer time of more than 2ns. The plasma thenexpands creating a larger scale length plasma and produce a larger, more uniform gain regionwhich allows for good soft x-ray laser propagation. The other three beams in 180 oppositionin a second line focus produced a plasma with an opposed density gradient, which helped


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Figure 28. Experimental setup of the saturated nickel-like soft x-ray lasers (Zhang et al 1997a)

Figure 29. Soft x-ray laser intensities forvariety of doublepulsecombinations(Zhang etal 1997c).

to compensate for the refraction of the x-ray laser beam from the first plasma. Samariumcoated flat slab targets (18 mm long) were used. The targets were aligned so that they wereparallel with an adjustable separation between the surface planes and an axial separation of500 m between the two targets. The output intensity of the samarium laser as a function ofthe target length is shown in figure 30. The distance between the two targets transverse tothe laser propagation was 175 m. The maximum length of a single target was 2 cm. Thecoupling efficiency at the optimized separation was quite high because of small deflection anddivergenceangles. Thegain coefficient was 8.4cm1. Theoutput intensityno longer increases

exponentially with targetlengthlonger than 18 mm,whichcorresponds toa gain-length productof 16. A saturated samarium x-ray laser beam has been demonstrated with an output energyof 0.3mJ in 50 ps. The output intensity was 2 1011 W cm2. The beam divergence was1.2 mrad. They have also demonstrated saturated silver soft x-ray laser at 13.9nm wavelengthusing almost the same experimental setup. The output intensity of the silver x-ray laser isplotted in figure 31 against plasma length. For those single target plasmas with length shorterthan 22 mm, the increase in output intensity of the laser line is a simple exponential form. Thegain coefficient was 7.2cm1. Beyond the length of 22 mm, where the gain-length product is


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Figure 30. Peak intensities of nickel-like samarium x-ray laser as a function of target length. Thesolid line shows experimental increase of the output intensity and the broken line shows the linearincrease of the output intensity in the saturation region. Solid squares are from single target data,and open diamonds from coupled target shots. Saturation intensity is reached at an approximategain-length product of 16. The gain coefficient = 8.4 cm (Zhang et al 1997c).

Figure 31. Peak intensity of nickel-like silver x-ray laser as a function of plasma length. The solidline shows exponential increase of the output intensityand thebrokenline shows the linear increasein the saturation region. Saturation is reached at an approximate gain-length product of 16 (Zhanget al 1997b).

more than 16, the output intensity increases linearly with the amplifying length. The outputlaser energy was90 J for an optimized separation between the two targets of 150 m whichis transverse to the x-ray laser propagation, while the axial distance between the two was fixed

at 500 m. The output intensity was 7 1010 W cm

2.A saturated amplification nickel-like palladium and silver x-ray laser has also beendemonstrated by the group of University of Bern using a 30 J, 100 ps glass laser (Tommasiniet al 1999a, b).

In 1998, thegroup at Osaka University performed thecharacterization of a 13.9 nm nickel-like silver collisional x-ray laser which was firstlydemonstratedby thesame group (Daido etal1996). Original interest in this work was to investigate the action of high-intensity pumpingpulse (8 1013 W cm2) on the amplification property of a medium atomic number plasma.


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The Gekko XII laser which can deliver up to 200J per 100 ps pulse duration from each beamis particularly adapted for such investigation. Single- and double-target geometry have beenstudied. The pumping configuration consisted of two pulses (a pre-pulse and a main pulse) of100 ps duration, separated by 3ns. The energy of the main pulse was typically 140J (intensity

on target = 8 1013 W cm2), while the pre-pulse has been varied from 0.1% to 10% of themain pulse energy. A stable and sufficiently efficient pre-pulse regime appeared between 1%and 10% of the main pulse energy. These results are slightly different from those obtainedin different laboratories using the same lasing element where an optimum of pre-pulse ratiosof 13% (Sebban et al 1997) and 1030% (Zhang et al 1997) has been identified. Thesediscrepancies between those experiments should be attributed to the intrinsic differences ofthe pumping laser profile, line focus homogeneity, surface quality of the target, irradiationgeometry (the use of a single or several superimposed laser beams) of each laser installation.These factors strongly influence the deposition of the laser energy on the target material andthen affect the geometry of pre-formed plasma as well as the gain medium (density gradient,transverse dimension). According to our results, we kept a 4% pre-pulse ratio during the restof the experiment in order to get an intense and stable x-ray laser emission.

Figure 32 shows the variation of the time-integrated intensity of the silver x-ray laserspectral line at the peak of the angular distribution versus the length of a plasma column.The intensity of x-ray laser pulse is observed to increase exponentially up to 8mm, at whichit begins to saturate. A fit of the data with the Linford formula (Linford et al 1974) yieldsa gain coefficient 19 cm1, a gain value which is significantly larger than that obtained inthe previous nickel-like experiment using 100 ps laser pumping pulses (Daido et al 1997).Saturated amplification is observed at a gain-length product of about 15. These results showthat thehigh-intensity100 ps laserpulse issuitable to reachtheappropriateelectron temperatureto maximize the collisional pumping while keeping a reasonable fraction of the lasing ions.

In order to increase the intensity and the optical quality of the x-ray laser beam, thedouble-target configuration has been investigated. The optimum separation transverse to thex-ray laser beam between the two targets has been found to be 300 m to maximize the x-raylaser intensity. Figure 33 shows the time- and angular-resolved spectra of the lasing line in

the forward and the backward direction of the quasi-travelling wave pumping. Due to thesaturated amplification, a weak increase of 1020% has been observed in the quasi-travellingwave direction. However, the spatial as well as the temporal profiles of the lasing signal

Figure 32. Heavily saturated silver x-ray laser intensity and the divergence as a function of thelength of the gain medium (Sebban et al 2000).


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appear very different in the two directions. The lasing in the forward direction shows smallerbeam deviation due to refraction compensation by the second target, as well as smaller beamdivergencedue to good coupling between the two targets and temporal broadening of the x-raylaser pulse duration (40ps for the single target and 60ps for the double target). This point is

probablytheresultoftheoverlapofthedouble-targetx-raylasersignalandtheonecomingonlyfrom the second target. Due to quasi-travelling wave, these two components could be slightlydelayed and modify the x-ray laser pulse duration in the direction of the quasi-travelling wave.This means that by varying the time-delay of the quasi-travelling wave, we could modify andcontrol the x-ray laser pulse duration which is very important for x-ray laser applications.

Figures 34(a) and (b) show the far field pattern of the 13.9 nm emission obtained in thesingle- and the doble-target geometry, respectively. A zirconium filter was used in order tostop the visible emission coming from the plasma and a flat molybdenum/silicon mirror wasused to cut the plasma emission and send the x-ray laser beam to a CCD detector. Fidiucialwires aligned in the path of the x-ray laser beam indicate the horizontal and vertical outputangle of the x-ray laser emission. The single- and the double-target x-ray laser beams showvery different spatial profiles. The beam pattern of the single-target x-ray laser shows a bean

Figure 33. The time- and angular-resolved spectra of the lasing line in the forward (left-hand side)

and the backward (right-hand side) direction of the quasi-travelling wave pumping. Due to thesaturated amplification, a weak increase of 1020% has been observed in the quasi-travelling wavedirection (Sebban et al 2000).

4.5 8 0 3

Deflection angle (mrad)

Figure 34. Far-fieldpatternsof thesingle- (a) anddouble-target (b) x-ray laser (Sebbanetal 2000).


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shape appearance with a maximum intensity at the central part. The beam pattern of thedouble-target x-ray laser beam shows a narrower horizontal divergence but is more extendedin theverticaldirectionwith twobrightcomponents vertically separatedby 5 mrad. This showsthat the second target strongly modifies the spatial profile of the beam in both directions. This

modification is attributed to x-ray refraction due to the electronic density gradients along thevertical direction in the second target, splitting the x-ray laser beam into two quasi-symmetriccomponents. It will be attractive to separately characterize these two bright x-ray laser spotsand simultaneously use them for application experiments requiring two synchronized x-raylaser beams. Using a calibrated detector, themeasured outputenergyof thedouble-target x-raylaser beam is 300 J (Sebban et al 2000).

4.9. The short wavelength nickel-like x-ray lasers

The shorter wavelength x-ray lasers, as short as 54 nm with a gain-length product of 2, 6 and 7for ytterbium, tantalum and tungsten, respectively, have been obtained using the exploding foiltechniques pumped by a single green laser pulse with several kJ energy at LLNL (MacGowan

et al 1987, 1990).For the pumping of short wavelength nickel-like x-ray lasers, a high-density and high-temperature plasma is needed as an amplifying medium. The desired electron temperature anddensity is 11.5 keV and 1.5 1021 cm3 for ytterbium and 1.41.8keV and 3.5 1021 cm3

for tungsten. The higher density provides higher gain but the duration and width of the gainare smaller. It makes thepropagation of an x-ray laser beam more difficult (Dekker 1998). Theimportant issue is the x-ray laser beam propagation through the lasing plasmas. The simplifiedray trace calculation for x-ray propagation at the wavelength less than 10 nm through theamplifying medium shows that, in contrast to the case at 20nm, the obliquely incident x-raylaser beam penetrates into and is absorbed in the solid density plasma. It does not refractback to the lower density gain region because of the high critical density which is inverselyproportional to the square of the wavelength and is 1 1025 cm3 at 10nm.

The laser beam of 1.053 m wavelength was focused to a line of 1.1 cm length and 50 maverage width (FWHM) for each target. The double-target configuration is almost the sameas shown in figure 2. The laser pulse train for pumping was composed of a pre-pulse anda main pulse with an individual pulse width of 100 ps. The pulse-to-pulse separation hasbeen changed from 600 ps to 3 ns for optimization. The laser pulse energies for each beamwere approximately 10J for the pre-pulse and 240J for the main pulse, which correspond tothe intensity on an individual line focus area of1 1013 W cm2, and 3 1014 W cm2,respectively. The optimum condition was judged on the basis of the angle-resolved x-raylasing intensity using the flat field spectrometer. The optimum time-delay was 1.5ns with theintensity ratio (pre-pulse/main pulse) of 4% where the x-ray laser intensity maximized as wellas minimum beam divergence was realized. Note that the cobalt-like resonance line intensityobserved with the crystal spectrometer increases and maximizes at the time-delay of 1.5 ns.The gap separation of the double-target which is transverse to the on-axis of the x-ray laser

should be also optimized. For the nickel-like hafnium laser, the gap separation was changed.Wider or narrower separation makes an x-ray laser weaker with wider divergence. The scalinglaw of the desired electron density predicts that the gap should be wider if the atomic numberdecreasesandvice versa. Forytterbium, hafnium and tantalum lasers, thegapseparations weredetermined to be 200 m, 150 m and 120 m, respectively. The expected scenario is thatwhen theplasmapre-formed by a pre-pulseexpands with thesound velocity, themain pumpingpulse hits the plasma and heats it. The pre-pulse intensity and the time-delay between the twopumping pulses give the desired electron temperature with appropriate density scale lengths.


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0

0

0

5.0

Carbon K-edge

(c)

4.6 4.5

Intensity(a.u

.)

(Hf)

(Yb)

(Ta)

(b)

(a)

Figure 35. Line graphs of the x-ray laser spectra. The carbon K edge at 4.38 nm represents theedge of the water window. Vertical dashed lines, wavelengths of (a) yitteribium, (b) Hafnium, and(c) tantalum lasing lines in nanometers. The peak counts for the lasing lines are 8011, 3181l and159 for Yb, Hf and tantalum, respectively.

The results indicate that the sufficiently high temperature with appropriate density is realizedby the optimized pre-pulse and the main pulse condition. The sharp intensity dependenceon the pulse separation is caused by, not only the population inversion, but also the goodpropagation condition through the two gain regions adjusted by the transverse gap separationwith an accuracy of 10 m.

Figures 35(a)(c) show the measured nickel-like ytterbium, hafnium and tantalum lasinglines at 5 nm, 4.7 nm and 4.5 nm, respectively which are close to the water window. The atomicnumber dependency seems to be fairly strong.

With the delay timeof 1.5 ns, measuredx-ray laser signals at the forward and the backwarddirection showed that the narrow and strong x-ray lasing signal was obtained in the forwarddirection, while the weaker and much wider divergence beam was observed in the oppositeside. The peak of the time-integrated x-ray laser intensity and the horizontal beam divergencewas measured with the CCD detector as a function of the target length.

The gain coefficients of the nickel-like ytterbium and hafnium lasing lines were 6.6 and3.6cm1 which corresponded to the gain-length product of 11 and 6, respectively. On theother hand, with the delay time of 600ps and the pre-pulse to main pulse intensity ratio of 4%,the gain coefficient of ytterbium laser was 1 cm1.

4.10. Transient collisional excitation scheme

An intense ultra-short laser pulse (pulseduration = 500 fs to a few ps) to irradiate a pre-formedplasma made by a preceded nanosecond laser pulse makes strongly non-equilibrium transientplasma in which the population inversion is efficiently made. The ionization stages such asneon-like and nickel-like stages can be mainly prepared by the pre-pulse, then a short pulse

will excite higher energy electrons from the ground state to the upper lasing levels where theexcitation energy is a few times larger than the temperature for these ionization stages (Daidoetal 1997). If the main pumping pulse is long enough to pump the upper lasing levels but shortfor other channels such as ionization, the scheme should work. Afanasev and Shylyaptsev(1989,1990)proposedthat the transientexcitation scheme includesseveralattractive propertiessuch as (a) the inversion in this scheme can occur at arbitrary electron density and it increaseswith larger electron density, (b) the gain coefficient in this scheme is several times higher, lesssensitive to the details of the kinetic model. This scheme works in the rapidly ionizing plasma


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Figure 36. Schematic diagram of the transient collisional excitation scheme at Max Born Institutein Berlin (Nickles et al 1995).

where the recombination processes are weaker, (c) there are no restrictions to an active mediadimension, (d) pumping laser energy requirements are impressive, i.e. enough to provide only0.10.3 J in a few hundred ps pulse and 1 J in 1 ps or 10 J in 10 ps pulse for a neon-like ironion soft x-ray laser at 20nm. Nickles et al (1997) have demonstrated the transient collisionalexcitation scheme experimentally using the facility schematically shown in figure 36. First,a relatively long 1.5ns pulse (the intensity on the target = 1012 W cm2) interacts with thesolid target and creates a plasma of required density, temperature and ion composition witha substantial abundance of neon-like titanium ions. A second short picosecond laser pulse(intensity = 1015 W cm2) is intended to provide the temperature jump of substantial energyof 0.5 keV which is the excitation energy for efficient excitation of the neon-like ions viaelectron collisions, and fast enough compared to the radiative and collisional relaxation timeof the upper laser level. Withonly a few J (46J)asa pre-pulse energyand 1.5 J asa picosecondlaser energy, a compact x-ray laser at 32.6 nm with a very high gain coefficient of 19 cm1 anda gain-length product of 9.5 was achieved.

Note that even though high gain coefficient was achieved, the gain region had a very smalllateral extension and it was characterized by a steep density gradient. The amplification wasvery sensitive to the plasma inhomogeneities and refraction. Actually, Nilsen etal (2000) havedone the modelling and the calculation of a picosecond laser driven neon-like titanium x-raylaser. They found that the transient nature of the gain is due to the ionization balance in theplasma, where the electron collisional excitation dominates rather than ionization because ofthe short period. They also described optimization of time-delay between the pre-pulse and

the main short pulse. The delay plays a significant role in preparing the plasma in the correctionization stage at an optimum density prior to the short-pulse heating of the plasma. Thelasing signal cannot be amplified in the gain region having a large density gradient. Theyperformed calculation on beam propagation including refraction, to understand which regionshave the right combination of high gain and low gradients for a actual contribution to theenhancement of the x-ray laser output.

Good lasing signals as short as 10 nm with gain coefficient of several tens per cm havebeen obtained using a few J to a few 10 J laser with various atomic number elements at several


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laboratories (Dunn et al 1998, 1999, Warwick et al 1998, Kado et al 1999, Lewis et al 1999,Klisnick et al 2000). The gain coefficients are 2060cm1 which are significantly higher thanthose pumped by a laser with a pulse width of few hundred ps.

The saturated amplification soft x-ray lasers provide the highest peak brightness x-ray

source at present. For various applications, this level of lasing pulse is quite important notonly for the photon flux but also for the beam quality. Several groups have achieved saturatedamplification using the transient collisional excitation scheme with a travelling wave pumpingtechnique (Kalachnikov et al 1998, Dunn et al 2000, Li et al 2000, Kawachi et al 2002). Kubaand Klisnick et al (2000) have found a new lasing line of nickel-like silver soft x-ray laser at16.1nm in addition to the 13.9nm 4d4p line using two colour pumping. For example, a greenbeam for a pre-pulse and an infrared beam for main short pulse are used for pumping. The newline was identified to be nickel-like 4f4p transition. Under specific irradiation conditions,strong lasing is also obtained on another spectral line at 16.05 nm that is identified as the 4f4dtransition in nickel-like silver ions.

At Advanced Photon Research Centre, Kawachi et al (2002) have employed a quasi-travelling wave pumping using a step mirror which was installed in the line-focusing system

(Ross et al 1987). The step mirror had six steps with a difference in the level of 600 m, andeach step corresponded to 1.2 mm length in the line focus, with a time-separation of 4 ps asshown in figures 37 and 38. Gain saturation behaviour was observed in the series of nickel-like x-ray lasers at a wavelength of around 10nm in the transient collisional excitation schemeusing a compact chirped pulse amplification Nd : glass laser with 12 J pumping energy. Forexample, figure 39 shows the relative intensity which is proportional to the photoelectroncounts of the CCD detector as a function of target length for nickel-like silver x-ray lasing at13.9nm. The gain coefficient was estimated to be 35 cm1 in the exponential amplificationstage, and the gain-length product of 13.6 was achieved with the target length of 3.8 mm. Thegain saturation can be seen when the target length is more than 3.8 mm. Figure 40 shows the

OAP

The direction ofthe traveling wave

target

M1

SM

Input14 J

wave front

M2

6 step Mirror

y

x

z

Figure 37. Schematic diagram of the line-focusing system in which step mirror technique forthe travelling wave pumping and the line-focusing technique using an off-axis parabolic mirror(denoted by OAP) and a spherical mirror (denoted by SM).


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Figure 38. Schematic drawing of the step mirrors for travelling wave pumping.

102

103

104

105

106

relativephoto-electroncounts

0.60.50.40.30.2

target length (cm)

Figure 39. Relative photo-electron counts which is proportional to the x-ray laser intensity as afunction of target lengths for nickel-like silver x-ray laser at 13.9nm. The gain coefficient is 35 cmand the saturated amplification stars at the target length of 3.8mm (Kawachi et al 2002).

typical spectra of nickel-like silver x-ray lasers with and without the travelling wave pumpingtechnique where the target lengths are 4 mm for both cases. They have also observed gainsaturation in the nickel-like tin laser at a wavelength of 12.0 nm, in which the gain coefficientof 30cm1 and the gain-length product of 13.2 were achieved with a pumping energy of14 J. The gain-length products of more than 13 with a beam divergence of 57 mrad has beenobtained. Although the transient collisional excitation scheme has not provided the waterwindow soft x-ray lasers, we have to pursue them because of a lot of fruitful applications witha small pumping installation. Dekker and London (1998) have proposed a compact nickel-like

tungsten soft x-ray laser operating on the 4d4p, J = 01 transition at 4.32 nm using bothsolid tungsten slabs and tungsten aerogel foams. They predict gains of 220 cm1 for 1 mlaser pump of intensity = 1 1017 W cm2.

Recently, Fiedorowicz and his collaborators at LLNL (2001) have demonstrated a highgain neon-like argon soft x-ray laser at 46.9nm using a gas-puff target. The elongated x-raylaser plasma column was produced by irradiating the gas-puff target with line-focused longand short picosecond laser pulses. At the Advanced Photon Research Centre, Lu et al (2002)have also demonstrated a higher gain neon-like argon soft x-ray laser with line-focused double


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traveling wave pump-off(l=6mm)

30

20

10

0

6004002000

6004002000

Si L-edge12.4nm

traveling wave pump-on(l=4.8 mm)

30

20

10

0

Ni-like Ag13.9 nm

Figure 40. Typical spectra of nickel-like silver x-ray lasers at 13.9nm with and without the

travelling wave pumping technique where the target lengths are 4.8mm for with the traveling wavepumping and 6 mm for without the travelling wave pumping, respectively. The travelling wavepumping contributes significantly to the enhancement of the x-ray laser beam intensity (Kawachiet al 2002).

1.5 ps laser pulses with a total energy of 9 J in a travelling wave excitation scheme. Thegain coefficient of 18.7cm1 and gain-length product of 8.4 have been obtained. The gastarget technique potentially provides us the wider plasma parameter space in space and timein conjunction with the practical advantages such as high repetition rate operation as wellas debris free operation. Note that the electron collisional excitation type palladium-like ionscheme using the optical field ionization will be described in section 5.

4.11. Summary

The electron collisional excitation scheme has given us many fruitful results such asdemonstration of saturated amplification, the water window x-ray lasers, high-qualitycoherentbeams and x-ray laser applications. The reduction of pumping energy has also been achievedusing the transient collisional excitation scheme. However, at present, this scheme does notprovide good quality coherent beams with narrow divergence and short wavelength x-raylasers as short as the water window spectral range. For the purpose of improvement of spatialcoherence, the oscillator and amplifier configuration which is also called the double-targetconfiguration and injection of high-order harmonics with picosecond time-duration are tryingto be performed experimentally (Hasegawa 2001). For applicationsof this type of x-ray lasers,although the efficiency is higher than those pumped by the long-pulse laser, the output energyis up to a few tens ofJ which is not sufficient for some of the applications especially for theplasma probing. Improvement of pumping efficiency is still necessary for this scheme.

5. Various plasma-based x-ray laser schemes other than the recombination and the

electron collisional excitation schemes

5.1. Introduction

Recently, we have developed good ultra-

review of soft x-ray laser researches and developments

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