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A review of Ni-like X-ray laser experiments undertaken using the VULCAN laser at the Rutherford Appleton Laboratory
C. R. Acad. Sci. Paris, t. 1, Série IV, p. 1053–1063, 2000 Électromagnetisme, optique/Electromagnetism, optics (Gaz, plasmas/Gas, plasmas)
LES DÉVELOPPEMENTS RÉCENTS DES LASERS À RAYONS X RECENT PROGRESS IN X-RAY LASERS
DOSSIER
A review of Ni-like X-ray laser experiments undertaken using the VULCAN laser at the Rutherford Appleton Laboratory Ciaran L.S. LEWIS a , Greg J. TALLENTS b a b
School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, UK Department of Physics, University of York, York YO10 5DD, UK E-mail: [email protected]
(Reçu le 1 septembre 2000, accepté le 11 septembre 2000)
Abstract.
Recent progress using the VULCAN laser at the Rutherford Appleton Laboratory to pump X-ray lasing in nickel-like ions is reviewed. Double pulse pumping with ∼ 100 ps pulses has been shown to produce significantly greater X-ray laser output than single pulses of duration 0.1–1 ns. With double pulse pumping, the main pumping pulse interacts with a pre-formed plasma created by a pre-pulse. The efficiency of lasing increases as there is a reduced effect of refraction of the X-ray laser beam due to smaller density gradients and larger gain volumes, which enable propagation of the X-ray laser beam along the full length of the target. The record shortest wavelength saturated laser at 5.9 nm has been achieved in Ni-like dysprosium using double pulse pumping of 75 ps duration from the VULCAN laser. A variant of the double pulse pumping using a single ∼ 100 ps laser pulse and a superimposed short ∼ 1 ps pulse has been found to further increase the efficiency of lasing by reducing the effects of over-ionisation during the gain period. The record shortest wavelength saturated laser pumped by a short ∼ 1 ps pulse has been achieved in Ni-like samarium using the VULCAN laser operating in chirped pulse amplified (CPA) mode. Nilike samarium lases at 7.3 nm. 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS X-ray laser / nickel-like ions / collisional excitation / travelling wave / saturated output / plasma
Revue de la recherché sur le laser X–UV à ions nickeloïdes au Rutherford Appleton Laboratory avec le laser VULCAN Résumé.
Nous passons en revue les progrès récents réalisés à l’aide du laser VULCAN du Rutherford Appleton Laboratory pour le pompage des lasers collisionnels X–UV à ions nickeloïdes. Le pompage à deux impulsions de durées voisines de 100 ps est significativement plus efficace que celui obtenu avec une impulsion solitaire de 0,1–1 ns de durée. Lors du pompage à deux impulsions, l’mpulsion principale de pompage interagit avec un plasma préformé créé par la pré-impulsion. Le rendement du laser est plus important car les effets de réfraction du faisceau laser X–UV sont réduits par les plus faibles gradients de densité et les plus grands volumes amplificateurs ; la propagation du faisceau X–UV peut avoir lieu sur toute la longueur de la cible. La plus courte longueur d’onde obtenue à ce jour a été atteinte avec le dysprosium nickeloïde en utilisant une double impulsion de 75 ps provenant du laser
Note présentée par Guy L AVAL. S1296-2147(00)01110-0/FLA 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. Tous droits réservés.
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VULCAN. Une variante du pompage par double impulsion utilisant une simple impulsion laser de 100 ps superposée à une impulsion brève de ∼ 1 ps augmente substantiellement le rendement du laser X–UV en réduisant les effets néfastes de la sur-ionisation pendant la durée d’existence du gain. La plus courte longueur d’onde a été obtenue avec le samarium nickeloïde en utilisant VULCAN en mode d’amplification par dérive de fréquence. Le samarium nickeloïde présente un effet d’amplification laser à 7,3 nm. 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS laser X / ions nickeloïdes / excitation collisionnelle / onde progressive / signal saturé / plasma
1. Introduction Initial, unequivocal demonstration of soft X-ray laser action in collisionally pumped systems was achieved in schemes based on neon-like ions [1], and this was quickly followed by successful operation of schemes based on nickel-like ions [2]. The nickel-like systems are potentially more interesting in that they offer prospects for scaling to the shortest wavelengths via both valence (3p6 3d9 4d–3p6 3d9 4p), and inner shell (3p5 3d10 4p–3p6 3d9 4p) electron transitions with relatively high quantum efficiency. For these reasons, significant effort has been invested in their development over the last fifteen years. The salient features associated with the relative scaling of the operating X-ray laser wavelengths using neon- and nickel-like ions as the lasant media are illustrated in figure 1 [3,4]. Much effort has been made in modelling the lasertarget interaction (for foil, slab, and gas targets) needed to achieve optimum hydrodynamics for plasma formation, and these models often include the atomic physics and rate coefficients needed to calculate space-time evolution of population inversions. In addition, simplified analytic scaling models are useful, as discussed in Section 2. Early experimental progress was largely limited to pumping high atomic number targets (Z < 80, with modest gain-length products achieved at wavelengths close to the water-window) by large, multi-kilojoule lasers found in ICF fusion laboratories [5,6]. Some work on Sm (Z = 62, lasing at 7.3 nm) with smaller pump lasers was also reported, but all devices were operating very far from saturation [7,8]. Significant progress was only made after it was appreciated that the use of pre-pulses to prepare a pre-plasma for
Figure 1. Left: schematic term diagram showing relative ionisation energies for neon-like arsenic and nickel-like molybdenum which both lase at ∼ 19 nm. The shaded region between ground state and continuum indicate spread of energy levels associated with upper and lower levels for valence and inner shell transitions. It takes ∼ 9 keV and ∼ 1.5 keV of ionisation energy to produce these neon and nickel like ions respectively. Right: wavelength scaling in region of water-window (boxed) of normal J = 0–1 and potential inner shell transitions vs. atomic number where 2s and 3p holes are created by pumping in Ne- and Ni-like ions.
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efficient interaction (i.e. heating/ionisation/pumping) with a main pulse had very beneficial effects in pumping Ne-like systems [9–13], and that the same technique was also useful for Ni-like systems [14]. This has now lead to saturated outputs at wavelengths as short as ∼ 6 nm with prospects for further progress as discussed in Section 3. It can be seen that the earliest Ni-like experiments used 0.5–1.0 ns duration drive pulses, but timeresolved measurements and simulations showed that there was no advantage in investing pump energy for longer than ∼ 100 ps, as the optimum plasma conditions for maximum gain could not be sustained on longer timescales in these rapidly evolving plasmas, which are typically ∼ 3 cm long with ASE (Amplified Spontaneous Emission) transit times of ∼ 100 ps. Consequently, many investigations operated with one or more pre-pulses, and/or main pulses of duration 50–100 ps in a regime which became known as the QSS (quasi-steady-state) pumping regime. This refers to the notion that if the electron temperature in the main plasma is kept sufficiently low during the main drive pulse, it is possible to sustain useful pumping of the inversion (on the 4d1 S0 –4p1 P1 lasing transition) through monopole collisional excitation into the upper laser level (3d9 4d) without excessively overionising the plasma beyond Ni-like during the pulse [15]. A variant of the QSS approach, and known as the TCE (transient collisional excitation) regime, relies on achieving very high pump rates and hence very large gain coefficients by having temperatures which are much higher (typically a factor of two) than those used in the QSS regime [16]. Clearly, if such conditions are sustained too long the plasma will strongly over-ionise and the gain will rapidly reduce. The basis for efficiently achieving this high gain mode in practice lies in using short (∼ 1 ps) drive pulses at high intensity (∼ 1015 W·cm−2 ) to interact with a pre-plasma generated in the optimum ionisation state; i.e. Ni-like ions should have a large fractional abundance and density at the spatial region where the high temperature can be achieved, and this must also be consistent with shallow electron density gradients so that the ASE pulse can propagate along the amplifier with minimal refraction effects. The pre-plasma in this case is typically formed just before the short pulse arrival using a longer (∼ 100 ps) pulse at 1013 –1014 W·cm−2 as described more fully in Section 4. 2. Modelling of Ni-like X-ray lasers Lasing on ions iso-electronic with nickel was initially modelled at the time of the first observations of collisionally pumped X-ray lasers [17]. Hagelstein calculated cross-sections for Ni-like gadolinium which were used to estimate gains for Ni-like lasing at 6.1 and 6.6 nm from exploding foil targets [18,19]. Early experiments and simulations were undertaken using single ∼ ns duration pulses [20]. The X-ray laser output was effectively dominated by refraction effects in these single pulse experiments as the plasma density gradients were steep. Experiments first showed that multiple pulsing increased X-ray laser output [14]. Simulations with both Ne- and Ni-like ions have now effectively explained how the multiple pulsing increases the output and efficiency of X-ray lasers [15,21,22]. Pre-forming a plasma using a pre-pulse produces much more shallow density gradients when the main pumping pulses are incident so that the X-ray laser beam does not refract significantly. The volume of plasma where lasing gain is high also increases, ensuring that the propagating X-ray laser beam stays in the gain region. In addition, the long scalelength pre-plasma absorbs a large fraction of the incident main pumping laser pulse [23]. It is possible to give a simple similarity model for the optimum ratio between the irradiance of a pre-pulse relative to the main pulse (the ‘pulse ratio’), and the temporal separation T between the pre-pulse and main pulse in double pulse pumped X-ray lasers. Simulations suggest that the plasma conditions of collisional excitation X-ray lasers pumped by double pulses can be quantified by a parameter, the energy density. We will approximate the energy density by θe /Vpre , where Vpre is the volume of the pre-plasma just before the arrival of the main pulse and θe is the peak electron temperature during the main pulse irradiation [21]. A higher energy density than the optimum value implies over-ionisation or a narrow gain region with steep electron density gradients, while a lower energy density than the optimum gives low gain and thus lower
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laser output. Assuming that the density profile during lasing is determined by the pre-pulse and a twodimensional plasma expansion, the volume of the pre-plasma Vpre ∝ ν 2 T 2 , where ν is the ion sound speed. Since the mass ablation of the target by the pre-pulse is proportional to νt, the lasing electron temperature is proportional to θe ∝ Imain /νt, where t is the pre-pulse duration and Imain is the peak irradiance of the a , where Ipre is the peak irradiance of main pulse. If we assume the ion sound speed is proportional to Ipre −3a −1 −2 t T . the pre-pulse and a is a constant, the energy density can be represented as θe /Vpre ∝ Imain Ipre Low irradiance pulses are absorbed such that a = 2/9. Such a value of a implies that electron temperatures will vary as θe ∝ I 4/9 , as observed under these conditions [24]. Assuming a constant value of θe /Vpre and a constant peak irradiance Imain then implies that the optimum pulse ratio Ropt = (Imain /Ipre )opt scales as Ropt ∝ T −3 . Such a scaling has been observed experimentally in our study of Ni-like Sm [25]. Ionisation of the Ni-like stage has been shown to be less stable than ionisation of Ne-like ions [14,21]. For comparable ionisation energy, Ni-like ions have twice the monopole excitation rate to the upper lasing levels compared to Ne-like ions. However, Ni-like ions can be rapidly ionised to Co-, Fe- and above ionisation stages, leading to reduced gain. McCabe and Pert show a reduced parameter range for gain in Ni-like Gd compared to Ne-like Ge as a consequence of this tendency to overionise [15]. Experimental resonance line spectra show emission from a range of ionisation stages under the conditions for Ni-like gain (see figure 2), thus confirming indirectly the importance of over-ionisation. Modelling shows that the atomic excitation dynamics of X-ray lasers pumped by double ∼ 100 ps pulses (the QSS approach), and those pumped by ∼ 1 ps pulses superimposed on a ∼ 100 ps pulse (the TCE approach), are similar. The excited populations adjust sufficiently quickly in both cases that the collisional and radiative processes into and out of each level are balanced for most of the gain duration [26]. Accurate
Figure 2. Resonance line spectra from a samarium target punped by two 75 ps pulses separated by 3.5 ns. The ratio of the pre-pulse to main pulse irradiance is indicated on the plot. Ni-, Co- and Mn-like emission is indicated. Peak irradiance on target was ≈ 4 × 1013 W·cm−2 .
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population and gain modelling can be undertaken treating only the ground level populations Ni of the different ionisation stages with a dNi /dt term.
Multiple pulsing was first shown to increase Ni-like X-ray laser output by Daido et al. in Ni-like Nd, where a gain length product of 8 was produced [14]. Similar small gain length products were reported by Nilsen and Moreno [27] and Li et al. [28]. To demonstrate the scaling of Ni-like lasers with useful output for possible applications, work at Rutherford Appleton Laboratory concentrated on driving the Nilike lasers into saturation with gain length products greater than 15. Zhang et al. demonstrated saturated lasing on several Ni-like ions including Ag and Sm at 14 nm and 7 nm, respectively [29–32]. The shortest wavelength saturated laser produced so-far is in Ni-like Dy at 5.9 nm, and was first reported by Smith et al. [33]. An experimental study was undertaken to optimise the output of the Ni-like Sm laser at Rutherford Appleton Laboratory [25]. Samarium stripes of 75 µm width were irradiated by two 75 ps duration pulses with a measured ratio of intensity between the pre-pulse and main pulse (termed the ‘pulse ratio’), and a set time between the two pulses (termed the ‘pulse separation’). Three beams of the VULCAN laser were overlapped onto the targets in a 19 mm × 75 µm width line focus to produce a peak irradiance of the main pulse on target of ≈ 6 × 1013 W·cm−2 . The targets were 14 mm long flat slabs consisting of 75 µm width and 1–2 µm thickness samarium stripes coated on glass substrates. The X-ray laser output was measured with a grazing angle flat field spectrometer, recording emission from 6–24 nm wavelength, and from −1 to 11 mrad angular deviation in the horizontal direction (perpendicular to the target surface) on a back thinned CCD detector. A typical recorded spectrum is shown in figure 3. The variation of the Sm X-ray laser output as a function of target length is shown in figure 4. The experimental data points have been fitted with a model of the ASE output as outlined by Lin et al. [32] and Strati and Tallents [34]. The Sm X-ray laser output variation with pulse ratio for different pulse intervals is shown in figure 5. The brightest Sm X-ray laser has been observed using 0.5% pre-pulse with a pulse interval of 3.5 ns, but the maximum optimised output with pulse intervals of 2.2, 3.5 and 5 ns differ by less than a factor 2.
Figure 3. X-ray laser spectrum from a single 14 mm long Sm target irradiated by double 75 ps pulses with a pulse ratio of 5% and a pulse interval of 2.2 ns. The two lasing lines can be seen repeated in 1st, 2nd and 3rd order diffraction from the flat field spectrometer grating.
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Figure 4. The variation of Ni-like Sm X-ray laser output at 7.3 nm as a function of the length of the gain medium. The curve is a fit of the calculated ASE output for small gain coefficient 9.5 cm−1 .
Figure 5. X-ray laser output at 7.3 nm as a function of the pulse ratio for various pulse intervals.
The Ni-like X-ray lasers exhibit gain on two J = 0–1 transitions emanating from the same upper quantum state. Atomic physics modelling shows that the gains for the two J = 0–1 lasing transitions are close to equal for Gd with atomic number Z = 64, but become increasingly unequal as Z deviates from this value [35]. Ni-like Dy (Z = 66) lasing was investigated at Rutherford Appleton Laboratory, and produced the current shortest wavelength saturated lasing output at 5.9 nm. Interestingly, the lower gain line at 6.4 nm reduces in output with increasing target length as the higher gain line is driven further into saturation. Extending the ASE model to include both lasing lines produces good model fits to the experimental data ( figure 6). The model and Ni-like Dy experimental data is explained in detail in the paper by Smith et al. [33].
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Figure 6. The variation for Ni-like Dy output at 5.86 nm (higher gain) and 6.37 nm (lower gain) as a function of the length of the gain medium. The curves are fits of the calculated ASE output. The lower gain line decreases with increasing medium length in the saturation regime because of stimulated emission depletion of the common upper quantum state to the saturation of the higher gain line.
4. CPA-pumped experiments The concept of multiple pulse pumping techniques was extended to include the variant of using a long pulse (< 1ns) combined with a very short pulse of ∼ 1 ps duration and high intensity to provide the plasma parameters to support high, but short-lived, gain conditions. The theory of this so-called TCE technique, was examined quite early [16,36] and experimental feasibility was verified with neon-like ions as soon as suitable lasers were available [37,38]. Typically, the short pump pulse is generated from a CPA (chirped pulse amplification) laser [39], and since the pump energy for ∼ 15 nm XRLs is modest at 1–2 J·mm−1 in a line focus for both long and short pulses, then for the first time a real option arose to optically pump X-ray laser systems with relatively small TT (table-top) lasers. In fact, development of Ne-like XRLs and the obvious extension to Ni-like XRLs pumped by CPA technology have occurred in parallel using both ICF-class and TT-class lasers, the latter being clearly potentially more interesting in terms of longer term application programmes of XRLs. The first demonstration of laser action in Ni-like ions in the TCE regime used the Vulcan laser in its CPA mode to irradiate tin (Sn) targets, lasing and saturating at 12 nm [40]. This was soon followed by gain (∼ 35 cm−1 ) at 14.7 nm (Pd) pumped by the TT laser COMET [41], and at ∼ 14 nm (Ag) pumped by the sub-picosecond CPA laser at LULI [42]. An important new issue in the TCE regime is that the short-lived gain conditions demand a mechanism to deliver the picosecond pulse energy into the pre-plasma in such a way that the ASE X-ray pulse developing always ‘sees’ high gain conditions as it propagates along the line plasma at a group velocity close to the speed of light. Such a TW (travelling-wave) excitation pump can be arranged in several ways, including use of diffraction gratings (which may also be the CPA compressor gratings) to tilt the incident beam wavefront at 45 degrees to the target, or simply by arranging a ‘stepped’ segmented cylindrical focusing optic [43,44].
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Vulcan experiments always used TW pumping and saturated outputs > 1010 W·cm−2 at ∼ 33 nm (Ti) and ∼ 12 nm (Sn) were readily achieved in both Ne-like [45] and Ni-like lasants [40,46] respectively for target lengths shorter than 10 mm. However, the true role of the TW pump was systematically demonstrated first with Ne-like Ge at RAL/VULCAN by plotting growth curves of XRL output as a function of target length with different TW excitation velocities [47]. Good general agreement was found with calculations from numerical and analytical models [48] and the TW technique is now used routinely to enhance the efficiency of both large scale and TT laser pumping [49,50]. Analytical models of TW pumping have been discussed by Strati and Tallents [34] and King and Pert [51]. The Ni-like samarium XRL is the shortest wavelength device pumped to date with a TW-CPA beam laser and its growth curve is shown in figure 7. This system lases at 7.3 nm and has reached saturated output intensities for plasma columns > 8 mm long with pulse characteristics as follows; energy is ∼ 1.5 µJ, divergence is < 3 mrad and the pulse duration is estimated to be < 5 ps [52]. An indication of the spectral brightness possible in Ni-like XRLs at ≈ 12 nm wavelength is shown in figure 8 where a line out of a Sn (11.9 nm) laser pumped in the TCE regime is shown alongside the output from an In (12.6 nm) laser pumped in the QSS regime. Although the saturated intensities are comparable in each case, the QSS In laser
Figure 7. Left: growth curve for TCE pumped samarium, lasing at 7.3 nm. The small signal gain coefficient is ∼ 19 cm−1 with a peak gain-length product reaching saturation level at the longest lengths. The XRL exit intensity from the gain medium is estimated to be ∼ 1010 W·cm−2 . Right: an angular lineout of the Sm XRL beam intensity showing < 3 mrad divergence.
Figure 8. The quasi-monochromatic spectra available from XRLs pumped in long pulse (∼ 100 ps) and short pulse (∼ 1 ps) mode are illustrated with lineouts from spectra obtained from indium and tin targets respectively. The lasing wavelengths are 12.6 nm and 11.9 nm with first and second order appearing in the flat-field spectrometer CCD output.
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is about 30 ps in duration while the Sn laser, based on time-resolved measurements on a similar Ag laser at ∼ 14 nm [53], is assumed to be about ten times shorter.
There has been rapid progress over the last five years in the development of Ni-like X-ray lasers and this has largely happened by extension of ideas first applied to neon-like systems. It is likely that this will also happen with pumping of inner shell transitions based on collisional ejection of 2s and 3p electrons in Nelike and Ni-like ions, respectively, with prospects of a faster route to shorter lasing wavelengths. There has been no firm experimental evidence to date that this scheme is viable, although modelling predicts it will be feasible. Further progress to shorter wavelengths using multiple 100 ps drive pulses can be expected as the large pump lasers develop. However, the recently demonstrated ability to pump XRLs with table-top lasers will encourage other workers without access to ICF-class lasers to become involved in the field. Prospects of 10 Hz, 10 µJ, 2 ps lasers at < 10 nm wavelengths are good and will likely bootstrap a community with applications for such sources. Acknowledgements. We gratefully acknowledge the contributions made by our students and colleagues to the results summarised in this paper. The work has been financially supported by the U.K. Engineering and Physical Sciences Research Council and by the EU Training and Mobility of Researchers programme.
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[14] Daido H., Kato Y., Murai K., Ninomiya S., Kodama R., Yuan G., Oshikane Y., Takagi M., Takabe H., Efficient soft X-ray lasing at 6 to 8 nm with nickel-like lanthanide ions, Phys. Rev. Lett. 75 (1995) 1074–1077. [15] McCabe S., Pert G.J., Computational investigation of the Ni-like Gd collisionally pumped X-ray laser, Phys. Rev. A 61 (2000) 033804 1–9. [16] Afanas’ev Yu.V., Shlyapstev V.N., Formation of a population inversion of transitions in Ne-like ions in steady-state and transient plasmas, Sov. J. Quantum Electron. 19 (1989) 1606–1612. [17] Rosen M.D., Hagelstein P.L., Matthews D.L., Campbell E.M., Hazi A.U., Whitten B.L., MacGowan B.J., Turner R.E., Lee R.W., Charatis G., Busch G.E., Shepard C.L., Rockett P.D., Exploding-foil technique for achieving a soft-X-ray laser, Phys. Rev. Lett. 54 (1985) 106–109. [18] Hagelstein P.L., Relativistic distorted-wave results for nickel-like gadolinium, Phys. Rev. A 34 (1986) 874–884. [19] Maxon S., Hagelstein P., Scofield J., Lee Y., Estimated gains for a Ni-like exploding foil target, J. Appl. Phys. 59 (1986) 293–295. [20] MacGowan B.J., DaSilva L.B., Fields D.J., Keane C.J., Koch J.A., London R.A., Matthews D.L., Maxon S., Mrowka S., Osterheld A.L., Scofield J.H., Shimkaveg G., Trebes J.E., Walling R.S., Short wavelength X-ray laser research at the Lawrence Livermore National Laboratory, Phys. Fluids B 4 (1992) 2326. [21] Lin J.Y., Tallents G.J., Demir A., Healy S.B., Pert G.J., Optimization of double drive pulse pumping in Ne-like Ge X-ray lasers, J. Appl. Phys. 83 (1998) 1863–1868. [22] Sims P.A., McCabe S., Pert G.J., Comparison on neon-like germanium inner shell and nickel-like gadolinium lasing at 62 Å and 66 Å by picosecond heating of a preformed plasma, Opt. Commun. 153 (1998) 164–171. [23] Tagviashvili M., Tallents G.J., Numerical investigation of the absorption of multipulse pumping, IOPP Conf. Ser. 159 (1998) 439–442. [24] Eker G., Design and Application of X-Ray Lasers, PhD thesis, University of Essex, 2000. [25] Lin J.Y., Tallents G.J., Smith R., MacPhee A.G., Zhang J., Eker G., Kennan R., Lewis C.L.S., Neely D., O’Rourke R.M.N., Pert G.J., Pestehe S.J., Wark J.S., Optimization of double pulse pumping for Ni-like Sm X-ray lasers, J. Appl. Phys. 85 (1999) 672–675. [26] Nilsen J., Li Y., Dunn J., Barbee W., Osterheld A.L., Modeling and demonstration of a saturated Ni-like Mo X-ray laser, in: Proc. 7th Int. Conf. on X-ray Lasers, St. Malo, France, June 2000 (to appear in Éditions de Physique, 2001). [27] Nilsen J., Moreno J.C., Lasing at 7.9 nm in nickel-like neodymium, Opt. Lett. 20 (1995) 1386–1388. [28] Li Y., Pretzler G., Lu P.X., Fill E.E., Demonstration of X-ray lasing in nickel-like tin, Phys. Rev. A 53 (1996) R652. [29] Zhang J., MacPhee A.G., Lin J., Barbee T.W., Danson C., Key M.H., Lewis C.L.S., Neely D., Nilsen J., O’Rourke R.M.N., Pert G.J., Smith R., Tallents G.J., Wark J.S., Wolfrum E., Recent progress in nickel-like X-ray lasers at RAL, Proc. SPIE Int. Soc. Opt. Eng. 3156 (1997) 53–64. [30] Zhang J., MacPhee A.G., Nilsen J., Lin J., Barbee T.W., Danson C., Key M.H., Lewis C.L.S., Neely D., O’Rourke R.M.N., Pert G.J., Smith R., Tallents G.J., Wark J.S., Wolfrum E., Demonstration of saturation in a Ni-like Ag X-ray laser at 14 nm, Phys. Rev. Lett. 78 (1997) 3856–3659. [31] Zhang J., MacPhee A.G., Lin J., Wolfrum E., Smith R., Danson C., Key M.H., Lewis C.L.S., Neely D., Nilsen J., Pert G.J., Tallents G.J., Wark J.S., A saturated X-ray laser beam at 7 nm, Science 276 (1997) 1097–1100. [32] Lin J.Y., Tallents G.J., Zhang J., MacPhee A.G., Lewis C.L.S., Neely D., Nilsen J., Pert G.J., O’Rourke R.M.N., Smith R., Wolfrum E., Gain saturation of the Ni-like X-ray lasers, Opt. Commun. 158 (1998) 55–60. [33] Smith R., Tallents G.J., Zhang J., Eker G., McCabe S., Pert G.J., Wolfrum E., Saturation behavior of two X-ray lasing transitions in Ni-like Dy, Phys. Rev. A 59 (1999) R47–50. [34] Strati S., Tallents G.J., Travelling wave effects on short pulse pumped X-ray lasers, in: Central Laser Facility Annual Report 1998–99, pp. 73–76. [35] Daido H., Ninomiya S., Imani T., Okaichi Y., Takagi M., Kodama R., Takabe H., Kato Y., Koike F., Nilsen J., Murai K., Atomic number scaling of the nickel-like soft X-ray lasers, Int. J. Mod. Phys. B 11 (1997) 945–990. [36] Shlyaptsev V.N., Nickles P.V., Schlegel T., Kalashnikov M.P., Osterheld A.L., Table top X-ray laser pumped with subnanosecond and picosecond pulses, Proc. SPIE Int. Soc. Opt. Eng. 2012 (1993) 111–118. [37] Nickles P.V., Shlyaptsev V.N., Kalachnikov M., Schnurer M., Will I., Sandner W., Short pulse X-ray laser at 32.6 nm based on transient gain in Ne-like titanium, Phys. Rev. Lett. 78 (1997) 2748–2751. [38] Warwick P.J., Lewis C.L.S., Kalachnikov M.P., Nickles P.V., Schnurer M., Behjat A., Demir A., Tallents G.J., Neely D., Wolfrum E., Observation of high transient gain in the germanium X-ray laser at 19.6 nm, J. Opt. Soc. Am. B 15 (1998) 1808–1814. [39] Danson C.N., Nickles P.V., Allott R., Behjat A., Collier J., Demir A., Kalachnikov M.P., Key M.H., Lewis C.L.S., Neely D., Pepler D.A., Pert G.J., Schnurer M., Sandner W., Shlyaptsev V.N., Tallents G.J., Warwick P.J., Wolfrum E., Zhang J., Implementation of a CPA line focus travelling-wave for highly efficient saturated lasing of Ne-like Ti and Ge, AIP Conf. Proc. 426 (1998) 473–478.
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[40] Tallents G.J., Lin J.Y., Zhang J., Behjat A., Demir A., Güzelgöz M.M., Lewis C.L.S., MacPhee A.G., Neely D., Pert G.J., Smith R., Wark J.S., Warwick P.J., Wolfrum E., The optimisation of soft X-ray laser output, in: OSA Tech. Digest Series (Applications of High Field and Short Wavelength Sources VIII), Vol. 7, 1997, pp. 47–49. [41] Dunn J., Osterheld A.L., Shepherd R., White W.E., Shlyaptsev V.N., Stewart R.E., Demonstration of X-ray amplification in transient gain nickel-like palladium scheme, Phys. Rev. Lett. 80 (1998) 2825–2829. [42] Klisnick A., Ros D., Zeitoun Ph., Albert F., Carillon A., Fourcade P., Hubert S., Jaegle P., Jamelot G., Lewis C.L.S., MacPhee A.G., O’Rourke R.M.N., Keenan R., Nickles P., Janulewicz K., Kalashnikov M., Warwick P.J., Chanteloup J.C., Salmon E., Sauteret C., Zou J.P., Joyeux D., Phalippou D., Generation of intense Ni-like X-ray lasers at LULI: from 130 ps to 350 fs pumping pulses, IOPP Conf. Series 159 (1999) 107–114. [43] Collier J.L., Danson C.N., Allott R.M., Hutchinson H.M.R., Lewis C.L.S., Neely D., Peplar D.A., Winstone T.B., Zhang J., Ultra-short pulse line focus travelling-wave implementation on the Vulcan laser, IOPP Conf. Series 159 (1999) 649–652. [44] Chanteloup J.C., Salmon E., Zou J.P., Migus A., Sauteret C., Zeitoun Ph., Klisnick A., Carillon A., Hubert S., Ros D., Lewis C.L.S., MacPhee A.G., O’Rourke R.M.N., Keenan R., Nickles P., Janulewicz K., Kalashnikov M., Warwick P.J., New method of travelling wave generation and characterization for use on X-ray laser transient pumping experiments, IOPP Conf. Series 159 (1999) 653–656. [45] Kalachnikov M.P., Nickles P.V., Schnürer M., Sandner W., Shlyaptsev V.N., Danson C., Neely D., Wolfrum E., Lewis C.L.S., Warwick P.J., Behjat A., Demir A., Tallents G.J., Saturated transient gain titanium X-ray laser at 32.6 nm, Phys. Rev. A 57 (1998) 4778–4783. [46] MacPhee A.G., O’Rourke R.M.N., Lewis C.L.S., Lin J.Y., Demir A., Tallents G.J., Collier J., Neely D., Ros D., Zeitoun Ph., McCabe S.P., Simms P.A., Pert G.J., Transient gain in travelling-wave pumped Ni-like X-ray lasers, IOPP Conf. Series 159 (1999) 75–78. [47] Lewis C.L.S., Keenan R., MacPhee A.G., Moore B., O’Rourke R.M.N., Tallents G.J., Dobosz S., Pestehe J., Strati F., Wark J.S., Wolfrum E., Pert G.J., MacCabe S.P., Simms P., Allott R., Collier J., Danson C.N., Djaoui A., Neely D., Progress with saturated soft X-ray lasers pumped by the Vulcan laser, Proc. SPIE Int. Soc. Opt. Eng. 3776 (1999) 292–301. [48] Lin J.Y., Tallents G.J., MacPhee A.G., Demir A., Lewis C.L.S., O’Rourke R.M.N., Pert G.J., Ros D., Zeitoun Ph., Travelling wave chirped pulse amplified transient pumping for collisional excitation X-ray lasers, Opt. Commun. 166 (1999) 211–218. [49] Klisnick A., Zeitoun Ph., Ros D., Carillon A., Fourcade P., Hubert S., Jamelot G., Lewis C.L.S., MacPhee A.G., O’Rourke R.M.N., Keenan R., Nickles P., Janulewicz K., Kalashnikov M., Warwick P.J., Chanteloup J.C., Migus A., Salmon E., Sauteret C., Zou J.P., Transient pumping of a Ni-like Ag X-ray laser with a sub-picosecond pump pulse in a travelling-wave irradiation geometry, J. Opt. Soc. Am. B 17 (2000) 1093–1097. [50] Dunn J., Li Y., Osterheld A.L., Nilsen J., Hunter H.R., Shlyaptsev V.N., Gain saturation regime for laser-driven tabletop, transient Ni-like ion X-ray lasers, Phys. Rev. Lett. 84 (2000) 4834–4837. [51] King R., Pert G.J., Modelling short pulse X-ray laser experiments, C. R. Acad. Sci. Paris Sér. IV 1 (8) (2000), this issue. [52] Lewis C.L.S., Keenan R., MacPhee A.G., O’Rourke R.M.N., Tallents G.J., Eker G., Lin J.Y., Pestehe S.J., Smith R., Wark J.S., Wolfrum E., Zhang J., Pert G.J., MacCabe S.P., Simms P.A., Burge R.E., Browne M.T., Charalambous P., Neely D., Collier J., Danson C.N., Overview of X-ray laser research in the UK, IOPP Conf. Series 159 (1999) 1–8. [53] Kuba J., Klisnick A., Ros D., Smith R., Schott R., Jamelot G., Chenais-Popovics C., Keenan R., Topping S., Lewis C.L.S., Strati F., Tallents G.J., Neely D., Clarke R., Collier J., MacPhee A.G., Bortolotto F., Janulewicz K.A., Nickles P., Duration of transient X-ray laser pulses: experimental investigation with high temporal resolution, in: Proc. 7th Int. Conf. on X-ray Lasers, St. Malo, France, June 2000 (to appear in Éditions de Physique, 2001).
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LES DÉVELOPPEMENTS RÉCENTS DES LASERS À RAYONS X RECENT PROGRESS IN X-RAY LASERS
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A review of Ni-like X-ray laser experiments undertaken using the VULCAN laser at the Rutherford Appleton Laboratory Ciaran L.S. LEWIS a , Greg J. TALLENTS b a b
School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, UK Department of Physics, University of York, York YO10 5DD, UK E-mail: [email protected]
(Reçu le 1 septembre 2000, accepté le 11 septembre 2000)
Abstract.
Recent progress using the VULCAN laser at the Rutherford Appleton Laboratory to pump X-ray lasing in nickel-like ions is reviewed. Double pulse pumping with ∼ 100 ps pulses has been shown to produce significantly greater X-ray laser output than single pulses of duration 0.1–1 ns. With double pulse pumping, the main pumping pulse interacts with a pre-formed plasma created by a pre-pulse. The efficiency of lasing increases as there is a reduced effect of refraction of the X-ray laser beam due to smaller density gradients and larger gain volumes, which enable propagation of the X-ray laser beam along the full length of the target. The record shortest wavelength saturated laser at 5.9 nm has been achieved in Ni-like dysprosium using double pulse pumping of 75 ps duration from the VULCAN laser. A variant of the double pulse pumping using a single ∼ 100 ps laser pulse and a superimposed short ∼ 1 ps pulse has been found to further increase the efficiency of lasing by reducing the effects of over-ionisation during the gain period. The record shortest wavelength saturated laser pumped by a short ∼ 1 ps pulse has been achieved in Ni-like samarium using the VULCAN laser operating in chirped pulse amplified (CPA) mode. Nilike samarium lases at 7.3 nm. 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS X-ray laser / nickel-like ions / collisional excitation / travelling wave / saturated output / plasma
Revue de la recherché sur le laser X–UV à ions nickeloïdes au Rutherford Appleton Laboratory avec le laser VULCAN Résumé.
Nous passons en revue les progrès récents réalisés à l’aide du laser VULCAN du Rutherford Appleton Laboratory pour le pompage des lasers collisionnels X–UV à ions nickeloïdes. Le pompage à deux impulsions de durées voisines de 100 ps est significativement plus efficace que celui obtenu avec une impulsion solitaire de 0,1–1 ns de durée. Lors du pompage à deux impulsions, l’mpulsion principale de pompage interagit avec un plasma préformé créé par la pré-impulsion. Le rendement du laser est plus important car les effets de réfraction du faisceau laser X–UV sont réduits par les plus faibles gradients de densité et les plus grands volumes amplificateurs ; la propagation du faisceau X–UV peut avoir lieu sur toute la longueur de la cible. La plus courte longueur d’onde obtenue à ce jour a été atteinte avec le dysprosium nickeloïde en utilisant une double impulsion de 75 ps provenant du laser
Note présentée par Guy L AVAL. S1296-2147(00)01110-0/FLA 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. Tous droits réservés.
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VULCAN. Une variante du pompage par double impulsion utilisant une simple impulsion laser de 100 ps superposée à une impulsion brève de ∼ 1 ps augmente substantiellement le rendement du laser X–UV en réduisant les effets néfastes de la sur-ionisation pendant la durée d’existence du gain. La plus courte longueur d’onde a été obtenue avec le samarium nickeloïde en utilisant VULCAN en mode d’amplification par dérive de fréquence. Le samarium nickeloïde présente un effet d’amplification laser à 7,3 nm. 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS laser X / ions nickeloïdes / excitation collisionnelle / onde progressive / signal saturé / plasma
1. Introduction Initial, unequivocal demonstration of soft X-ray laser action in collisionally pumped systems was achieved in schemes based on neon-like ions [1], and this was quickly followed by successful operation of schemes based on nickel-like ions [2]. The nickel-like systems are potentially more interesting in that they offer prospects for scaling to the shortest wavelengths via both valence (3p6 3d9 4d–3p6 3d9 4p), and inner shell (3p5 3d10 4p–3p6 3d9 4p) electron transitions with relatively high quantum efficiency. For these reasons, significant effort has been invested in their development over the last fifteen years. The salient features associated with the relative scaling of the operating X-ray laser wavelengths using neon- and nickel-like ions as the lasant media are illustrated in figure 1 [3,4]. Much effort has been made in modelling the lasertarget interaction (for foil, slab, and gas targets) needed to achieve optimum hydrodynamics for plasma formation, and these models often include the atomic physics and rate coefficients needed to calculate space-time evolution of population inversions. In addition, simplified analytic scaling models are useful, as discussed in Section 2. Early experimental progress was largely limited to pumping high atomic number targets (Z < 80, with modest gain-length products achieved at wavelengths close to the water-window) by large, multi-kilojoule lasers found in ICF fusion laboratories [5,6]. Some work on Sm (Z = 62, lasing at 7.3 nm) with smaller pump lasers was also reported, but all devices were operating very far from saturation [7,8]. Significant progress was only made after it was appreciated that the use of pre-pulses to prepare a pre-plasma for
Figure 1. Left: schematic term diagram showing relative ionisation energies for neon-like arsenic and nickel-like molybdenum which both lase at ∼ 19 nm. The shaded region between ground state and continuum indicate spread of energy levels associated with upper and lower levels for valence and inner shell transitions. It takes ∼ 9 keV and ∼ 1.5 keV of ionisation energy to produce these neon and nickel like ions respectively. Right: wavelength scaling in region of water-window (boxed) of normal J = 0–1 and potential inner shell transitions vs. atomic number where 2s and 3p holes are created by pumping in Ne- and Ni-like ions.
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efficient interaction (i.e. heating/ionisation/pumping) with a main pulse had very beneficial effects in pumping Ne-like systems [9–13], and that the same technique was also useful for Ni-like systems [14]. This has now lead to saturated outputs at wavelengths as short as ∼ 6 nm with prospects for further progress as discussed in Section 3. It can be seen that the earliest Ni-like experiments used 0.5–1.0 ns duration drive pulses, but timeresolved measurements and simulations showed that there was no advantage in investing pump energy for longer than ∼ 100 ps, as the optimum plasma conditions for maximum gain could not be sustained on longer timescales in these rapidly evolving plasmas, which are typically ∼ 3 cm long with ASE (Amplified Spontaneous Emission) transit times of ∼ 100 ps. Consequently, many investigations operated with one or more pre-pulses, and/or main pulses of duration 50–100 ps in a regime which became known as the QSS (quasi-steady-state) pumping regime. This refers to the notion that if the electron temperature in the main plasma is kept sufficiently low during the main drive pulse, it is possible to sustain useful pumping of the inversion (on the 4d1 S0 –4p1 P1 lasing transition) through monopole collisional excitation into the upper laser level (3d9 4d) without excessively overionising the plasma beyond Ni-like during the pulse [15]. A variant of the QSS approach, and known as the TCE (transient collisional excitation) regime, relies on achieving very high pump rates and hence very large gain coefficients by having temperatures which are much higher (typically a factor of two) than those used in the QSS regime [16]. Clearly, if such conditions are sustained too long the plasma will strongly over-ionise and the gain will rapidly reduce. The basis for efficiently achieving this high gain mode in practice lies in using short (∼ 1 ps) drive pulses at high intensity (∼ 1015 W·cm−2 ) to interact with a pre-plasma generated in the optimum ionisation state; i.e. Ni-like ions should have a large fractional abundance and density at the spatial region where the high temperature can be achieved, and this must also be consistent with shallow electron density gradients so that the ASE pulse can propagate along the amplifier with minimal refraction effects. The pre-plasma in this case is typically formed just before the short pulse arrival using a longer (∼ 100 ps) pulse at 1013 –1014 W·cm−2 as described more fully in Section 4. 2. Modelling of Ni-like X-ray lasers Lasing on ions iso-electronic with nickel was initially modelled at the time of the first observations of collisionally pumped X-ray lasers [17]. Hagelstein calculated cross-sections for Ni-like gadolinium which were used to estimate gains for Ni-like lasing at 6.1 and 6.6 nm from exploding foil targets [18,19]. Early experiments and simulations were undertaken using single ∼ ns duration pulses [20]. The X-ray laser output was effectively dominated by refraction effects in these single pulse experiments as the plasma density gradients were steep. Experiments first showed that multiple pulsing increased X-ray laser output [14]. Simulations with both Ne- and Ni-like ions have now effectively explained how the multiple pulsing increases the output and efficiency of X-ray lasers [15,21,22]. Pre-forming a plasma using a pre-pulse produces much more shallow density gradients when the main pumping pulses are incident so that the X-ray laser beam does not refract significantly. The volume of plasma where lasing gain is high also increases, ensuring that the propagating X-ray laser beam stays in the gain region. In addition, the long scalelength pre-plasma absorbs a large fraction of the incident main pumping laser pulse [23]. It is possible to give a simple similarity model for the optimum ratio between the irradiance of a pre-pulse relative to the main pulse (the ‘pulse ratio’), and the temporal separation T between the pre-pulse and main pulse in double pulse pumped X-ray lasers. Simulations suggest that the plasma conditions of collisional excitation X-ray lasers pumped by double pulses can be quantified by a parameter, the energy density. We will approximate the energy density by θe /Vpre , where Vpre is the volume of the pre-plasma just before the arrival of the main pulse and θe is the peak electron temperature during the main pulse irradiation [21]. A higher energy density than the optimum value implies over-ionisation or a narrow gain region with steep electron density gradients, while a lower energy density than the optimum gives low gain and thus lower
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laser output. Assuming that the density profile during lasing is determined by the pre-pulse and a twodimensional plasma expansion, the volume of the pre-plasma Vpre ∝ ν 2 T 2 , where ν is the ion sound speed. Since the mass ablation of the target by the pre-pulse is proportional to νt, the lasing electron temperature is proportional to θe ∝ Imain /νt, where t is the pre-pulse duration and Imain is the peak irradiance of the a , where Ipre is the peak irradiance of main pulse. If we assume the ion sound speed is proportional to Ipre −3a −1 −2 t T . the pre-pulse and a is a constant, the energy density can be represented as θe /Vpre ∝ Imain Ipre Low irradiance pulses are absorbed such that a = 2/9. Such a value of a implies that electron temperatures will vary as θe ∝ I 4/9 , as observed under these conditions [24]. Assuming a constant value of θe /Vpre and a constant peak irradiance Imain then implies that the optimum pulse ratio Ropt = (Imain /Ipre )opt scales as Ropt ∝ T −3 . Such a scaling has been observed experimentally in our study of Ni-like Sm [25]. Ionisation of the Ni-like stage has been shown to be less stable than ionisation of Ne-like ions [14,21]. For comparable ionisation energy, Ni-like ions have twice the monopole excitation rate to the upper lasing levels compared to Ne-like ions. However, Ni-like ions can be rapidly ionised to Co-, Fe- and above ionisation stages, leading to reduced gain. McCabe and Pert show a reduced parameter range for gain in Ni-like Gd compared to Ne-like Ge as a consequence of this tendency to overionise [15]. Experimental resonance line spectra show emission from a range of ionisation stages under the conditions for Ni-like gain (see figure 2), thus confirming indirectly the importance of over-ionisation. Modelling shows that the atomic excitation dynamics of X-ray lasers pumped by double ∼ 100 ps pulses (the QSS approach), and those pumped by ∼ 1 ps pulses superimposed on a ∼ 100 ps pulse (the TCE approach), are similar. The excited populations adjust sufficiently quickly in both cases that the collisional and radiative processes into and out of each level are balanced for most of the gain duration [26]. Accurate
Figure 2. Resonance line spectra from a samarium target punped by two 75 ps pulses separated by 3.5 ns. The ratio of the pre-pulse to main pulse irradiance is indicated on the plot. Ni-, Co- and Mn-like emission is indicated. Peak irradiance on target was ≈ 4 × 1013 W·cm−2 .
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population and gain modelling can be undertaken treating only the ground level populations Ni of the different ionisation stages with a dNi /dt term.
Multiple pulsing was first shown to increase Ni-like X-ray laser output by Daido et al. in Ni-like Nd, where a gain length product of 8 was produced [14]. Similar small gain length products were reported by Nilsen and Moreno [27] and Li et al. [28]. To demonstrate the scaling of Ni-like lasers with useful output for possible applications, work at Rutherford Appleton Laboratory concentrated on driving the Nilike lasers into saturation with gain length products greater than 15. Zhang et al. demonstrated saturated lasing on several Ni-like ions including Ag and Sm at 14 nm and 7 nm, respectively [29–32]. The shortest wavelength saturated laser produced so-far is in Ni-like Dy at 5.9 nm, and was first reported by Smith et al. [33]. An experimental study was undertaken to optimise the output of the Ni-like Sm laser at Rutherford Appleton Laboratory [25]. Samarium stripes of 75 µm width were irradiated by two 75 ps duration pulses with a measured ratio of intensity between the pre-pulse and main pulse (termed the ‘pulse ratio’), and a set time between the two pulses (termed the ‘pulse separation’). Three beams of the VULCAN laser were overlapped onto the targets in a 19 mm × 75 µm width line focus to produce a peak irradiance of the main pulse on target of ≈ 6 × 1013 W·cm−2 . The targets were 14 mm long flat slabs consisting of 75 µm width and 1–2 µm thickness samarium stripes coated on glass substrates. The X-ray laser output was measured with a grazing angle flat field spectrometer, recording emission from 6–24 nm wavelength, and from −1 to 11 mrad angular deviation in the horizontal direction (perpendicular to the target surface) on a back thinned CCD detector. A typical recorded spectrum is shown in figure 3. The variation of the Sm X-ray laser output as a function of target length is shown in figure 4. The experimental data points have been fitted with a model of the ASE output as outlined by Lin et al. [32] and Strati and Tallents [34]. The Sm X-ray laser output variation with pulse ratio for different pulse intervals is shown in figure 5. The brightest Sm X-ray laser has been observed using 0.5% pre-pulse with a pulse interval of 3.5 ns, but the maximum optimised output with pulse intervals of 2.2, 3.5 and 5 ns differ by less than a factor 2.
Figure 3. X-ray laser spectrum from a single 14 mm long Sm target irradiated by double 75 ps pulses with a pulse ratio of 5% and a pulse interval of 2.2 ns. The two lasing lines can be seen repeated in 1st, 2nd and 3rd order diffraction from the flat field spectrometer grating.
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Figure 4. The variation of Ni-like Sm X-ray laser output at 7.3 nm as a function of the length of the gain medium. The curve is a fit of the calculated ASE output for small gain coefficient 9.5 cm−1 .
Figure 5. X-ray laser output at 7.3 nm as a function of the pulse ratio for various pulse intervals.
The Ni-like X-ray lasers exhibit gain on two J = 0–1 transitions emanating from the same upper quantum state. Atomic physics modelling shows that the gains for the two J = 0–1 lasing transitions are close to equal for Gd with atomic number Z = 64, but become increasingly unequal as Z deviates from this value [35]. Ni-like Dy (Z = 66) lasing was investigated at Rutherford Appleton Laboratory, and produced the current shortest wavelength saturated lasing output at 5.9 nm. Interestingly, the lower gain line at 6.4 nm reduces in output with increasing target length as the higher gain line is driven further into saturation. Extending the ASE model to include both lasing lines produces good model fits to the experimental data ( figure 6). The model and Ni-like Dy experimental data is explained in detail in the paper by Smith et al. [33].
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Figure 6. The variation for Ni-like Dy output at 5.86 nm (higher gain) and 6.37 nm (lower gain) as a function of the length of the gain medium. The curves are fits of the calculated ASE output. The lower gain line decreases with increasing medium length in the saturation regime because of stimulated emission depletion of the common upper quantum state to the saturation of the higher gain line.
4. CPA-pumped experiments The concept of multiple pulse pumping techniques was extended to include the variant of using a long pulse (< 1ns) combined with a very short pulse of ∼ 1 ps duration and high intensity to provide the plasma parameters to support high, but short-lived, gain conditions. The theory of this so-called TCE technique, was examined quite early [16,36] and experimental feasibility was verified with neon-like ions as soon as suitable lasers were available [37,38]. Typically, the short pump pulse is generated from a CPA (chirped pulse amplification) laser [39], and since the pump energy for ∼ 15 nm XRLs is modest at 1–2 J·mm−1 in a line focus for both long and short pulses, then for the first time a real option arose to optically pump X-ray laser systems with relatively small TT (table-top) lasers. In fact, development of Ne-like XRLs and the obvious extension to Ni-like XRLs pumped by CPA technology have occurred in parallel using both ICF-class and TT-class lasers, the latter being clearly potentially more interesting in terms of longer term application programmes of XRLs. The first demonstration of laser action in Ni-like ions in the TCE regime used the Vulcan laser in its CPA mode to irradiate tin (Sn) targets, lasing and saturating at 12 nm [40]. This was soon followed by gain (∼ 35 cm−1 ) at 14.7 nm (Pd) pumped by the TT laser COMET [41], and at ∼ 14 nm (Ag) pumped by the sub-picosecond CPA laser at LULI [42]. An important new issue in the TCE regime is that the short-lived gain conditions demand a mechanism to deliver the picosecond pulse energy into the pre-plasma in such a way that the ASE X-ray pulse developing always ‘sees’ high gain conditions as it propagates along the line plasma at a group velocity close to the speed of light. Such a TW (travelling-wave) excitation pump can be arranged in several ways, including use of diffraction gratings (which may also be the CPA compressor gratings) to tilt the incident beam wavefront at 45 degrees to the target, or simply by arranging a ‘stepped’ segmented cylindrical focusing optic [43,44].
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Vulcan experiments always used TW pumping and saturated outputs > 1010 W·cm−2 at ∼ 33 nm (Ti) and ∼ 12 nm (Sn) were readily achieved in both Ne-like [45] and Ni-like lasants [40,46] respectively for target lengths shorter than 10 mm. However, the true role of the TW pump was systematically demonstrated first with Ne-like Ge at RAL/VULCAN by plotting growth curves of XRL output as a function of target length with different TW excitation velocities [47]. Good general agreement was found with calculations from numerical and analytical models [48] and the TW technique is now used routinely to enhance the efficiency of both large scale and TT laser pumping [49,50]. Analytical models of TW pumping have been discussed by Strati and Tallents [34] and King and Pert [51]. The Ni-like samarium XRL is the shortest wavelength device pumped to date with a TW-CPA beam laser and its growth curve is shown in figure 7. This system lases at 7.3 nm and has reached saturated output intensities for plasma columns > 8 mm long with pulse characteristics as follows; energy is ∼ 1.5 µJ, divergence is < 3 mrad and the pulse duration is estimated to be < 5 ps [52]. An indication of the spectral brightness possible in Ni-like XRLs at ≈ 12 nm wavelength is shown in figure 8 where a line out of a Sn (11.9 nm) laser pumped in the TCE regime is shown alongside the output from an In (12.6 nm) laser pumped in the QSS regime. Although the saturated intensities are comparable in each case, the QSS In laser
Figure 7. Left: growth curve for TCE pumped samarium, lasing at 7.3 nm. The small signal gain coefficient is ∼ 19 cm−1 with a peak gain-length product reaching saturation level at the longest lengths. The XRL exit intensity from the gain medium is estimated to be ∼ 1010 W·cm−2 . Right: an angular lineout of the Sm XRL beam intensity showing < 3 mrad divergence.
Figure 8. The quasi-monochromatic spectra available from XRLs pumped in long pulse (∼ 100 ps) and short pulse (∼ 1 ps) mode are illustrated with lineouts from spectra obtained from indium and tin targets respectively. The lasing wavelengths are 12.6 nm and 11.9 nm with first and second order appearing in the flat-field spectrometer CCD output.
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is about 30 ps in duration while the Sn laser, based on time-resolved measurements on a similar Ag laser at ∼ 14 nm [53], is assumed to be about ten times shorter.
There has been rapid progress over the last five years in the development of Ni-like X-ray lasers and this has largely happened by extension of ideas first applied to neon-like systems. It is likely that this will also happen with pumping of inner shell transitions based on collisional ejection of 2s and 3p electrons in Nelike and Ni-like ions, respectively, with prospects of a faster route to shorter lasing wavelengths. There has been no firm experimental evidence to date that this scheme is viable, although modelling predicts it will be feasible. Further progress to shorter wavelengths using multiple 100 ps drive pulses can be expected as the large pump lasers develop. However, the recently demonstrated ability to pump XRLs with table-top lasers will encourage other workers without access to ICF-class lasers to become involved in the field. Prospects of 10 Hz, 10 µJ, 2 ps lasers at < 10 nm wavelengths are good and will likely bootstrap a community with applications for such sources. Acknowledgements. We gratefully acknowledge the contributions made by our students and colleagues to the results summarised in this paper. The work has been financially supported by the U.K. Engineering and Physical Sciences Research Council and by the EU Training and Mobility of Researchers programme.
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