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DOI:10.1007/s00340-004-1529-z Appl. Phys.B (2004) Lasers and Optics AppliedPhysicsB f.yan1 j.zhang1,u x.lu1 j.y.zhong1,2 Similarity of plasma conditions of some Ne-like X-ray lasers and their partner Ni-like X-ray lasers 1Laboratory of Optical Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, P.R. China 2National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, P.R. China Received: 31 October 2003/Revised version: 29March 2004 Published online: 20 May2004 Springer-Verlag 2004 ABSTRACTPlasma conditions for the Ni-like Ag, Cd, In, Sn, Sb X-ray lasers and the Ne-like Fe, Co, Ni, Cu, Zn X-ray lasers are studied, using a one-dimensional hydrodynamic code. The results suggest that the main hydrodynamic characteristics and plasmaconditions of these Ni-like X-raylasers and their corres- ponding partner Ne-like X-ray lasers aresimilar. This similarity enables us to predict the performance of some Ni-like X-ray lasers using rather simple simulations of their partner Ne-like X-ray lasers. PACS52.25.Jm; 52.50.Jm; 42.55.Vc; 82.20.Wt 1Introduction Since the fi rst demonstration of the amplifi cation of X-ray lasers in a laboratory using the collisional excitation scheme 1, tremendous progress has been made in the devel- opment of X-ray lasers using the prepulse technique 26. The saturated output of X-ray lasers has been demonstrated atwavelengthslessthan10nm7,8.Ultra-shortpulsepump- ing has signifi cantly enhanced the effi ciency to drive X-ray lasers912. Due to high quantum effi ciency,Ni-like X-ray lasers, in principle, have a more favorable scaling of laser wavelength withdriveenergythanNe-likeX-raylasers13.However,the population kinetics ofNi-like ions in general is much more sensitivetoplasmaconditionsthanthatofNe-likeions.More- over, it is more diffi cult to calculate atomic data ofNi-like ions because of the complicated level structure. By compari- son, some codes has been developed to successfully simulate Ne-likeX-raylasers,forexample,LASNEX14,JB-1915, Med10316. Inthis paper bycomparing thehydrodynamiccharacteris- tics of plasma conditions for X-ray laserNi-like andNe-like plasma conditions, we fi nd a similarity of plasma conditions between someNi-like X-ray lasers and their partnerNe-like X-ray lasers. Based on this similarity we can predict the per- formance of someNi-like X-ray lasers using rather simple hydrodynamicandatomicsimulationsoftheirpartnerNe-like X-raylasers. u Fax: +86-10/82649356, E-mail: jzhang 2Simulation of plasmaconditions of the Ne-like Fe and Ni-like Ag X-ray lasers Simulations are carried out in this paper using the code MED103, which is a one-dimensional Lagrangian hy- drodynamic code. The validity of the code in the description of laser-plasma interaction has been demonstrated by many experiments and simulations 17,18. In the simulations we use Gaussian pulses at1.053mand100-m-thick slab tar- gets. The drive pulse duration is set at2nsand the peak irra- diance isoptimized to produceoptimumplasmacondition. In our previous work 19, we optimized the preplasma conditions fortheNe-likeFe(25.5nm,3p 3s, J = 0 1) X-ray laser. An optimized plasma condition was achieved with a largeNe-like ion abundance and a high gain of the X-ray laser. The same drive condition is used in this paper to calculate the plasma condition of theNi-likeAgX-ray laser. Figure 1 gives the contours of ion abundance vs space and FIGURE 1Contours of ion abundance vs space and time for Ni-like Ag (a) and Ne-like Fe ions (b). The color in the fi gure from lightness to dark stands for an ion abundance over 10%, 50%, 70%, respectively. The time of the peak irradiance is at 3000 ps and the target surface is at 100 m Applied Physics B Lasers and Optics FIGURE 2Contours of ion abundance vs space and time for the Co-like Ag ions (a) and the F-like Fe ions (b). The color from the light to the dark stands for the ion abundance over 1 %, 5%, 10% (a) and 1 %, 3 %, 5%, r es pectively FIGURE 3Contours of ion population density vsspace and time for the Ni- like Ag and the Ne-like Fe X-ray lasers. The color from lightness to dark represents the ion population density over 11017cm3, 11018cm3, 11019cm3, respectively time forNi-likeAg(a) andNe-likeFe(b) ions, respectively. The target surface is located at100mand the drive pulse reaches its peak at3000psin Fig. 1. Both theNe-likeFeand theNi-likeAgX-ray lasers can reach high ion abundance (70%) under the same drive conditions. Their distribution contours in space and time are similar, although for theNe- FIGURE 4Contours of electron temperature for the Ni-like Ag and Ne-like Fe X-ray lasers vs. space and time likeFecase, the area for high ion abundance is lager and appears earlier in time. The next higher ionization stage of theCo-like ions andF-like ions are also calculated under the same drive condition. As shown in Fig. 2, the ion abundance of theCo-likeAgions reaches10%while theF-likeFeions only reaches5%. In order to avoid over-ionization, we carry out another calculation at reduced drive irradiance. When the maximum ion abundance of theCo-likeAgions equals that of theF-likeFe(5%) ions, theNi-likeAgion abundance is toolowtoachieveanoptimumplasmaconditionforhighgain operation. This implies that it is necessary to tolerate some- what over-ionization for an optimum operation of theNi-like AgX-ray laser. Figure 3 gives the contours of ion population density vs. space and time for theNi-likeAgand theNe-like Feions. These two contours in space and time are similar. TheiondensityoftheNi-likeAgionsat11019cm3region has less space/time extent than that of theNe-likeFeions, due to the largerCo-likeAgion population than theF-likeFe ion population. Figure 4 shows the contours of the electron temperature(Te)for theNe-likeFeand theNi-likeAgX-ray lasersvsspaceandtime.Asimilarityalsoexistsindistribution shapethough the electron temperature for theNi-likeAgcase is lowerthan that fortheNe-likeFeX-raylaser. 3Simulation of Ne-likeFe and Ni-likeAg X-ray laser We have analyzed the plasma conditions for the Ne-likeFeandNi-likeAgX-ray lasers. Nextwecalculate the localgainfortheNe-likeFeandNi-likeAgX-raylasersbased on theresultsobtained intheabovesection. In our previous work 19, we optimized the preplasma conditions for theNe-likeFeX-ray laser (25.5nm,3p 3s, J = 0 1).Under anoptimum preplasmacondition gen- erated by laser beam focused at61011W/cm2in2ns YANet al. Similarity of plasma conditions of some Ne-like X-ray lasers and their partner Ni-like X-ray lasers FIGURE 5Contours of local gain for the Ni-like Ag X-ray laser vs. space and time pulses,amainpulsewith1psdurationand 11015W/cm2peak irradiance was followed. When the de- lay time between the two pulses is zero, a gain with a value higherthan150cm1wasgenerated. In this paper, we investigate theNi-likeAgX-ray laser at13.9nm(4d 4p, J = 0 1) using the MED103 code coupled with an atomic data package. We treat the plasma conditions ofNe-likeAgions obtained in above section as preplasmaconditions.Thepeakirradianceandthedurationof the main pulse and the delay time between the prepulse and the main pulse are optimized to generate high gain. We fi nd that high gain can be generated using a1 psmain drive pulse at11015W/cm2peak irradiance when the delay time be- tween the prepulse and main pulse is1.0ns. Figure 5 gives contours of local gain vs space and time for theNi-likeAg X-ray laser. The main drive pulse reaches its peak at4000ps. The color from the light to the dark represents gain over 50, 100,150cm1, respectively. Fromtheresult wecan conclude that high gain operation can occur under the plasma condi- tions obtained in the above section, the same as those for the Ne-likeFe X-ray laser. The conclusion also further verifi es thatthereisasimilarity ofplasmaconditionsbetween theNe- likeFeand theNi-likeAgX-raylasers. 4Simulation of other partners of Ne-like and Ni-like X-ray lasers Similarly, we simulate the preplasma conditions fortheNe-likeCo,Ni,Cu,ZnX-raylasers.Thelaserpulsedu- ration is fi xed at2nsand the peak irradiance is optimized in ordertogenerateoptimumconditionsforhighgainoperation. Theoptimized intensities areshownin Table 1. The plasma conditions under the corresponding drive irradiance for the above elements have highNe-like ion abundance (70%) and lowF-like ion abundance. Comparing with the plasma conditions for theNe-likeFeX-ray laser, we conclude that high gain operation can occur under these ElementsFeCoNiCuZn Drive irradiance0.60.81.21.72.1(1012W/cm2) TABLE 1The optimized irradiance for some Ne-like X-ray lasers plasma conditions. Using the drive intensities in Table 1, plasma conditions for their partnerNi-like X-ray lasers are simulated. By analyzing ion abundance electron temperature and ion population density, our simulations show that the plasma conditions for theNi-likeCd,In,Sn,SbX-ray lasers under the corresponding drive intensities(0.8,1.2,1.7,2.1, (1012W/cm2)are also suitable to produc high gain. We compare theSnplasma condition andCuplasma condi- tion obtained under the same drive condition (2 nsand 1.71012W/cm2). Figure 6 gives the distribution of ion abundance vs. space-time for theNi-likeSnions and the Ne-likeCuions. Similar to the distribution for theNe-like Feions and theNi-likeAgions, theNe-like (Ni-like) ion abundance reaches70%population. Figure 7 shows the dis- tribution of ion abundance vs space and time for theCo-like Snions andF-likeCuions. The ion abundance of theCo- likeSnions is larger than that of theF-likeCuions. This shows the overionization is easier to happen for theNi-like X-raylasers.Figure8showsthedistributionofionpopulation density vs space and time for theNi-likeSnand theNe-like CuX-ray lasers. The two ion population distribution region in space/time are similar, especially in the density region of about11018cm3. Figure 9 describes the distribution of electron temperature vs.spaceand timefor theNi-likeSnand Ne-likeCuX-ray lasers. Although with a lower temperature and a narrower region in space and time for theNi-likeSn X-ray laser, theTedistribution is similar to that of theNe-like CuX-raylaser. Comparison of the plasma conditions of theseNe-like X-ray lasers with their partnerNi-like X-ray lasers show that there is a similarity of plasma conditions between someNe- like X-ray lasers and their partnerNi-like X-ray lasers. The FIGURE 6Contours of ion abundance vs space-time for the Ni-like Sn (a) and the Ne-like Cu (b). The color in the fi gure from lightness to dark represents the ion abundance over 10%, 50%, 70% Applied Physics B Lasers and Optics FIGURE 7Contours of ion abundance vs space-time for the Co-like Sn (a) and F-like Cu X-ray laser (b). The color from the light to the dark represents the ion abundance over 10%, 15%, 20% (a) and 1%, 5%, 10% FIGURE 8Contours of ion population density vsspace and time for the Ni- like Sn and the Ne-like Cu X-ray lasers. The color from the light to the dark represents the ion population density over 11017cm3, 11018cm3, 11019cm3, respectively similarity also applies to plasma conditions ofNe-likeCo X-ray laser andNi-likeCdplasma conditions, etc. as shown in Fig. 10. The arrows represent the similarity relation be- tween theseNe-like X-ray lasers and their partnerNi-like X-ray lasers. The degree of similarity is generally weakened from the left to the right. The main reason is that theNi-like FIGURE 9Contours of electron temperature for the Ni-like Sn and the Ne- like Cu X-ray lasers vs space and time. The color from the light to the dark stands for the electron temperature over 100 eV, 200eV, 250 eV FIGURE 10Similarity between Ni-like plasma and Ne-like plasma. The thinner lines stands for weakened similarity ions are much easier to be over-ionized to the next ionization stage than theNe-like ions with the increase of atom num- ber. Although the degree of similarity is weakened generally with the increase of atom number, this still refl ects a part- nership between someNe-like plasma conditions and their partnerNi-like plasma conditions under certain drive condi- tions. Because of the lower value and narrower region of ion abundance, population density and electron temperature for theNi-like case, we can predict that theNi-like X-ray lasers generally have lower gain and smaller high gain region than theNe-like X-raylasersunder thesamedriveconditions. 5 Comparision of the electron confi guration of some Ne-like ions and their partner Ni-like ions Ne-like ions have ten bound electrons, which con- fi gureagroundstatewith1s22s22p6closedshells.Population ofthe3plevelsisprovidedthroughcollisionalexcitationfrom the ground state, cascading from higher-nstates, and a com- bination ofthree-bodyradiativeanddielectron recombination YANet al. Similarity of plasma conditions of some Ne-like X-ray lasers and their partner Ni-like X-ray lasers FeFe15+:489.3Fe14+:457AgAg18+:499Ag17+:469 CoCo16+:546.8Co15+:512CdCd19+:544Cd18+:513 NiNi17+:607.2Ni16+:571InIn20+:592In19+:559 CuCu18+:671Cu17+:633SnSn21+:641Sn20+:607 ZnZn19+:737Zn18+:689SbSb22+:691Sb21+:657 TABLE 2Ionization energy for some ions (eV) from theF-like ions. Electrons in then = 3shell will usu- ally rapidly decay back to thegroundstate byfast3s 2por 3d 2pdipole transitions. The3pelectrons are radiatively metastable to the ground state. Inversion is hence created on various3p 3stransitions in theNe-likeions. Similar toNe-like X-ray ions,Ni-like ions also have a closed outer shell. InNi-like X-ray lasers, the upper laser level3d94d 1S0 is populated through the monopole colli- sional excitation from the ground state3d10 1S0, the strong lasing lines are dominated by the3d94d 1S0 3d94d 1P1 and 3d94d 1S0 3d94d 3D1 transitions. The energy level interval between4dand4plevelsfortheNi-likeionsislargerthanthat between3pand3slevels fortheNe-likeions whilethebound energyofthegroundstateforNi-likeandNe-likeionsissimi- lar. This leads to higher quantum effi ciency forNi-like X-ray lasersthanNe-likeX-raylasers. To further understand this similarity, we also compare the ionization energy for theseNe-like ions with their partnerNi- like ions used in the above sections. The ionization energy in Table 2 is calculated by Cowan and MCDF atomic-physics packages. The ionization energies forFe15+ions andAg18+ ions are489.26eVand499eV, respectively. And the ioniza- tion energy ofFe14+ions is close to that ofAg17+ions. So we conclude that the pumping condition forNe-like andNi- like X-ray laser is similar. According to the values in Table 2, there is a similar correspondence between theNe-like X-ray laser ions andNi-like ions, in which the ionization energy for Ne-likeFe,Co,Niions are more similar to that ofAg,Cd,In ions than the paris ofNe-likeCu,Znand that ofNi-likeSn, Sbions. Therefore the conclusion drawn from the compari- son of the ionization energy supports the conclusion from the hydrodynamicsimulation. 6Conclusion WehavesimulatedtheplasmaconditionsoftheNi- likeAg,Cd,In,Sn,SbX-raylasersandtheNe-likeFe,Co,Ni, Cu,ZnX-raylasers.Bycomparingthehydrodynamiccharac- teristicsofionabundance,ionpopulationdensityandelectron temperature for theNi-likeAg,Snand theNe-likeFe,Cu X-raylasersindetail,oursimulationsshowthatthereisasim- ilarity of plasma conditions between someNe-like and their partnerNi-like X-ray lasers. In particular, the plasma condi- tions of theNi-likeAgX-ray lasers is similar to that of the Ne-likeFeandNi-likeCdplasma condition is similar to that ofNe-likeCo, etc. However, this similarity only holds for the elements of medium atomic number and their partner. The degree of similarity between theNe-like andNi-like X-ray lasers is generally weakened for elements with higher atomic number. ACKNOWLEDGEMENTSThiswork is jointly supported by the NSFC under Grant Nos. 10176034, 10374114 and the NKBRSF under Grant No. G1999075206 and the National Hi-tech ICF program. REFERENCES 1 D.L. Matthews, P.L. Hagelstein, M.D. Rosen, M.J. Eckart, N.M. Ceglio, A.U. Hazi, H. Medecki, B.J. MacGowan, J.E. Trebes, B.L. Whit- ten, E.M. Campbell, C.W. Hatcher, A.M. Hawryluk, R.L. Kauffman, L.D. Pleasance, G. Rambach, J.H. Scofi eld, G. Stone, T.A. Weaver: Phys. Rev. Lett. 54, 110 (1985) 2 J. Nilsen, B.J. MacGowan, L.B. Da Silva, J.C. Moreno: Phys. Rev. A 48, 4682 (19