203 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 203, Dublin, Ireland Radiative Properties of Krypton Plasma & Emission of Krypton DPP Source in Water-Window Spectral Range Vassily Zakharov zakharovvas@gmail.com EPPRA, France Keldysh Institute of Applied Mathematics, Russia NRC Kurchatov Institute, Moscow, Russia
Abstract Krypton- and zirconium-based plasmas are considered as possible candidates for a source of soft X-ray emission in water window waveband alongside with nitrogen- and bismuth-based radiation plasma sources. Such discharge and laser produced plasmas used in soft X-ray (and EUV) sources are in non-equilibrium state as a rule. This leads to a mismatch between the actual conditions of the plasma and its theoretical/computational estimations because of different effects like self-absorption etc. leading to changes in ionization states, state populations, emission intensity and spectrum. Krypton has a UTA at higher ionization degree than zirconium and thus less preferable but krypton plasma source delivers from debris issues in operation cycle comparing to zirconium and bismuth. Due to wide array of transitions the krypton plasma is less opaque to radiated emission than nitrogen. In the paper the radiance and emission properties of non-equilibrium krypton plasma is examined and the optimal emission temperature conditions for soft X-ray emission output in water window region are explored. Kinetic parameters for non-equilibrium plasma including major inelastic ion interaction processes, radiation and emission data are obtained in the approach based on Hartree-Fock-Slater (HFS) quantum-statistical model and distorted waves approximation. The emission spectral efficiency for krypton up to 25% is achieved at 30 ev, comparable to the one for zirconium (40% at 90 ev). Results of plasma dynamics modeling in capillary discharge by Z* code are presented. Calculated emission energy up to 300mJ per pulse in water window band corresponds to the conversion efficiency (CE) around 7%. 203 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 203, Dublin, Ireland
Krypton VII XII Lines Krypton line strengths in water-window region 0 KrVII [Ar] 3d 4s2 0 KrVIII [Ar] 3d 4s 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 0 KrIX [Ar] 3d 0 KrX [Ar] 3d9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 0 KrXI [Ar] 3d8 0 KrXII [Ar] 3d7 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 Satellite lines for transitions 4f-3d in Kr IX excited ([Ar]3d 9 4p ) are in water-window range but their strengths and populations of double excited states shouldn t be enough for meaninul radiation output Line strengths of Kr ions computed with Flexible atomic code 203 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 203, Dublin, Ireland
Krypton XIII XVIII Lines Krypton line strengths in water-window region 0 KrXIII [Ar] 3d6 0 KrXIV [Ar] 3d5 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 0 KrXV [Ar] 3d4 0 KrXVI [Ar] 3d3 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 0 KrXVII [Ar] 3d2 0 KrXVIII [Ar] 3d 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 Resonant transitions 4f-3d in Kr XIV (~4.3nm), Kr XV (~4.nm), Kr XVI (~3.9nm), Kr XVII (~3.7nm) intensively emit into water-window range Line strengths of Kr ions computed with Flexible atomic code 203 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 203, Dublin, Ireland
Krypton XIX XXIII Lines Krypton line strengths in water-window region 0 KrXIX [Ar] 0 KrXX [Ne] 3s2 3p5 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 0 KrXXI [Ne] 3s2 3p4 0 KrXXII [Ne] 3s2 3p3 0 2 3 4 5 6 7 8 9 KrXXIII [Ne] 3s2 3p2 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 Resonant transitions 4d-3p and 4f-3p in Kr XIX (~2.8nm and ~3.3nm), Kr XX, Kr XXI, Kr XXII and Kr XXIII (~2.5nm and ~2.8nm) contribute in water-window range Line strengths of Kr ions computed with Flexible atomic code 203 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 203, Dublin, Ireland
Non-Equilibrium Model System of Kinetic equations To calculate spectrum of emission we need to resolve the system of kinetic equations to obtain relative populations n µ of levels dn dt μ = ν ν μ n ν α ν μ ( N i n, N ν e μ ν μ, T, ρ, F) α μ ν ( N i, N e, T, ρ, F), μ n μ =, α ν μ and α μ ν - total rates of the processes leading to increase and decrease the population n μ of level μ, N i and N e number of ions and electrons, T temperature, ρ density. Total rates include a different set of processes depending of model, kind of modelling etc. Quasi-neutrality: z μ charge of the ion of level μ, Z 0 - average charge N e = Z 0Ni, Z 0 = z μ nμ, μ 203 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 203, Dublin, Ireland
Non-Equilibrium Model Processes included To process to a correct solution of system of kinetic equations for non-equilibrium plasma the set of impact and radiative processes should be taken into account via rates of the processes. The processes taken into account leading to increase the population n μ of level μ and to decrease the population n ν of level ν are following: Impact recombination and ionization ν μ, Excitation and deexcitation ν μ, Dielectronic capture and autoionization ν μ, Photorecombination and photoionization ν μ, Emission and absorption in lines ν μ. In general case the rates are calculated from cross-sections of concordant processes (and for given distribution functions of electrons and spectral functions) in the approach based on Hartree-Fock-Slater (HFS) quantum-statistical model and distorted waves approximation. Complete system of kinetic equations is nonlinear and self-consistent. 203 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 203, Dublin, Ireland
Krypton Non-equilibrium Plasma Krypton ionization Kr ion fractions for **20 8 /ccm electron density Kr ionization degree for **20 8 /ccm e-density 35 XI XII XIII XIV XV XVI XVII 30 Relative portion Average charge 25 20 5 5 60 80 0 20 40 Plasma temperature, ev 0 0 20 40 60 80 0 20 40 Plasma temperature, ev Best conditions for emission in water window range are expected at T > 90 ev when Kr XIV - Kr XVII ions are dominant in the plasma composition Ion populations simulated by authors kinetic code with rates&cross-sections of impact and radiative processes computed in distorted-wave approach and based on self-consistent Hartree-Fock-Slater quantum-statistical model 203 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 203, Dublin, Ireland
Krypton Plasma Radiance Krypton line emission in water-window range Krypton line emission spectra Krypton line emission spectra 0.006 0.005 70 ev 80 ev 90 ev 0 ev 0.006 0.005 ev 20 ev 30 ev 40 ev Radiance, a.u. 0.004 0.003 0.002 Radiance, a.u. 0.004 0.003 0.002 0.00 0.00 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 Resonant lines of Kr XIV-Kr KVII start to contribute in WW range at T >90eV (average charge Z 0 ~3) and provide maximum output at T~30eV (Z 0 ~5.5): 3.7nm by Kr XVI & 3.9nm by Kr XVII Emission spectra modelling done by authors kinetic code with rates&cross-sections of impact and radiative processes computed in distorted-wave approach and based on self-consistent Hartree-Fock-Slater quantum-statistical model 203 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 203, Dublin, Ireland
Krypton plasma emission efficiency Krypton plasma spectral efficiency Krypton spectral efficiency vs Zirconium Krypton line emission spectra vs Zirconium 50 Kr Zr 0.008 0.007 Kr@30eV Zr@90eV 40 0.006 Relative portion 30 20 Radiance, a.u. 0.005 0.004 0.003 0.002 0.00 0 0 60 80 0 20 40 2 3 4 5 6 7 8 9 Plasma temperature, ev Spectral Efficiency (SE) for Kr reaches its maximum (~25%) at plasma temperature T~30 ev Maximum SE for Zirconium is ~40% at T ~90 ev (for N e = 9 ) Emission spectra modelling and SE calculations done by authors kinetic code with rates&cross-sections of impact and radiative processes computed in distorted-wave approach and based on self-consistent Hartree-Fock-Slater quantum-statistical model 203 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 203, Dublin, Ireland
Soft X-ray emission DPP Source Pulsed power capillary discharge Pulsed-power Energy storage line Liquid dielectric & coolant Voltage Current Pulse Capillary dimensions Various electrode geometries Gas: Kr - 2 Torr gradients 5 J 25 kv 9 ka ~53 ns.6 mm L = 8 mm Energy storage line Experimental set up capillary Example of the central part of simulated geometry Soft-X Capillary discharge dynamics & emission features: E-beam, plasma channelling (ε >> ) Volumetric MHD compression (skin depth >>plasma diameter) Highly ionized ions (fast electrons) 203 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 203, Dublin, Ireland
Z(cm) Krypton Soft X-ray Source: Z* modeling 27 26.5 26 25.5 Capillary discharge: Z* modeling results Time integrated 3 Oct 203 ZSTAR - code output, cell values Emission energy density Time integrated Capillary -0.2 0 0.2 R(cm) Capillary Qx(J/ccm) 2500 220.86 799.2 526.35 294.87 98.49 93.898 790.569 670.674 568.96 482.674 409.473 347.374 294.692 250 22.086 79.92 52.635 29.487 9.849 93.898 79.0569 67.0674 56.896 48.2674 40.9473 34.7374 29.4692 25 Emission, MW 35 30 25 20 5 5 Emission power in WW range 0 0 5 5 20 25 30 35 40 45 Time, ns Maximum emission power @ 22 ns Soft X-ray emission pulse duration ~ 5 ns Energy emitted in WW range ~ 300 mj/pulse Conversion efficiency (CE) ~ 7% Plasma dynamics and emission are done by Z* code 203 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 203, Dublin, Ireland
Krypton Soft X-ray Source: Z* modeling Frame 3 Oct 203 ZSTAR - code output, cell values Z(cm) 27 26.5 26 25.5 Capillary discharge: Z* modeling results Density distribution @ max emission t= 2.90ns Capillary -0.2 0 0.2 R(cm) Capillary Ne(Av).000E-05 8.483E-06 7.97E-06 6.5E-06 5.79E-06 4.394E-06 3.728E-06 3.62E-06 2.683E-06 2.276E-06.93E-06.638E-06.389E-06.79E-06.000E-06 8.483E-07 7.97E-07 6.5E-07 5.79E-07 4.394E-07 3.728E-07 3.62E-07 2.683E-07 2.276E-07.93E-07.638E-07.389E-07.79E-07.000E-07 Frame 3 Oct 203 ZSTAR - code output, cell values Emission power @ max emission t= 2.90ns Z(cm) 27 26.5 26 25.5 Capillary -0.2 0 0.2 R(cm) Capillary Gx(MW/ccm) 5.9E+05 4.367E+05 3.726E+05 3.79E+05 2.72E+05 2.34E+05.974E+05.684E+05.437E+05.226E+05.046E+05 8.924E+04 7.64E+04 6.496E+04 5.542E+04 4.728E+04 4.034E+04 3.442E+04 2.936E+04 2.505E+04 2.37E+04.824E+04.556E+04.327E+04.32E+04 9.662E+03 8.243E+03 7.033E+03 6.000E+03 Plasma dynamics and emission are done by Z* code 203 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 203, Dublin, Ireland
Conclusion Conclusion Krypton ions XIV - XXII emit intensively in water window range: 4p-3d, 4f-3d and 5p-3d transitions Maximum spectral efficiency for emission in water window range reaches over 20% for Kr plasma at temperature of ev and hotter Compare to Zirconium, Krypton plasma provides less spectral efficiency and needs to be hotter: SE Kr =25%@30eV versus SE Zr =40%@90eV Krypton pulsed-power soft X-ray source based on capillary discharge may produce up to 300 mj of radiation in water window range and with conversion efficiency ~ 7% The results were obtained in frame of FP7 FIRE Marie Curie action 203 International Workshop on EUV and Soft X-Ray Sources, November 3-7, 203, Dublin, Ireland