Plasmas occur over a vast range of conditions Temperature. Spectroscopy of Dense Plasmas. Population Kinetics Models

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1 Spectroscopy of Dense Plasmas H.-K. Chung Atomic and Molecular Data Unit Nuclear Data Section Joint ICTP- Advanced School on Modern Methods in Plasma Spectroscopy Trieste, Italy 19 March 15 International Atomic Energy Agency Advances in plasma generation access new regimes of matter Plasmas occur over a vast range of conditions Temperature 1-6 K 1 kev (1 9 K) Density cm -3 Astrophysical observations CHANDRA/XMM Plasma processing Fusion research ICF (Inertial confinement fusion) Laser-produced plasma Beam-produced plasma Z-pinch plasmas MCF (Magnetic confinement fusion) Tokamak plasma Ultracold plasmas A new state of matter achieved experimentally requires new theories and modeling capabilities NIF (National Ignition Facility) USP: Ultra short pulse laser (RAL, LULI, Titan, Texas) Hydrogen phase diagram HDM occurs in: Supernova, stellar interiors, accretion disks Plasma devices : laser, ion beam and Z-pinches Hotter and denser matter Pulse Power: X-Pinches, Z-Pinches... (Sandia, Cornell, UNR) Transient states of matter XFEL: X-ray free electron lasers (SLAC, European XFEL, SACLA) Directly driven inertial fusion plasmas WDM occurs in: Cores of large planet Systems that start solid and end as a plasma Astronomical X-ray applications Warm dense matter the strong coupling parameter is ratio of the interaction energy to the kinetic energy μ is the degeneracy parameter X-ray driven implosion Population Kinetics Models Mean ionization states, Charge state distributions, Spectral intensity, Emissivity, Opacity, Equation of state, Electrical conductivity require population distributions of ions in the plasma. DENSITY EFFECTS ON POPULATION KINETICS Autoionizing states DR EA Recombined ion n=3 n= n=1 ground state states of recombininon Coronal plasmas (low N e ) Rate formalism Charage state distributions are determined by rates of collisional ionization and excitation-autoionization (EA) & radiative recombination and dielectronic recombination (DR) originating from the ground states LTE plasmas (high N e ) Statistical distributions Collisional processes are dominant and the population distribution is governed by Boltzmann relations and Saha equation. Collisional-radiative plasmas (intermediate N e ) Rate equation model A population distribution is determined by rate equations considering collisional and radiative processes at a given temperature and density. The results should converge to coronal or the LTE limit at low and high N e limits, respectively. Non-LTE plasmas have well documented problems for experiment and theory DR and EA treatments are the main sources of discrepancy Au M-shell emission Glenzer et al. PRL (1) 1 st Non-LTE workshop (1996) documented large differences between codes for Au Mean ion charges for Ar case, n e = 1 1 cm -3 agree very well among different codes if Dielectronic Recombination (DR) and Excitation Autoionization (EA) processes are turned off. NLTE Workshops, HEDP 9, 645 (13)

2 DR and EA treatments are the main sources of discrepancy Mean ion charges for Gold case, n e = 1 1 cm -3 agree very well if Dielectronic Recombination (DR) and Excitation Autoionization (EA) processes are turned off Without DR With DR Processes of dielectronic recombination (DR) and excitation autoionization (EA) DR is a two-step process: An electron is captured leaving the recombined ion at autoionizing (Ai) states. Subsequently, the states stabilize either to the bound states completing recombination process or back to the ion by Auger process Electron capture (EC) can enhance resonant collisional excitation (CE) when the state autoionizes to the excited state of the recombininon EA process is a reverse process to DR and an electron is excited to Ai states which subsequently ionize by Auger processes Autoionizing states (Ai) EA EC Recombined ion CE ground state states of recombininon Stepwise Ionization: Excited states contribute to ionization and recombination processes Average charge states He-like Kr Ne-like Kr coronal Ne=1E16 Ne=1E18 Ne=1E Ne=1E Ne=1E T [kev] e Ground state of ion Z Average charge states are sensitive to the treatment of high-lying states at High N e Due to the 3-body recombination processes, the average charge state decreases after reaching the maximum value as N e increases, then increases again due to the ionization potential depression. Highly excited states are in Saha equilibrium with the continuum at high densities At Equilibrium, the collisional recombination rate coefficient is given by the detailed balance with collisional ionization rate coefficient Recombination rates to high lying hydrogenic levels are proportional to n 4 and inversely proportional to T. For Saha Equilibrium R=(n i /n i+1 ) Non-LTE /(n i /n i+1 ) Saha ~ 1 I p 1/n n um Ground dstate te eofion Z Plasma effects: Ionization potential depression & Rate changes Ionization potentials are a function of plasma conditions High-lying states are no longer bound due to interactions with neighbouring atoms and ions. (pressure ionization) 1 kev 4 kev Krypton 1 kev T e =.5 ev-1 kev 475 ev N e = cm -3 1 ev I p p I p Isolated atom continuum Ionization potential depression (IPD) Embedded atom continuum For a given n e,t e, the IPD, is calculated using a Stewart-Pyatt type model Where r i and r d are the ion sphere and Debye radii 1 ev =.16x1-7 z 1 r 3 d r i r i / 3 r d r i (ev ) Average charge states are sensitive to the treatment of high-lying states at High N e Due to the 3-body recombination processes, the average charge state decreases after reaching the maximum value as N e increases, then increases again due to the ionization potential depression. 1 kev 4 kev Krypton 1 kev T e =.5 ev-1 kev 475 ev N e = cm -3 Radiative rates should be modified by self-absorption at high density () ) I() () max η: Emissivity χ: Opacity τ: Optical Depth Planar geometry = Z= Z max 1 ev 1 ev Pressure Ionization Lowering Ionization Potential Depression B ji J ij A B ij ij J ij

3 Escape probability: Modified radiative rates due to optical depth effects Escape probability reduces the total A rate Λ() : Escape Probability A ij A ij B ji J ij A B ij J ij Frequency-averaged escape probabilities () : line profile ij Lowering, Opacity effects and Opacity broadening DENSITY EFFECTS ON PLASMA SPECTROSCOPY Line shape and intensity changes with opacity effects for dense plasmas Opacity broadening due to line-core absorption τ = line-center optical depth Line Width Analysis of argon plasma influenced by opacity effects n e diagnostics are derived from Stark broadened line widths Population kinetics needed for correct optical depths Statistical Fitting Analysis of Opacity- and Stark-Broadened Ar + Line Profiles Measured in Ion Beam Transport Experiments H.K. Chung et al, JQSRT, vol. 65, p. 135 () Without Opacity With Opacity data calc Boltzmann plot analysis should include opacity effects for correct T e analysis P i is the line escape probability Line intensity and width analysis should include opacity effects Analysis of measured spectra from the initial phase of the ion-beam plasma formation using NLTE populations reveals that IPROP (a PIC/Fluid hybrid code) using simple population model overestimates T e Note that IPROP uses a simple breakdown ionization model With Opacity Without Opacity Without opacity effect With opacity effect mean charge state Line intensity analysis with opacity effects and plasma space gradients Measured ratios between Ly-α and He-α lines increase with opacity effects RAL experiments: Strong axial and transverse T e gradients in.5 ps 3J irradiation of.5 μm Al + 5μm Cu target (5) Cu Solid, T e = kev, N hot =% kev Spectral intensities are senstive to opacity effects Line emission from two different (front & back) regions can t be used for single T e determination He- Cu K shell spectrum has 3:1 front :back intensity ratio in He- Sat. Hot Plasma Ly α emission Is the rear side hotter? He Ly- Measured ratios between Ly- and He- lines are only possible for very high temperatures, T e > 1 kev for optically thin case. Sat. Ly Cold Plasma He α emission

4 Disappearance of Line radiation Hoarty, PRL 11, 653 (13) Short-pulse laser heating and compression by laser driven shocks 1-1 g/cc Al dot (1 μm x.15μm) buried in plastic foils or diamond sheet XFEL irradiated solid Al experiments: Observed K-edges and IPD models K α line intensities are observed as a function of XFEL photon energy Observed K-edge shifts from the atomic edge for non-equilibrium solid density plasmas as a function of temperature and density 9 g/cc 5.5 g/cc 4 g/cc.5 g/cc 1. g/cc Nature 48, 59 (1 PRL 19, 65 (1) Understanding of IPD is critical to explain spectral features 183 ev 17 ev PRL 19, 65 (1) SP model challenged after more than 4 years of extensive uses in astrophysics, cosmology, planetary science and inertial confinement fusion research. Model completeness of dense matter with high energy particles (K spectra) Generally CR codes use the minimum set of configurations for NLTE plasmas This may lead to inaccurate K emissivities for dense matter (T e 1eV) 165 ev 185 ev 163 ev 16 ev 178 ev 175 ev 158 ev 17 ev Model Completeness: the set of configurations should be expanded Silver : <Z> and total K emissivities Solid density and N e = 1 4 cm -3 Hot e - of 1 cm -3 at 1 MeV Copper : K spectra Emissivity [ev/s/cm -3 ] x x1 35 1x1 35 5x1 34 (Yield) SCFLY (Yield) Te[eV] <Z> SCFLY <Z> zbar Emissivity[erg/s/Hz/cm ] 6x1 6 5x1 6 4x1 6 3x1 6 x1 6 1x1 6 3 ev <Z>=17.8 (K 1 L 6 )M 1 (K 1 L 6 ) SCFLY (K 1 L 6 )M 1 (K 1 L 6 ) + (K 1 L 6 )M 3 (K 1 L 6 )M N 1 (K 1 L 6 )M 1 N (K 1 L 6 )M (K 1 L 6 )M 1 N Energy GENERALIZED POPULATION KINETICS MODEL <Z> is good; but, emissivities may not be good enough for warm dense matter Analysis with limited configuration sets can give higher T e in K diagnostics Need for Generalized CR models Screened Hydrogenic Model If PLTE condition exists If the plasma state is coronal, CR or LTE If a line is optically thick If strongly transient plasmas upward or downward If excitation flow results in different distribution of population densities If excitation temperature T exc differs from T e Survey spectra low spectral resolution Total line intensities medium spectral resolution Line profiles high spectral resolution

5 Model : simple, but complete Application to a wide range of Z and experiments: Excitation autoionization (EA) /Dielectronic recombinationa (DR) processes are modeled with doubly-excited and inner-shell (IS) excited states Low Z atom High Z atom HULLAC / FAC / MCDF (n) (nl) (nlj) (detailed-term) Promotion of IS electrons leads to states far from continuum limit and rarely matters in CSD Promotion of IS electrons can lead to states near the continuum limit and EA/DR process of IS is critical 1s 1 l Z+1 nl 3l 17 4l z nl Inner- Shell 3l 16 4l z+1 nln l Screened hydrogenic energy levels with relativistic corrections Dirac Hartree-Slater (DHS) oscillator strengths and photoionization cross-sections Fitted collisional cross-section to PWB approximation Semi-empirical cross-sections for collisional ionization Detailed counting of autoionization and electron capture processes lowering (Stewart-Pyatt) Doublyexcited 1s l Z-1 3l nl L-shell Ion 1s l Z+1 L-shell Ion 1s l Z Inner- Shell Doublyexcited 3l 17 4l z+1 nl 3l 18 4l Z-1 5l nl N-shell Ion 3l 18 4l z+1 N-shell Ion 3l 18 4l z Total line emissivity and energy-dependent spectral intensity in the STA formalism Screened Hydrogenic Model Total line emissivity: plots show approximate line emission spectra and provides information on energy range of dominant emission ( ) n A A AB E AB ( ) A AB i A: j B i A: j B S n u A ul E ul /N e exp(e i exp(e i ) n A exp(e i E ij ( ) i A: j B E AB [evcm 3 /s/atom] Spectral emissivity is computed in the STA formalism using configurationaverage atomic data generated by the DHS(Dirac-Hartree-Slater) code (M.Chen) i A: j B i A: j B i A: j B exp(e i ) exp(e i E ij exp(e i AB [ergs/s/hz/cm 3 /ster] STA width exp(e i E ij E AB exp(e i i A: j B i A: j B Applications to Plasma Research Short-pulse laser-produced plasmas Arbitrary electron energy distribution function Time-dependent ionization processes K- shifts and broadening: diagnostics Long-pulse laser-produced plasmas Average charge states Spectra from a uniform plasma Gas bag, Hohlraum (H), Underdense foam Z-pinch plasmas: photoionizing plasmas Proton-heated plasmas: warm dense matter EBIT: electron beam-produced plasmas EUVL: Sn plasma ionization distributions TOKAMAK: High-Z impurities Time-dependent Ti K emissivities 8eV SiO -Ti foam exp Tin charge state distributions 3eV Activities at AMD Unit : Databases on Atomic and Molecular Data for Fusion. ALADDIN The atomic and molecular, plasma-surface interaction database AMBDAS The bibliographical database GENIE A search engine on different databases on the web OPEN-ADAS A joint development between the ADAS Project and Online Computing Heavy Particles collisions Cross sections for excitation and charge transfer for collisions Los Alamos atomic physics codes An interface to run several Los Alamos atomic physics codes Average Approximation An average approximation cross sections Rate coefficients collisional radiative calculations with the Los Alamos modeling codes to obtain total radiated power, average ion charge, and relative ionization populations Coordinate Research Projects 36eV Light Element Atom, Molecule and Radical Behaviour in the Divertor and Edge Plasma Regions Characterization of Size, Composition and Origins of Dust in Fusion Devices Data for Surface Composition Dynamics Relevant to Erosion Processes Spectroscopic and Collisional Data for Tungsten from 1 ev to kev Available to the community at passwordprotected NIST website: Advantages: simplicity and versatility applicability <Z> for fixed any densities: electron, ion or mass Mixture-supplied electrons (eg: Argon-doped hydrogen plasmas) External ionizing sources : a radiation field or an electron beam. Multiple electron temperatures or arbitrary electron energy distributions Optical depth effects Outputs: population kinetics code and spectral synthesis <Z> and charge state distribution Radiative Power Loss rates under optically thin assumption Energy-dependent spectral intensity of uniform plasma with a size Caveats: simple atomic structures and uniform plasma approximation Less accurate spectral intensities for non-k-shell lines Less accurate for low electron densities and for LTE plasmas When spatial gradients and the radiation transport affect population significantly Spectroscopic diagnostics of plasmas: Theoretical plasma spectroscopy Atoms respond to perturbations of the ensemble of surrounding particles and/or external fields Electronic transitions Photon-atom interactions Atomic level shifts and broadens time graph Observed photons energy The microscopic response of the atom carried by photons provides information on the macroscopic environment T e and n e Electromagnetic fields Plasma wave modes

6 <Z> spread at low N e decreases at higher N e due to the reduced DR/EA Coronal Limits (low densities) At low densities, 99% of population lies in the ground states. Excited state population densities are so low that they are assumed to be populated from the ground state by collisional excitation C E and depopulated by spontaneous emission A E. Hence the excited population density is proportional to N e. Charge state distributions are determined by rates of collisional ionization (CI) and excitation-autoionization (EA) & radiative recombination (RR) and dielectronic recombination (DR) originating from the ground states. Charge state distribution is independent of N e C E N e nuu High-n states A E E c N e R R A I Ground state of ion Z+1 C I N e Ground dstate t of fion Z Coronal Model LTE Limits (high densities) Collisional-Radiative Regime Collisions dominate population/depopulation and rates should be in detailed balance. 3-body recombination rates are proportional to N e and n 4 of recombined state. Hence high-lying states are important for charge state balance. A population distribution is an explicit function of local plasma conditions, governed by Boltzmann statistics and Saha equations. Ionization potential depression (IPD) important g j n E j ion Z+1 I p ~n - Population distribution is obtained by rate equations considering collisional and radiative processes, along with plasma effects Excited states are substantially populated and increase the total ionization by step-wise ionization processes while 3-body recombination to these states is proportional to n 3 and they significantly enhance the total recombination. Plasma effects such as non-local radiation transport, fast particle collisions and density effects should be included in the model. ion Z+1 Ground state of ion Z For optically thick lines, the self-absorption should be included to reduce the radiative processes. Ground state of ion Z LTE Model Collisional-Radiative Model Born approximation for collisional excitation Comparison of FAC, HULLAC & JJATOM Comparison of Fit & JJATOM Born approximation using DHS wave functions and YK Kim s threshold scaling (JJATOM) gives reasonable cross-sections