Introduction to FLYCHK H. K. Chung May 8 th , 2019 Joint - PowerPoint PPT Presentation

Introduction to FLYCHK H. K. Chung May 8 th , 2019 Joint ICTP-IAEA School on Atomic and Molecular Spectroscopy in Plasmas Trieste, Italy 1

FLYCHK COLLISIONAL-RADIATIVE MODEL

Population Kinetics Modeling Rate equations are solved for level population distributions for given plasma conditions N max N max dn i n W n W ∑ ∑ = − + i ij j ji dt j i j i ≠ ≠ RR DR 2 W B J n C n W A B J n D n ( ) n = + + + α + α + δ = + + β + γ ij ij ij e ij ij e ij ji ij ji ji e ji e ji ji e ij A ij Spontaneous emission B ij Stimulated absorption B ij Stimulated emission C ij Collisional excitation D ij Collisional deexcitation γ ij Collisional ionization α ijDR Dielectronic recombination β ij Photoionization (+st. recom) α ijRR Radiative recombination δ ij Collisional recombination

FLYCHK uses screened hydrogenic levels (super configurations)

Level energy obtained with ionization potential from its 1 st continuum level

Atomic processes included in FLYCHK

FLYCHK Model : simple, but complete HULLAC / FAC / MCDF FLYCHK (detailed-term) (nl) (nlj) (n) • Screened hydrogenic energy levels with relativistic corrections • Relativistic Hartree-Slater oscillator strengths (M. Chen) and photoionization cross-sections (J. Scofield,+ Kramer) • Fitted collisional cross-section to PWB approximation (M. Chen) • Semi-empirical cross-sections for collisional ionization (A. Burgess) • Detailed counting of autoionization and electron capture (M. Chen) • Continuum lowering (Stewart-Pyatt, Ecker-Kroll)

Application to a wide range of Z & experiments: 
 Excitation autoionization (EA) /Dielectronic recombinationa (DR) processes 
 are modeled with extensive inner-shell (IS) states Low Z atom High Z atom Promotion of IS electrons leads to states Promotion of IS electrons can lead to far from continuum limit and rarely states near the continuum limit and matters in CSD (charge state distribution) hence EA/DR process is critical in CSD 3 l 17 4 l z nl 1 s 1 2 l Z+1 nl ” 3 l 16 4 l z+1 nln ’ l ’ Inner- Shell 3 l 17 4 l z+1 nl 1 s 2 2 l Z-1 3 l ’ nl ” Inner- Shell Doubly- excited Doubly- excited L-shell Ion Bound N-shell Ion 1 s 2 2 l Z Bound 3 l 18 4 l z L-shell Ion 1 s 2 2 l Z+1 N-shell Ion 3 l 18 4 l z+1

FLYSPEC SPECTROSCOPIC MODULE

FLYSPEC uses detailed (H, He, Li-like) and Super Transition Array for spectra

Data Types for Spectroscopic Model Z < 27 H, He and Li FLY model Z > 27 H, He and Li HULLAC data (term levels up to n=4) Be-like and lower Super Transition Array (STA) charge states made with Configurations (jj) 1s, 2s, 2p - , 2p + , 3s, 3p - , 3p + , 3d - , 3d + , Up to n=6

Energy-dependent spectral intensity in the STA formalism Spectra for specific E/ ranges: STA formalism Spectra using configuration-average atomic data generated by the DHS (Dirac-Hartree-Slater) code (M.Chen) ∑ n A g i exp( − E i / kT e ) A ij E ij φ ( ν ) [ergs/s/Hz/cm 3 /ster] i ∈ A : j ∈ B η ( ν ) = n A A AB E AB φ ( ν ) = ∑ g i exp( − E i / kT e ) STA width i ∈ A : j ∈ B 2 ∑ ∑ g i exp( − E i / kT e ) A ij ⎡ ∑ ⎤ g i exp( − E i / kT e ) A ij E ij 2 g i exp( − E i / kT e ) A ij E ij ⎢ ⎥ 2 = i ∈ A : j ∈ B A AB = i ∈ A : j ∈ B i ∈ A : j ∈ B E AB = 2 − E AB µ AB ⎢ ⎥ ∑ ∑ g i exp( − E i / kT e ) ∑ g i exp( − E i / kT e ) A ij g i exp( − E i / kT e ) A ij ⎢ ⎥ ⎣ ⎦ i ∈ A : j ∈ B i ∈ A : j ∈ B i ∈ A : j ∈ B

Total line emissivity in the STA formalism Approximate total line emissivity: A plot show approximate line emission spectra and provides information on energy range of dominant emission [eVcm 3 /s/atom] S = n u A ul E ul / N e

FLYCHK APPLICATIONS

FLYCHK Help Pages • http://nlte.nist.gov/FLY/Doc/ Manual_FLYCHK_Nov08.pdf • http://nlte.nist.gov/FLY/README.html • http://nlte.nist.gov/FLY/EXAMPLE.html • Click on the Question Marks – http://nlte.nist.gov/FLY/Help/runfile.html – http://nlte.nist.gov/FLY/Help/opacity.html ……

Available to the community at password- protected NIST website: http://nlte.nist.gov/FLY 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

Example: Radiative loss rates are important as an energy loss mechanism of high-Z plasmas # of radiative transitions Calculated Kr radiative cooling rates per N e using HULK code [eV/s/atom/cm -3 ] Ion HULLAC+DHS 4x10 -7 1 3049 coronal Ne=1E16 Ne=1E18 2 27095 Ne=1E20 Ne=1E22 3x10 -7 3 30078 Ne=1E24 4 404328 5 3058002 2x10 -7 6 5882192 7 7808014 1x10 -7 8 6202123 9 5544814 0 10 1050919 1 1.5 2 2.5 3 3.5 4 4.5 5 T e (keV) 11 841094 30,851,708 Sum

Data for Radiation Hydrodynamics: 
 Kr Radiative loss rates over (Ne, Te) The radiative loss rates For a given T e , <Z> stays show the similar coronal constant up to N e =10 17 and behavior up to N e =10 17 and increases from the coronal the rate/N e stays constant. value to higher values as N e As N e increases, the rate/N e increases. decreases from the coronal Then, <Z> starts to decrease value at low T e due to 3-body recombination processes become substantial.

Example: Gold ionization balance in high temperature hohlraum (HTH) experiments • High-T hohlraum reach temperatures: ~ 10 keV • Spectrum from n e ~ 4x10 21 cm -3 , T e ~ 7-10 keV measured for first time Spectroscopic data and calculation L-shell gold spectra (K. Widmann) FLYCHK gives an estimate of Gold L-shell spectra

Long pulse laser plasmas: 
 Gold L-shell spectroscopy

STA spectra compared with configuration- average spectra

Example: Cu K α radiation measured by single hit CCD spectrometer and 2-D imager for T e diagnostics K α yield (photons/Sr/J) 8.048 keV 500x500x30 100x100x20 100x100x5 100x100x1 Target volume ( µµ 3 ) Single Hit CCD K α yield is higher than that of 2-D imager for smaller target volumes : An experimental evidence of shifting and broadening of K α emission lines in small targets with high temperatures

Shifts and Broadening of K α emission as a function of electron thermal temperature FLYCHK simulations Average T e (eV) of targets 100x100x1 100x100x5 100x100x20 500x500x30 2d spacing uncertainty Target volume ( µµ 3 )

Short pulse laser plasmas: 
 Cu K α Spectroscopy

Example: Photoionized plasmas produced by Z- Machines – Astrophysical model benchmark Z-pinch ξ =20-25 ergs-cm/s

Charge state distribution is a function of N e and Radiation field strength N e =1.95E19cm -3 Radiation field of 165 eV and 0.01 dilution Without Radiation Field With Radiation Field

Photoionization equilibrium plasmas: Fe Z- Pinch Plasma

Example: XFEL provides an opportunity for HEDS plasma spectroscopy Long-pulse laser is used to create warm- 1 s 0 2 l Z-1 nl ” dense-matter plasmas and then XFEL is used 1 s 0 2 l Z nl ” to probe the internal state. t = 0 laser 1 s 1 2 l Z-2 nl ” irradiates CH Visible 
 with Mg dot 1 s 1 2 l Z-1 nl ” laser 0.1 µm CH 1 s 1 2 l Z nl ” 1 s 1 2 l Z+1 nl ” 25 µm Mg Inner- t > 1 ps XFEL Shell pumps Mg XFEL plasma 1 s 2 2 l Z-2 1.85 keV T e = 30-50 eV 5x10 10 photons Doubly- N e =10 23 cm -3 excited 1 s 2 2 l Z-1 spectrometer 1 s 2 2 l Z Bound 1 s 2 2 l Z+1

In Warm Dense Matter regime the hollow ions provide time- resolved diagnostic information • XFEL forms unique states and provides in situ diagnostics with ~100 fs res. – 5x10 10 1.85 keV photons in 30 µ m spot into a n e =10 23 cm -2 plasma – Strong coupling parameter, Γ ii = Potential/Kinetic Energy ~ 10 • Steady-state Spectra at various T e • At high n e emisson lasts ~100 fs