Atomic Processes in Spectroscopic modeling and their application

Atomic Processes in Spectroscopic modeling and their application to EBIT plasma Guiyun Liang 梁贵云 National Astronomical Observatories, CAS Beijing, China Atom. DB 2014 workshop, Sep. 6 -9, Tokyo, Japan

Collaborators UK APAP network Gang Zhao Jiayong Zhong Feilu Wang Huigang Wei Fang Li, Bo Han, Kai Zhang, Xiaoxin Pei Jose R. Crespo Lopeza-Urrutia Thomas Baumann Laboratory Astrophysics team Yong Wu

Outline • • Background Atomic processes in modeling — SASAL EBIT and the EUV spectroscopy Applications to EBIT plasma (1) Density diagnostic (2) Overlap factor between the electron beam and ion cloud (3) Pressure diagnostic in EBIT center

Background Our understanding to universe is from what we observed, e. g. Imaging, spectra, as well as imaging + spectroscopy. • The imaging at different photon energy give information from different regions. i. e. Optical: Photosphere UV: Chromosphere EUV+X-ray: Corona • SDO/AIA: 7 EUV channels (~2 -10Å) O’ Dwyer et al. (2010) A&A, Dudik et al. (2014) Ap. J

New line identification from Fe IX around 94 filter, improves the response of the AIA/94 channel Dudik et al. (2014) Ap. J, Foster & Testa (2011) Ap. J

• With aid of its high spatial resolution and high time cadence (<10 s) of SDO, we can known: 1. temperature structure 2. plasma dynamics for a given region. However, a detailed dynamics (what velocity? ) is still from spectroscopy with high spectral resolution, i. e. Hinode/EIS observation. EIS 284Å TRACE 171Å Milligan (2011) Ap. J

• Solar winds with planetary/cometary atmospheres Observation comet and vernus Lisse et al. (1996) Simulation of solar wind ions on Martian, Modolo et al. (2005) What components in solar wind? And/or what velocity of these ions? Spectroscopy Bodewits et al. (2006)

The understanding to observed data depends on underlying models for emitters. Optical thin approximation ionization equilibrium • • CHIANTI v 7 (Solar, UK/USA) Atom. DB v 2 (Stars/galaxy, etc, Cf. A) e - Collision MEKAL ADAS v 2 (generalized CR, UK) for fusion plamsa Cloudy Xstar (various photoionized, NASA) Photoionization MOCASSIN SASAL (EBIT, coronal-like, etc, China)

Recently, Chianti (v 7. 3) and Atom. DB (v 3. 0) have been improved a lot by incorporating recent and more accurate atomic data. Landi et al. (2013); Foster et al. (2012)

Fitting to obs. Example: SASAL model Output: emissivity Approx. coding Atomic data Physics: Liang et al. (2014) Ap. J

Atomic Processes in modeling (SASAL) • • Radiative decay (Aij) Excitation (EIE) Photo-excitation (PE) Collisional Ionization (CI) Photoionization (PI) Charge-exchange (CE) Radiative recombination (RR) Dielectronic recombination (DR) For different cases (e-collisional, photoionized, CXRec), different processes are included, a hybrid also can be done.

• Structure and radiative decay Schrödinger/Dirac equation, many method: Cowan, CIV 3, Super. Structure, FAC, HULLAC, Autostructure, Grasp, Hartree. Fock etc. Online data calculation by using FAC/AS based on predefined atomic model (configurations) H-like, He-like, Li-like, Belike, B-like, F-like, Ne-like, Na-like, Al-like sequences

AUTOSTRUCTURE usage— S 11+ (S XII) Function: • • • RUN=‘’ Atomic structure (level energy、gf value) DE Electron excitation（DW） PI Non-resonant photoionization DR Dielectronic recombination RR Radiative recombination PE Photon excitation Badnell JPB, 1986, 19 827; CPC 2011, 182 1528 http: //www. apap-network. org

• Electron/Photon impact scattering 1. Distorted-wave UCL-DW, LADW, FAC, HULLAC, ASDW (Badnell, 2011, CPC) 2. R-matrix Breit-Pauli, ICFT (intermediatecoupling frame transformation), DARC, CCC, B-spline Converged CC

R-matrix: dividing space into internal and external regions (Breit-Pauli, ICFT, DARC) J r, E

Automation of ICFT R-matrix calculation Developed by Whiteford, and implemented by Witthoeft, Liang and Ballance Analysis package: RAP, IDL routines Results: Figures, tables

EIE for iso-electronic sequence Data available at website http: //www. apap-network. org • Method (ICFT) • Atomic model (large CI, computable CC) • Parallel calculation (Cluster-64 cores, HPC) Energy points： Partial wave: Consume time: Product: 200 000 350 000 Jmax = 41, above Jmax, ‘top-up’ proceture 1－2 day 49 core／ion 1 -3. 5 GB/ion

Under UK APAP-network, about 8 iso-electronic sequence data available now

When the resonances included, the effective collision strength is NOT varied smoothly with nuclear number, so ‘interpolation’ is not valid to obtain those missed data

Big Data • • • Na-like sequence: Ne-like sequence: Li-like sequence: Si X: Fe XIV: S 8+ — S 11+ : 11. 8 Gb + 0. 4 Gb 71. 4 Gb 88. 7 Gb + 2. 7 Gb 481 Mb 5. 6 Gb +1. 4 Gb (wo correct) 767 Mb (6. 2 Gb) + 475 Mb +7. 6 Gb + 2. 1 Gb Below only effective collision strength available • He-like: 4. 8 Mb • F-like: 6. 5 Mb

• Collisional ionization Direct ionization, and excitation autoionization • Level resolved ionization data are calculated by using FAC for Helike, L-shell, Ne-like iso-electronic sequence ions from Li to Zn with pre-defined atomic model. • For some Si and Fe ions, a detailed check has been done with available experimental data.

• Radiative recombination • Dielectronic recombination • Photoionization The data is from published papers, e. g. APAP, Witthoeft, Nahar’s calculation, Venner’s compilation etc.

• Charge exchange Treatment of CX cross-section: Donors: • • H (13. 61) He (24. 59) H 2 (15. 43) CO (14. 10) CO 2 (13. 78) H 20 (12. 56) CH 4 (12. 6) • Default is parameterized Landau-Zener approximation • Collection from published data (RARE!) • Hydrogenic model

2 s 2 p 3 d • Obtain the average energy of captured nl (3 d) orbital • Using parameterized MCLZ approximation obtain the nlmanifold CX cross-section • Statistical weight to get the nl. J -resolved cross-section In Hydrogenic model: • Obtain the principle quantum number with peak fraction. 2 s 2 2 p Si 10+ projectile (ground) Smith et al. (2012) • ‘Landau-Zener’ weight as • Statistical weight

How about this resultant CX cross-section? Not too bad! Solar Winds Rough data is better than no data available at all for astronomers.

Test by soft x-ray spectroscopy from Comet Because charge-exchange cross-section is a function of recipient velocity. We estimate a velocity of 600 km/s, being consistent with that (592 km/s) from direct sensor of ACE mission.

A brief illustration of SASAL— Collision (EBIT) Original collision strength/cross-section was stored as post-database for various electron energy distribution, including R-matrix, DW data

• Emission at non-equilibrium

• Metastable effect • Non-equilibrium

An approximate treatment relative to GCR model in ADAS We obtain the level population without contribution from ionization/recombination, this corresponds to the effective excitation to other metastable levels followed by ionization and/or recombination in GCR model.

Very simple treatment at here with assumption of optical thin • electron excitation • photo-excitation • collision with neutral

• The application to Z-pinch measurement reveals it is reliable. • Electron density will shorten the time-scale to equilibrium, e. g. at ne=1018 cm-3，it takes only a few ns. Obs. Theo. Si XIII 1. 3 1. 51 S XV 1. 1 1. 32 Ar XVII 0. 8 0. 97

Features of this model: • An extensive database composed of quantum calculation: Based on Chianti v 7 and our recent calculations, including level energies, and radiative decay rates for HCIs • On-line calculations with ‘quantum’ method for some necessary parameter, including Levels, decay rates, excitation (DW), ionization, autoionization, CX cross-section: For CX, Multi-channel Landau-Zener with rotational coupling approximation is used, Hydrogenic model are also implemented into the present system. On-line CTMC calculation for CX cross-section is in plan. • Collection for published data with advanced treatment: Including R-matrix, Atomic-orbital and/or molecular-orbital close coupling, classical-trajectory Monte-carlo (CTMC) • Graphic interface for user operation and command line for extension with other hydrodynamics models

Electron beam ion trap (EBIT) Electron beam ion trap has a powerful ability help us to benchmark the model: • Produce ions of a desired charge state Epp et al. (2010) Jp. B; Beiersdorfer (2003) ARAA

• Determine which lines come from which charge stage. • Study emission by selecting specific line formation processes Liang et al. (2009) Ap. J; Martínez Ph. D thesis (2005)

Some peoples in Laboratory astrophysics community try to benchmark theory on laboratory facility. The long debating 3 C/3 D Nearly 40 years, the difference between theory and observation is a hot topic. There are many explanation, such as • Opacity; • Blending of inner-shell excitation of Fe XV ions • Recent measurement by LSLC laser and EBIT demonstrates that this is due to the high ratio of gf values in theory. Really? Bernitt et al. (2012) Nature

EUV spectra measurement in EBIT • Heidelberg FLASH/Tesla EBIT • EUV spectrometer Grazing grating: 2400 l/mm CCD 2048× 2048, 13. 5 m/pixel • Beam energies: 100 — 3000 e. V • Energy step: 10 or 20 e. V • Photon energies: 90 — 260 Å • Photon resolution: ~0. 3 Å • Pressure: ~ 10 -8 mbar Epp Ph. D thesis (2007)

In the global fitting, the profile of ‘evolution curve’ also affect by the relative line ratios of given ion. Our detail model analysis overcome this problem.

EUV spectroscopic application to EBIT 1. Diagnostic to electron density in trap

Line ratios involved emission lines with its upper level is dominantly populated from metastable levels

2. Overlap factor between e-beam and trapped ions

Symbols with error bars are diagnostic results from He-like spectra at the same trap conditions. So this deviation is due to the different overlap factor? Chen et al. (2004) Ap. J

3. Pressure diagnostic to trap center The central space is very small (55 mmx 10/3 mm) to located a vacuum gauge, and that is separate from other space. What we measured pressure (108 mbar) represents the value around the chamber wall.

• The module of charge stage distribution Plasma type: Thermal EBIT/R with escape Phi. BB CXERec

For #Fe 1008 measurement, there is total 50 beam energies. By an automatic fitting code, we obtain the observed count by a single run with predefined line-list. Ebeam = 1772 e. V

Iobs( ) = Ai(E) ( , E) Here, Ai(E) is the ionic abundance as a function of beam energy, ( ) is the efficiency of the spectrometer, and ( , E) is the line emissivity, where E refers to the beam energy There is two method to generate the ‘evolution curve’ Ai(E) • Global fitting • Single line fitting Line emissivity: ~ (E) or =Aij. Nj • For resonant lines, the uncertainty of (E) is within 5% • Cascading effect will have <10% contribution for line emissivity.

Adopting global fitting, at each pixel channel and at a given energy,

Evolution curve of ionic fraction

Monte-Carlo method is adopted to obtain optimized neutral density with 300× 300 tests • At low beam energies, the uncertainty (~10 e. V) may be due to estimation of space charge potential, because only beam current at high energy recorded for #Fe 1008 and #Fe 1208

Fe XVIII Fe XIX Fe XXI

The resultant neutral density at the trap center without consider the overlap factor between electron beam and ion cloud At a current of 165 m. A, and the beam energy 2390 e. V, the largest central electron density is about 1. 4× 1013 cm-3 An effective electron density is diagnosed to be 2. 6× 1012 cm-3

Fe XVIII Fe XIX The resultant pressure in trap center is obtained, that is still higher than expectation.

In the central region, NO ‘quantitative’ value available, except for a ‘qualitative’ estimation. The present diagnostic strongly depends on the underlying model. A further analysis is on-going.

Coulomb heating: Energy transfer between ions: Ion escape (radial, axial): Energy loss due to escaping ions: Vradial Vaxial Penetrante et al. (1991)

Evolution of ions and ionic temperature: Penetrate et al. PRA (1991)

Summary • Background • Atomic processes in theoretical modelling • Application to EBIT plasma a. Density diagnostic b. Diagnostic for overlap factor between beam and ions c. Diagnostic to the pressure in the EBIT center

Thanks you for your attention!