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

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

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 (~2-10 Å ) O’ Dwyer et al. (2010) A&A, Dudik et al. (2014) ApJ

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

With aid of its high spatial resolution and high time cadence (<10s) 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. Milligan (2011) ApJ TRACE 171 Å EIS 284 Å

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)

CHIANTI v7 (Solar, UK/USA) AtomDB v2 (Stars/galaxy,etc, CfA) MEKAL ADAS v2 (generalized CR, UK) for fusion plamsa Cloudy Xstar (various photoionized, NASA) MOCASSIN SASAL (EBIT, coronal-like, etc, China) The understanding to observed data depends on underlying models for emitters. Optical thin approximation ionization equilibrium Photoionization e - Collision

Recently, Chianti (v7.3) and AtomDB (v3.0) have been improved a lot by incorporating recent and more accurate atomic data. Landi et al. (2013); Foster et al. (2012)

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

Atomic Processes in modeling (SASAL) Radiative decay (A ij ) 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, CIV3, SuperStructure, FAC, HULLAC, Autostructure, Grasp, Hartree- Fock etc. Online data calculation by using FAC/AS based on pre- defined atomic model (configurations) H-like, He-like, Li-like, Be- like, B-like, F-like, Ne-like, Na-like, Al-like sequences

AUTOSTRUCTURE usage— S 11+ (S XII) Atomic structure (level energy 、 gf value) DE Electron excitation （ DW ） PI Non-resonant photoionization DR Dielectronic recombination RR Radiative recombination PE Photon excitation Function: RUN=‘’ Badnell JPB, 1986, ; CPC 2011,

Electron/Photon ion impact scattering 1. Distorted-wave UCL-DW, LADW, FAC, HULLAC, AS-DW (Badnell, 2011, CPC) 2. R-matrix Breit-Pauli, ICFT (intermediate- coupling 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 Analysis package: RAP, IDL routines Results: Figures, tables Developed by Whiteford, and implemented by Witthoeft, Liang and Ballance

Method (ICFT) Atomic model (large CI, computable CC) Parallel calculation (Cluster-64 cores, HPC) EIE for iso-electronic sequence Energy points ：  Partial wave: J max = 41, above J max, ‘top-up’ proceture Consume time: 1 － 2 day 49 core ／ ion Product: GB/ion Data available at website

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: 11.8Gb Gb Ne-like sequence: 71.4Gb Li-like sequence: 88.7Gb + 2.7Gb Si X: 481 Mb Fe XIV: 5.6 Gb +1.4 Gb (wo correct) S 8+ — S 11+ : 767 Mb (6.2 Gb) + 475Mb +7.6 Gb 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 He- like, 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.

Donors: H (13.61) He (24.59) H2 (15.43) CO (14.10) CO2 (13.78) H20 (12.56) CH4 (12.6) Treatment of CX cross-section: Default is parameterized Landau-Zener approximation Collection from published data (RARE!) Hydrogenic model Charge exchange

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

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 600km/s, being consistent with that (592km/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 n e =10 18 cm -3 ， it takes only a few ns. Obs.Theo. Si XIII S XV Ar XVII

An extensive database composed of quantum calculation: Based on Chianti v7 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 Features of this model:

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

Determine which lines come from which charge stage. Study emission by selecting specific line formation processes Liang et al. (2009) ApJ; Martínez PhD thesis (2005)

Nearly 40 years, the difference between the 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? Some peoples in Laboratory astrophysics community try to benchmark theory on laboratory facility. The long debating 3C/3D Bernitt et al. (2012) Nature

Heidelberg FLASH/Tesla EBIT EUV spectrometer Grazing grating: 2400l/mm CCD 2048×2048, 13.5  m/pixel Beam energies: 100 — 3000 eV Energy step: 10 or 20 eV Photon energies: 90 — 260 Å Photon resolution: ~0.3 Å Pressure: ~ mbar EUV spectra measurement in EBIT Epp PhD 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

Chen et al. (2004) ApJ 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?

3. Pressure diagnostic to trap center The central space is very small (55mmx10/3mm) to located a vacuum gauge, and that is separate from other space. What we measured pressure ( mbar) represents the value around the chamber wall.

Plasma type: Thermal EBIT EBIT/R with escape PhiBB CXERec The module of charge stage distribution

For #Fe1008 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. E beam = 1772 eV

I obs (  ) = A i (E)  (  )  ( , E) Here, A i (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’ A i (E) Global fitting Single line fitting Line emissivity:  ~  (E) or  =A ij N j 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

At low beam energies, the uncertainty (~10 eV) may be due to estimation of space charge potential, because only beam current at high energy recorded for #Fe1008 and #Fe1208 Monte-Carlo method is adopted to obtain optimized neutral density with 300×300 tests

Fe XVIII Fe XIX Fe XX 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 mA, and the beam energy 2390 eV, the largest central electron density is about 1.4×10 13 cm -3 An effective electron density is diagnosed to be 2.6×10 12 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: Penetrante et al. (1991) V axial V radial

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!