Atomic Processes in Spectroscopic modeling and their application to EBIT plasma

Guiyun Liang梁贵云

National Astronomical Observatories, CASBeijing, China

AtomDB 2014 workshop, Sep.6-9, Tokyo, Japan

Collaborators

Gang ZhaoJiayong ZhongFeilu WangHuigang WeiFang Li, Bo Han, Kai Zhang, Xiaoxin Pei

Jose R. Crespo Lopeza-UrrutiaThomas 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

BackgroundOur 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) 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 171Å

EIS 284Å

• 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? SpectroscopyBodewits 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 (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 decaySchrödinger/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

)22

(1

2

N

i

N

ij ijii rr

ZH

EH

AUTOSTRUCTURE usage— S11+ (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, 19 827; CPC 2011, 182 1528

http://www.apap-network.org

• 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

ar

k

ijBi

k

jkikij ER

EEaER

)(

1)(

i ikNiijkNij NNNNNk bxxarurrxxxx )()();()( 111

1111111

Automation of ICFT R-matrix calculation

tcc

Perladas8#lgy.pl

str

inner

nonx

outer

born adas

dasradial function

dstg1dstg3dstg3H.DAT

dstgfdstgicf

dstg1 dstg2 dstgjkTCCDW.DAT

dstg1/2/3dstgfdstgicf

das adasexj.inOMEGAU adf04

add

me

rge

limit value

rscript.inp

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 ： 200 000350 000 Partial wave: Jmax = 41, above Jmax, ‘top-up’ procetureConsume time: 1 － 2 day 49 core ／ ionProduct: 1-3.5 GB/ion

Data available at website http://www.apap-network.org

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 + 0.4 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)• S8+ — S11+ : 767 Mb (6.2 Gb) +

475Mb +7.6 Gb + 2.1 Gb

Below only effective collision strength available• He-like: 4.8 Mb• F-like: 6.5 Mb

• Collisional ionizationDirect 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

Si10+ projectile

2s2 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

200 300 400 500 600 700 800100

101

102

103 b)

Obs.

Fitting

C5+

C6+

N6+

N7+

O7+

O8+

Mg

10+

Ca

14+

Si 10+

Inte

nsity

(arb

. uni

t)

Photon energy (eV)

=1.4

FWHM=66 eV

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

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

• 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

10 100 1000

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0.9

500 1000 1500 2000 2500

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1.0

Ion

frac

tion

Temperature (eV)

Fe X

VII

Fe X

VIII

Fe X

IX F

e XX

Fe X

XI

Fe X

XII

Fe X

XIII

Fe X

XIV

Ion

frac

tion

Electron beam energy (eV)

Fe XVII Fe XVIII Fe XIX Fe XX Fe XXI Fe XXII Fe XXIII Fe XXIV

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

800 900 1000 1100 1200 1300 14001.5

2.0

2.5

3.0

3.5

4.0

3C/3

D

Electron Energy (eV)

Old theory (before 2000 year) Solar (Flare/AR and QS) StellarAstrophysical

observations

• Heidelberg FLASH/Tesla EBIT• EUV spectrometer Grazing grating: 2400l/mm CCD 2048×2048, 13.5m/pixel • Beam energies: 100 — 3000 eV• Energy step: 10 or 20 eV• Photon energies: 90 — 260 Å• Photon resolution: ~0.3 Å• Pressure: ~ 10-8 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 centerThe central space is very small (55mmx10/3mm) to located a vacuum gauge, and that is separate from other space. What we measured pressure (10-

8mbar) represents the value around the chamber wall.

(e,Xq+) refers to the overlap factor between the electron beam and ions with charge of q+, the last term represent a continuous injection of neutrals with density of n0+. Charge-exchange rates depends on the relative velocity (100 eV) of recipient (ions) and donor (neutrals).

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.

Ebeam = 1772 eV

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

5 10 15 20 25 301E-3

0.01

0.1

1

rela

tive s

pect

rom

ete

r re

sponse

Wavelength (nm)

Hitachi grating efficiency CCD with SiO2 layer number of electrons generated per photon (normalised to 5 nm) relative factor (electrons/photon)

There is two method to generate the ‘evolution curve’ Ai(E) • Global fitting• Single line fitting

Line emissivity: ~ (E) or=AijNj

• 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

1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300

0.0

0.2

0.4

0.6

0.8

1.0

Fe1008 F

e XV

III F

e XIX

Fe X

X F

e XX

I F

e XX

IIFe1208 F

e XV

III F

e XIX

Fe X

X F

e XX

I F

e XX

II F

e XX

III

Rel

ativ

e Io

nic

Frac

tion

Electron Beam Energy (eV)

• 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 1.4×1013cm-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:

Penetrante et al. (1991)Vaxial

Vradial

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!