Atomic Processes in Spectroscopic modeling and their application to EBIT plasma
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Transcript of Atomic Processes in Spectroscopic modeling and their application to EBIT plasma
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
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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
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tive s
pect
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ete
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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
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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!