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
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
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•
•
•
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) ApJ
New line identification from Fe IX around 94 filter, improves
the response of the AIA/94 channel
Dudik et al. (2014) ApJ, Foster & Testa (2011) ApJ
•
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.
EIS 284Å
TRACE 171Å
Milligan (2011) ApJ
•
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 v7 (Solar, UK/USA)
• AtomDB v2 (Stars/galaxy,etc, CfA) e - Collision
• MEKAL
• ADAS v2 (generalized CR, UK) for fusion plamsa
• Cloudy
• Xstar (various photoionized, NASA)
Photoionization
• MOCASSIN
• SASAL (EBIT, coronal-like, etc, China)
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)
Fitting to
obs.
Example: SASAL model
Output:
emissivity
Approx.coding
Atomic
data
Physics: Liang et al. (2014) ApJ
Atomic Processes in modeling (SASAL)
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•
•
•
•
•
•
•
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, CIV3, SuperStructure, FAC,
HULLAC, Autostructure, Grasp, HartreeFock etc.
H  E
N
2Z N 2
2
H   (i 
 )
ri
i 1
j i rij
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— S11+ (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 ion impact scattering
1. Distorted-wave
UCL-DW, LADW, FAC, HULLAC,
AS-DW (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)


k ( x1  xN 1 )  ij  ( x1  xN ; rN 1 N 1 )rN11u(rN 1 )aijk  i i ( x1  xN 1 )bik
J
1 ik jk
Rij ( E )  
 RiB ( E ) ij
a k Ek  E
r,E
r a
Automation of ICFT R-matrix calculation
Developed by Whiteford, and
implemented by Witthoeft,
Liang and Ballance
str
das
radial function
inner
dstg1
dstg3
dstg3
H.DAT
nonx
dstg1/2/3
dstgf
dstgicf
Perl
adas8#lgy.pl
rscript.inp
dstgf
dstgicf
merge
add
outer
born
das
limit value
adas
adasexj.in
OMEGAU
adf04
Analysis package:
RAP, IDL routines
tcc
dstg1
dstg2
dstgjk
TCCDW.DAT
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
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•
•
•
•
•
Na-like sequence:
Ne-like sequence:
Li-like sequence:
Si X:
Fe XIV:
S8+ — S11+ :
11.8Gb + 0.4 Gb
71.4Gb
88.7Gb + 2.7Gb
481 Mb
5.6 Gb +1.4 Gb (wo correct)
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 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)
H2
(15.43)
CO (14.10)
CO2 (13.78)
H20 (12.56)
CH4 (12.6)
• Default is parameterized Landau-Zener approximation
• Collection from published data (RARE!)
• Hydrogenic model
2s 2p 3d
• Obtain the average energy of
captured nl (3d) orbital
• Using parameterized MCLZ
approximation obtain the nlmanifold CX cross-section
• Statistical weight to get the
nlJ-resolved cross-section
In Hydrogenic model:
• Obtain the principle quantum
number with peak fraction.
2s2 2p (ground)
• ‘Landau-Zener’ weight as
Si10+ projectile
Smith et al. (2012)
• 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
10
3

b)
 =1.4
Intensity (arb. unit)
10
10
Obs.
Fitting
5+
C
6+
C
6+
N
7+
N
7+
O
8+
O
10+
Mg
14+
Ca
10+
Si
FWHM=66 eV
2
1
0
10
200
300
400
500
600
700
800
Photon energy (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
Features of this model:
• 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
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
0.9
0.8
Fe XVII
Fe XVIII
Fe XIX
Fe XX
Fe XXI
Fe XXII
Fe XXIII
Fe XXIV
Ion fraction
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
10
100
1000
Temperature (eV)
1.0
Ion fraction
0.8
0.6
0.4
0.2
Fe XVII
Fe XVIII
Fe XIX
Fe
Fe
Fe
Fe
Fe
XX
XXI
XXII
XXIII
XXIV
0.0
500
1000
Epp et al. (2010) JpB; Beiersdorfer (2003) ARAA
1500
2000
Electron beam energy (eV)
2500
•
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)
Some peoples in Laboratory astrophysics community try to benchmark
theory on laboratory facility. 4.0
The long debating 3C/3D
3.5
3.0
3C/3D
Nearly 40 years, the difference
between the theory and
observation is a hot topic. There
are many explanation, such as
2.5
• 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?
2.0
1.5
800
Old theory (before 2000 year)
Solar (Flare/AR and QS)
Stellar
Astrophysical
observations
900
1000
1100
1200
Electron Energy (eV)
Bernitt et al. (2012) Nature
1300
1400
EUV spectra measurement in EBIT
• 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: ~ 10-8 mbar
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
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) ApJ
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 (108mbar) represents the value around the
chamber wall.
𝑓(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).
•
The module of charge stage distribution
Plasma type:
Thermal
EBIT
EBIT/R with escape
PhiBB
CXERec
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
There is two method to generate the
‘evolution curve’ Ai(E)
• Global fitting
• Single line fitting
Line emissivity:  ~ (E) or
=AijNj
relative spectrometer response
1
• For resonant lines, the uncertainty of
(E) is within 5%
• Cascading effect will have <10%
contribution for line emissivity.
0.1
0.01
Hitachi grating efficiency
CCD with SiO2 layer
number of electrons generated per photon (normalised to 5 nm)
relative factor (electrons/photon)
1E-3
5
10
15
20
Wavelength (nm)
25
30
Adopting global fitting, at each pixel channel and at a
given energy,
Evolution curve of ionic fraction
Relative Ionic Fraction
Fe XVIII
Fe XIX
Fe XX
Fe XXI
Fe XXII
Fe XVIII
Fe XIX
Fe XX
Fe XXI
Fe XXII
Fe XXIII
0.8
Fe1008
Fe1208
1.0
0.6
0.4
0.2
0.0
1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300
Electron Beam Energy (eV)
Monte-Carlo method is adopted to obtain optimized neutral density
with 300×300 tests
•
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
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:
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!