Data Quality and Needs for
Collisional-Radiative Modeling
Yuri Ralchenko
National Institute of Standards and Technology
Gaithersburg, MD, USA
Joint ITAMP-IAEA Workshop, Cambridge MA
July 9, 2014

Basic rate equation
...
 

N
Z , i
...


Vector of atomic states populations d
ˆ dt
 t

,
 
, N e
,
Rate matrix
N i
, T e
, T i
...


 
I ij

N i

A ij

E ij
2

autoionizing states ionization limit
(de)excitation rad. transitions
Continuum
Z Z+1
3
Collisional-
Radiative
Model

Collisional-radiative models are generally problem-taylored

Atomic states
Superconfiguration
1 2 2 4 3 4 4 4 5 2
1
Term
P
3s 2 3p3d 2 4p
Average atom
1
1
2
2
2
2
8
8
3
3
5
6
4 1
3s 2 3p 3 4s
Configuration
1 D
3 P
3 S
3 D
5 S
BUT: field modifications, ionization potential lowering
Level
3 D
3
3 D
2
3 D
1
6

How good are the energies?
• The current accuracy of energies (better than
0.1%) is sufficient for population kinetics calculations
• For detailed spectral analysis, having as accurate as possible wavelengths/energies is crucial
(blends)
• May need >1,000,000 states

Radiative Autoionization
• Allowed: generally very good if the most advanced methods
(MCHF, MCDHF, etc) are used
• Forbidden: generally good, less important for kinetics
• Acceptable for kinetics,
(almost) no data for highlycharged ions

Collisions and density limits
• High density
▫ Different for different ion charges
▫ LTE/Saha equilibrium
 Collisions are much stronger than non-collisional processes
 𝑁 𝑖
= 𝑁
0 𝑔 𝑖 𝑔
0 𝑒 −∆𝐸 𝑖0
/𝑇 𝑒
 Populations only depend on energies , degeneracies , and
(electron) temperature
 BUT: need radiative rates for spectral emission
• Low density (corona)
▫ All data are (generally) important
▫ Line intensities (mostly) do
NOT depend on radiative rates, only on collisional rates pLTE
Corona

e-He excitation and ionization

Neutral beam injection:
Motional Stark Effect
I ij
,a.u.
σ
π
H

W. Mandl et al.
PPCF 35 1373 (1993)
-4 -2
λ(H
α
)
0 2
Displacement of H
α
Example: 𝐼 𝜋
= 𝐼 𝜎
;
4
𝑰 𝝈𝟏
/ 𝑰 𝝈 0
= 0.353
0.42

Solution: eigenstates are the parabolic states
E = v×B

E parabolic states n i k i m i
 =  /2 for MSE
Radiative channel n i k i m i
→ n j k j m j
π – components with Δm=0
σ – components with Δm= ± 1

 v n i l i m i
– spherical states
Standard approach: n i l i m i
→ n j l j m j
Only one axis: along projectile velocity
There is another axis: along the induced electric field E
How to calculate the collisional parameters for parabolic states?

Answer
• Express scattering parameters (excitation cross sections) for parabolic states ( nkm ) quantized along z in terms of scattering parameters (excitation cross sections AND scattering amplitudes) for spherical states
( nl
 m

) quantized along z’
O. Marchuk et al, J.Phys. B 43, 011002 (2010) 𝜎
2±10
=
1
2 𝜎
2𝑠0
+
1
2 𝑐𝑜𝑠
2 𝛼 𝜎
2𝑝0
+
1
2 𝑠𝑖𝑛
2 𝛼 𝜎
2𝑝1
∓ cos 𝛼 𝑅𝑒 𝜌
2𝑝0
2𝑠0

Collisional-radiative model
• Fast (~50-500 keV) neutral beam penetrates hot (2-20 keV) plasma
• States: 210 parabolic nkm (recalculate energies for each beam energy/magnetic field combination) up to n=10
• Radiative rates + field-ionization rates are well known
• Proton-impact collisions are most important
▫ AOCC for 1-2 and 1-3 (D.R. Schultz)
▫ Glauber (eikonal approximation) for others
• Recombination is not important (ionization phase)
• Quasy-steady state

Theory vs. JET and Alcator C-Mod
E. Delabie et al (2010)
I. Bespamyatnov et al (2013)

How important is dielectronic recombination?

How to compare CR models?..
• Attend the Non-LTE Code
Comparison Workshops !
• Compare integral characteristics
▫ Ionization distributions
▫ Radiative power losses
• Compare effective (averaged) rates
• Compare deviations from
equilibrium (LTE)
• 8 NLTE Workshops
▫ Chung et al, HEDP 9, 645 (2013)
▫ Fontes et al, HEDP 5, 15 (2009)
▫ Rubiano et al, HEDP 3, 225
(2007)
▫ Bowen et al, JQSRT 99, 102
(2006)
▫ Bowen et al, JQSRT 81, 71
(2003)
▫ Lee et al, JQSRT 58, 737 (1997)
• Typically ~25 participants, ~20 codes
Validation and Verification
18

E
R
E
R
E
R
EBIT : DR resonances with M-shell (n=3) ions
EBIT extracted ions electron beam
1s 2 2s 2 2p 6 3s 2 3p 6 3d n
Fast beam ramping
LMN resonances:
L electron into M , free electron into N time

Strategy
1.
Scan electron beam energy with a small step (a few eV)
2.
When a beam hits a DR, ionization balance changes
3.
Both the populations of all levels within an ion and the corresponding line intensities also change
4.
Measure line intensity ratios from neighbor ions and look for resonances
5.
EUV lines: forbidden magnetic-dipole lines within the ground configuration
Ca-like W 54+
Ionization potential
A( E1 ) ~ 10 15 s -1
A( M1 ) ~ 10 5 -10 6 s -1
I = N

A

E (intensity)

[Ca]/[K]
𝑊 54+ 3𝑑 2
𝐽=2
𝑊 55+ 3𝑑
3/2
− 3𝑑 2
𝐽=3
− 3𝑑
5/2
THEORY: no DR

[Ca]/[K]
𝑊 54+ 3𝑑 2
𝐽=2
𝑊 55+ 3𝑑
3/2
− 3𝑑 2
𝐽=3
− 3𝑑
5/2
THEORY: no DR isotropic DR
Non-Maxwellian (40-eV Gaussian) collisional-radiative model: ~10,500 levels

[Ca]/[K]
Non-Maxwellian (40-eV Gaussian) collisional-radiative model: ~18,000 levels
𝑊 54+ 3𝑑 2
𝐽=2
𝑊 55+ 3𝑑
3/2
− 3𝑑 2
𝐽=3
− 3𝑑
5/2
THEORY: no DR isotropic DR anisotropic DR
J atomic level degenerate magnetic sublevels m=+J m=-J
Impact beam electrons are monodirectional

Monte Carlo analysis: uncertainty propagation in CR models
• Generate a (pseudo-)random number between 0 and 1
• Using Marsaglia polar method, generate a normal distribution
• Randomly multiply every rate by the generated number(s)
• To preserve physics, direct and reverse rates (e.g. electronimpact ionization and three-body recombination) are multiplied by the same number
• Ionization distribution is calculated for steady-state approximation

We think in logarithms…
• Sample probability distribution
▫
▫ Normal distribution with the standard deviation 
1 𝑓 𝑥 = 𝜎 2𝜋 𝑒 − 𝑥−𝜇
2
/2𝜎
2
▫ Normal distribution is applied to log(Rate)
 log-normal distribution

Ne: fixed Ion/Rec rates
N e
= 10 8 cm -3
T e
= 1-100 eV
Ionization stages:
Ne I-IX
ONLY ground states
MC: 10 6 runs
NOMAD code
(Ralchenko & Maron,
2001)

Ne: + stdev=0.05

Ne: + stdev=0.30

Ne: + stdev=2

Ne: + stdev=10

Only stdev=10
Structures appear!

Only stdev=10

Lines: two ions populated

1
Z Z+n 𝛔
𝟐
𝑍 = 𝑍 + 𝑛 ∙ 1 − 𝛼 n= 1 , 2 , >2

C: 10 6 , 10 17 , 10 19 , and 10 21 cm -3

Needs and conclusions (collisions)
• CROSS SECTIONS, neither rates nor effective collision strengths
▫ EBITs, neutral beams, kappa distributions,…
• Scattering amplitudes (off-diagonal density matrix elements)
▫ Also magnetic sublevels
• Complete consistent (+evaluated) sets (e.g., all excitations up to a specific n max
)
• Do we want to have an online “dump” depository ? AMDU IAEA?
VAMDC?
• Need better communication channels