Data quality and needs for collisionalradiative modeling

Report
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
2
Basic rate equation
 ... 


ˆ
N   N Z ,i 
 ... 


Vector of atomic states
populations
dNˆ t  ˆ ˆ
 A t , N t , N e , N i , Te , Ti ...  Nˆ t 
dt


Rate matrix
I ij  N i  Aij  Eij
3
autoionizing
states
CollisionalRadiative
Model
Continuum
ionization limit
(de)excitation
rad. transitions
Z
Z+1
Collisional-radiative models are
generally problem-taylored
6
Atomic states
Term
Superconfiguration
1P
1224344452
3s23p3d24p
3P
12283541
Average
atom
122836
3D
3
1D
3D
2
3s23p34s
Configuration
3S
3D
3D
1
Level
5S
BUT: field modifications, ionization potential lowering
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
• Allowed: generally very good
if the most advanced methods
(MCHF, MCDHF, etc) are used
• Forbidden: generally good,
less important for kinetics
Autoionization
• 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

  = 0    −∆0/
0
 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
• Completeness
• Consistency
• Quality
• Evaluation
Neutral beam injection:
Motional Stark Effect
σ
π
Iij,a.u.
-4
-2
0
2
W. Mandl et al.
PPCF 35 1373 (1993)
H
4
λ(Hα)
Displacement of Hα
Example:
 =
 ;
/0 = 0.353
0.42
Solution: eigenstates are the parabolic
states

E = v×B
E
parabolic states nikimi
Radiative channel
nikimi→ njkjmj
π – components with Δm=0
σ – components with Δm=±1

 = /2 for MSE

v
nilimi – spherical states
Standard approach: nilimi→ njljmj
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)
2±10
1
1
1
20
2
= 20 +   20 + 2  21 ∓ cos   20
2
2
2
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)
Fraction
How important is dielectronic recombination?
18
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
EBIT: DR resonances with M-shell (n=3) ions
EBIT
electron
beam
1s22s22p63s23p63dn
extracted
ions
LMN resonances:
L electron into M,
free electron into N
Fast beam ramping
ER
ER
ER
time
Strategy
1.
2.
3.
4.
5.
Scan electron beam energy
with a small step (a few eV)
When a beam hits a DR,
ionization balance changes
Both the populations of all
levels within an ion and the
corresponding line
intensities also change
Measure line intensity ratios
from neighbor ions and look
for resonances
EUV lines: forbidden
magnetic-dipole lines within
the ground configuration
Ca-like W54+
Ionization potential
A(E1) ~ 1015 s-1
A(M1) ~ 105-106 s-1
I = NAE (intensity)
[Ca]/[K]
 54+ 3 2=2 − 3 2=3
 55+ 33/2 − 35/2
THEORY:
no DR
[Ca]/[K]
 54+ 3 2=2 − 3 2=3
 55+ 33/2 − 35/2
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
 54+ 3 2=2 − 3 2=3
 55+ 33/2 − 35/2
THEORY:
no DR
isotropic DR
anisotropic DR
J
atomic
level
m=+J
m=-J
degenerate
magnetic
sublevels
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
− − 2 /2 2

 2
▫ Normal distribution is applied to log(Rate)
 log-normal distribution
Ne: fixed Ion/Rec rates
Ne = 108 cm-3
Te = 1-100 eV
Ionization stages:
Ne I-IX
ONLY
ground states
MC: 106 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
 =+∙ 1−
 =  −  ∙  +  − 
n=1, 2, >2
C: 106, 1017, 1019, and 1021 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 nmax)
• Do we want to have an online “dump” depository? AMDU IAEA?
VAMDC?
• Need better communication channels

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