data quality and needs for collisional-radiative modeling yuri ralchenko national institute of...
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Data Quality and Needs for Collisional-Radiative Modeling
Yuri Ralchenko
National Institute of Standards and TechnologyGaithersburg, MD, USA
Joint ITAMP-IAEA Workshop, Cambridge MAJuly 9, 2014
2
Basic rate equation
tNTTNNtNtAdt
tNdieie
ˆ...,,,,ˆ,ˆˆ
...
...ˆ
,iZNN Vector of atomic statespopulations
Rate matrix
ijijiij EANI
3
Z Z+1
Continuum
ionization
recombination
autoion
ization
dielectronic capture
charge exchange
(de)excitation
ionization limit
autoionizingstates
rad. transitions
Collisional-RadiativeModel
6
Atomic states
Averageatom
122836
1224344452
12283541
Superconfiguration
3s23p34s
3s23p3d24p
Configuration 5S
3S3D
1D
3P
1P
Term
3D1
3D2
3D3
Level
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 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 highly-charged ions
Collisions and density limits
• High density▫ Different for different ion
charges▫ LTE/Saha equilibrium
Collisions are much stronger than non-collisional processes
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
Neutral beam injection:Motional Stark Effect
Displacement of Hα
-4 -2 4 0 2
Iij,a.u. σπ
λ(Hα)
Example: ;
/0 = 0.353
W. Mandl et al. PPCF 35 1373 (1993)
H
0.42
Solution: eigenstates are the parabolic states
parabolic states nikimi
nilimi – spherical states
Radiative channelnikimi→ njkjmj π – components with Δm=0σ – components with Δm=±1
Standard approach: nilimi→ njljmj
Only one axis: along projectile velocity
There is another axis:
along the induced electric field E
E
v
= /2 for MSEE = v×B
How to calculate the collisionalparameters 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
(nlm) quantized along z’
O. Marchuk et al, J.Phys. B 43, 011002 (2010)
𝜎 2±10=12𝜎2 𝑠0+
12𝑐𝑜𝑠2 (𝛼 )𝜎 2𝑝 0+
12𝑠𝑖𝑛2 (𝛼 )𝜎 2𝑝1∓ cos𝛼𝑅𝑒 (𝜌2𝑠 0
2𝑝 0 )
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
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 codesValidation and Verification
EBIT: DR resonances with M-shell (n=3) ions
LMN resonances:L electron into M,free electron into N
1s22s22p63s23p63dn
EBIT electronbeam
extractedions
time
ER
ER
ER
Fast beam ramping
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
A(E1) ~ 1015 s-1
A(M1) ~ 105-106 s-1
I = NAE (intensity)
Ionization potential
Ca-like W54+
[Ca]/[K]
𝑊 54+¿3 𝑑2𝐽 =2−3𝑑 2
𝐽=3
𝑊 55+¿ 3𝑑3 /2−3 𝑑5/2 ¿¿
THEORY:no DRisotropic DR
Non-Maxwellian (40-eV Gaussian) collisional-radiative model: ~10,500 levels
[Ca]/[K]
𝑊 54+¿3 𝑑2𝐽 =2−3𝑑 2
𝐽=3
𝑊 55+¿ 3𝑑3 /2−3 𝑑5/2 ¿¿
THEORY:no DRisotropic DRanisotropic DR
atomic level degenerate
magneticsublevels
Jm=-J
m=+J
Non-Maxwellian (40-eV Gaussian) collisional-radiative model: ~18,000 levels
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. electron-impact 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
▫Normal distribution is applied to log(Rate)
log-normal distribution
Ne: fixed Ion/Rec ratesNe = 108 cm-3
Te = 1-100 eV
Ionization stages:Ne I-IX
ONLY ground states
MC: 106 runs
NOMAD code(Ralchenko & Maron,2001)
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