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

Collisional-radiative models aregenerally problem-taylored

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

e-He excitation and ionization

•Completeness•Consistency•Quality•Evaluation

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

Theory vs. JET and Alcator C-Mod

I. Bespamyatnov et al (2013)

E. Delabie et al (2010)

How important is dielectronic recombination?

Fra

ctio

n

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 DR

[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)

Ne: + stdev=0.05

Ne: + stdev=0.30

Ne: + stdev=2

Ne: + stdev=10

Only stdev=10

Structuresappear!

Only stdev=10

Lines: two ions populated

1-

Z Z+n

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