Data requirements for simula0ng vapor shielding with radia0on- - - PowerPoint PPT Presentation

LLNL-PRES-748293

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC

Data requirements for simula0ng vapor shielding with radia0on- hydrodynamic and collisional-radia0ve modeling

IAEA Consultancy Mee1ng on Vapor Shielding in Fusion Devices Howard Sco? March 19-20, 2018

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§ Where do collisional-radia1ve models fit in a radia1ve-hydrodynamics code? § What requirements are put on the models? § Examples

— Hydrogen edge plasma w/ op1cal depth effects — Li data set for pellet injec1on — Sn data set for EUV genera1on

Outline

Note: My experience has been gained primarily with laser-produced plasmas

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σ ij × Jij , Jij + 2hνij

3

c2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ Jij = φνJν

∫

dν

§ At high densi1es (ni > 1020 cm-3)

— Plasma can be op1cally thick to con1nuum radia1on — Radia1on is coupled strongly to free electrons — Absorbed radia1on is redistributed thermally — Energy transferred between radia1on and ma?er:

§ At low densi1es (ni < 1018 cm-3)

— Plasma can be op1cally thick to line radia1on — Radia1on is coupled strongly to bound electrons — Radia1on is coupled indirectly to free electrons — Absorbed radia1on is redistributed within line profiles — Radia1ve excita1on / de-excita1on rates:

Collisional-radia0ve (CR) models in radia0ve- hydrodynamic codes

ανJν −ην

( )

∫

dν

absorption coefficient emission coefficient angle-integrated intensity line profile

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§ High density: averaged material informa1on

— Radia1ve proper1es: broadband absorp1on and emission coefficients — Equa1on of state: ioniza1on balance, internal energy

§ Low density: detailed material informa1on

— Radia1ve proper1es: absorp1on and emission profiles — Equa1on of state: popula1ons

§ Both regimes require “full” atomic models

— All significant transi1ons between coupled states induced by collisions w/

electrons and photons: excita1on, ioniza1on + autoioniza1on

— Low temperature à collisions w/ ions and neutrals + molecules

The physical regime determines the use of CR models

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§ High density:

— Extensive state space / configura1on coverage — Mul1ple excita1ons from valence shell (can extend to inner shells) — Collisional broadening à detailed structure less important — Autoionizing state coverage more important than autoioniza1on / DR

§ Low density:

— Most ioniza1ons / excita1ons directly out of ground state — Detailed structure + line profiles important for radia1on transfer — High-n excited states important for charge exchange — Autoionizing states cri1cal for dielectronic recombina1on (DR)

The use determines the content of atomic models

Non-LTE Code Comparison Workshops have been extremely valuable in iden1fying requirements for atomic models

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Plasmas at the tokamak edge are op0cally thick to line radia0on on length scales < 1 cm

§ Absorp1on coefficient for thermally-broadened Lyman α: § Simula1ons show large effects from radia1on fields § PIP: Self-consistent treatment which includes

— par1ally-ionized plasma transport — non-LTE atomic kine1cs — line radia1on transport — excited state transport — magne1c effects on line profiles

2 1 14 ev

1 0.3 cm 10

• n

e n f mc T π α ν π

−

⎛ ⎞ = ≈ ⎜ ⎟ Δ ⎝ ⎠

H.A. Sco? and M.L. Adams, “Incorpora1ng Radia1on Effects into Edge Plasma Transport Models with Extended Atomic Data Tables”, EPS Conference on Plasma Physics, 2004

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Detached divertor simula0ons exhibit large radia0on effects

Specifica1ons: L=2 m, N=1020 m-3, qin=10 MW/m2, b=0.1

Qualita1ve descrip1on of the detached divertor region remains unchanged. Quan1ta1ve details of the par1cle and power balance change drama1cally.

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Op0cally-thick hydrogen lines affect divertor power balance

Flux qin Qr qout CR +1.000

• 0.805

+0.195 NLTE +1.000

• 0.555

+0.445 CR : PIP w/ op1cally-thin collisional-radia1ve model (tabulated data) NLTE : PIP w/ collisional-radia1ve model with full line transfer

qin : incident heat flux Qr : radia1ve heat flux qout : par1cle heat flux on target plate

Radia1on effects increased the divertor target plate incident heat flux by a factor 2.3

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Atomic data in plasma transport codes

§ Plasma transport models explicitly treat ion and (ground state) neutral

atoms

§ Excited states are assumed to be in equilibrium on transport 1mescales: § Transport model uses effec1ve ioniza1on / recombina1on and energy

loss coefficients which account for excited state distribu1ons, e.g.

§ Tabulated coefficients are evaluated with a collisional-radia1ve code in

the coronal (op1cally-thin) limit

, ,

, ( , )

g i g i g i x x g x i x x e e

n f n f n f f n T = + =

( ) ( )

,

i n i i i n r i n n i n r i

n n n Pn P n n Pn P n t t ∂ ∂ + ∇⋅ = − + ∇⋅ = − + ∂ ∂ V V

In the coronal limit, coefficients depend only on ne and Te

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Atomic data is condensed into effec0ve rates: P- and H-rates

§ P-rates are constructed from the atomic rate equa1ons: § H-rates are constructed from the electron energy equa1on:

t t t tt tx t x x x xt xx x

t ⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎛ ⎞ ∂ + ∇⋅ = ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ∂ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎝ ⎠ N N V A A N N N V A A N

( )

1 x xt t xx x x xx xt t xt t

t

−

∂ = + = ⇒ = − ≡ ∂ N A N A N N A A N B N

( ) ( )

t t t tt t tx x tt tx xt t t

t ∂ + ∇⋅ = + = + ≡ ∂ N N V A N A N A A B N N P

t : transported state x : excited state N : number density A : atomic rate matrix

( )

' ' ' ' , , ' j jk jk t t t t t x t x xt t t j k j t t t t t

N A E E E

≠ ≠

Δ = Δ + Δ ≡

∑ ∑ ∑

A A B N H N

( ) ( )

,

3 3 5 2 2

e i e i e i i e e i i e j jk jk j k j ei

m n T T nT n T nT N A E t Mτ

≠

− ∂ ⎛ ⎞ ⎡ ⎤ + ∇⋅ + − ⋅∇ + = Δ ⎜ ⎟ ⎢ ⎥ ∂ ⎝ ⎠ ⎣ ⎦

∑

V q V

This generalized the approach of Stotler, Post and Reiter (1993)

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§ Radia1on introduces spa1al

dependence into the atomic rates through the radia1on field

§ Rates are parameterized by the

(approximate) op1cal depth of Lyman α:

§ Tabulated values generated with

escape factors for midpoint of uniform plasma of depth 2τ

§ Can be applied in arbitrary mul1-

dimensional geometry

Radia0on effects are incorporated through the P- and H-rates

( ) ( ) ( )

s 14

, , , , 10 ' '

e e e e n

P n T P n T n s ds τ τ → = ∫

'

e

P n P =

Parameterized tables were tested in UEDGE

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Op0cal depth parameteriza0on allows coverage from coronal to LTE regimes

Coronal regime LTE regime

( )

r,i r,i r,i

' 13.6eV

e

H n H P = − ± ×

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Excited state popula0ons follow from effec0ve rates

§ Determined from ground state and ion densi1es

n2=f20ni + f21ng , n3=f30ni + f31ng

Op1cal depth can change popula1ons by orders of magnitude

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§ Constructed from semi-classical formulas § Johnson-Hinnov collisional rates § Doppler + collisional + (approximate) Stark broadening § No fine structure

Comments

§ Ly-α fine structure spliqng negligible compared to broadening § Stark line shapes did not affect energe1cs, but are important for diagnos1cs § Zeeman spliqng due to a large magne1c field might decrease τ enough to ma?er

H data for edge plasma

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§ Fine structure data calculated with FAC (Flexible Atomic Code) § Single excita1ons to n=8, double excita1ons to n=5 § E1, M1, E2 radia1ve transi1ons

H-like: 64 levels, 1.1e3 transi1ons He-like: 252 levels, 1.1e4 transi1ons Li-like: 270 levels, 1.2e4 transi1ons Comments:

§ FAC and similar codes are quite accurate for low-Z elements (except neutrals?) § Datasets remain reasonably compact and fast for low densi1es

– but –

§ Including enough DR channels could be problema1c

Li data for killer pellets (for P. Parks of GA)

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Li evalua0on @ ne = 1015 cm-3

3.0 2.5 2.0 1.5 1.0 0.5 0.0 <Z> 20 15 10 5 T (eV) 0.01 0.1 1 10 Radiative power (erg/cm

3/s)

20 15 10 5 T (eV)

total bound-bound bound-free free-free

Average ionization state Radiative power loss

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§ Fine structure energy levels / oscillator strengths from LANL code § Special a?en1on paid to configura1on interac1on § Dataset restricted to structure + oscillator strengths for 33-50 electrons

— Sufficient structure for low densi1es (except for DR channels)

Comments:

§ High-fidelity calcula1ons of complex ions

are difficult but possible

§ Adding other transi1ons for NLTE work

increases expense greatly but might be done with semiclassical methods

Sn data for EUV genera0on (from J. Colgan of LANL)

10

1

10

2

10

3

10

4

• scillator strength

10 8 6 4 2 frequency (eV)

Sn

0+

Sn

1+

Sn

2+

• J. Colgan, et al, HEDP 23 (2017) 133-137

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§ Combine levels by configura1on and energy spread § Averaged transi1ons between combined levels § Aim to maintain oscillator strength distribu1on in each charge state

(LTE) Radiative emission of averaged models

Carefully averaged data maintains the spectral structure

1.0x10

18

0.5 0.0 emissivity (erg/cm

3/s/Å)

180 160 140 120 100 wavelength (Å)

none 1 eV 5 eV 10 eV (n,l ) mixed

averaging energy levels transitions none 1.85e6 4.6e8 1 eV 29668 4.4e6 5 eV 8471 5.2e5 10 eV 5091 2.2e5 (n,l) 1258 2.0e4 mixed 11072 1.1e6 Sn+0 – Sn+17 T = 20 eV Ni = 1018 cm-3

Data from fine-structure model of J. Colgan

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§ NLTE atomic kine1cs + radia1on transport for 1 eV-averaged model § T = 30 eV + maximum Ni = 1018 cm-3 § Density profile Ni ∝ r-2 (fit from rad-hydro simula1on)

Testing averaged models with radiation transport

Bandpass flux is insensi1ve to frequency resolu1on

2 1

• ptical depth

180 160 140 120 100 wavelength (Å)

• ptical depth

ionization

6 5 4 3 2 1 flux (erg/cm

2/s/Å)

180 160 140 120 100 wavelength (Å)

escaping flux

high resolu1on low resolu1on

13 12 11 charge state 0.05 0.04 0.03 0.02 0.01 position (cm)

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§ What are expected density / temperature ranges?

— will help set model parameters

§ Which molecular reac1ons can occur?

— use a complete set of transi1ons or a chemistry model?

§ Do non-thermal electrons play any role? § Comparisons of data + simula1ons are both helpful

Ques0ons / Sugges0ons