IAEA, Vienna, July 03 2013

Predrag S. Krstić

U. Of Tennessee, Knoxville (Joint Institute of Computational Sciences & Dept. of Physics & Astronomy), TN, USA

Support from: US DoE, NSF, IAEA &NCCS(DOE) & JICS/NICS(NSF) Computing

SURVEY OF ROVIBRATIONALLY RESOLVED

COLLISION DATA WITH HYDROGEN MOLECULES

CRP: ”Atomic and Molecular Data for State-Resolved Modelling of

Hydrogen and Helium and Their Isotopes in Fusion plasma”

Basics of terrestrial fusion?

d-t fusion (more efficient) T=150 mil K Alpha-particles and neutrons carry most of the energy

Fusion on earth (Controlled fusion!)

Vac.

Supercon–ducting magnet

Shield Blanket

Turbine generator

Plasma

a

Plasma heating

(rf, microwave, . . .)

Schematic magnetic fusion reactor ITER, DEMO

3

PMI strategy is evolving thru ITER towards DEMO reactor

3

Divertor chamber

DEMO (> 2030?): • Steady-state, power flux ~ 10 MW/m2

• Hot walls (>600 C )

• Refractory metals

• Neutron irradiation 14.1 MeV (~ 100 dpa)

Parameter range inaccessible in present devices

F valid extrapolation needed!

ITER (> 2020) uses multi-matl walls

Pulses ~ hundreds of sec ~Be Main chamber wall(700m2 )

Low Z + oxygen getter

~W Baffle/Dome (100 m2)

Funnels exhaust to divertor chamber

Low erosion, long lifetime

~ C Divertor Target (50 m2) (Graphite)

Minimize high-Z impurities

(which lead to large radiative losses)

Atomic physics for magnetically

confined fusion: Where does it meet the

planetary science?

- 17 Mev per d+t fusion in plasma core (> 50 mil. K) ; 80% transferred by n to Li blanket which fuel t; 20% carried by a, 1/4 supports the plasma, rest needs to be exhausted by e, p, a via atomic inelastic processes: - SOL plasma ( 50-300 eV), absence of neutrals and molecules, electron-impurity ion processes, radiative plasma cooling

- Divertor region, 50 - 1 eV, 1014 -15 cm3,

H, H2 dominant, He, He+,++, impurities;

neutral particle transport, helium removal,

recombination, collision with surfaces:

Key for thermal power exhaust problem

Planetary science is in a lower, partially overlapping region of collision energies!

Guiding principle:

If Edison had a needle to find in a haystack, he would proceed at

once with the diligence of the bee to examine straw after straw

until he found the object of his search… I was a sorry witness of

such doings, knowing that a little theory and calculation would

have saved him 90% of his labor.

–Nikola Tesla, New York Times, October 19, 1931

Shooting data at random approach to a large categories of atomic data for fusion (excited states, molecules,…) is becoming prohibitively slow and costly, programmatic problems, funding problems.

Need clearly to identify the problems, data needed and accuracy 5

LET US THINK!!!

Model validation is usually defined to mean “substantiation that a computerized model within its domain of applicability possesses a satisfactory range of accuracy consistent with the intended application of the model.” (Schlesinger at al 1979). Comparison with experiment :: qualitative toward quantitative Calculation needs to mimic the experiment as close as possible

Model verification is often defined as “ensuring that the computer code of the computerized model and its implementation are correct”. Code testing against simple models; Overlap of different adjacent time and spatial scales by various methods

Uncertainty quantification science tries to determine how likely certain outcomes are if some aspects of the system are not exactly know. Here: Model parameters may vary between different instances of the same object for which predictions are sought. Example: Monte-Carlo approach to trajectories over the surface

What are the requirements for of the computer simulation and modeling of the atomic data?

In fusion plasma

1. Typical for the divertor region is formation of the molecules, particularly H2, H2+,

hydrocarbons (if carbon facing plasma material), vib-rot excited, metals, inert gases,…

2. Huge increase of the cross sections (as n4 for charge transfer) necessitates

electronically excited atomic and molecular states!!!

3. Vibrationally resolved collisions for volume plasma recombination schemes MAR

and MAD for hydrogen and hydrocarbons; For in frared emission p lasma

diagnostics; For CR models of H2/D2 plasma.

4. High rotational temperatures of hydrogen molecules indicated!!!

5. Tritium codeposition in tokamaks (with carbon, with tungsten around grain boundaries, too)

closely linked with the plasma chemistry relevant molecules in plasma.

6. EXAMPLES from carbon chemistry

D. Coster et al, D. Reiter et al, H. Summers et al, others?

Also:

Why does fusion/plasma need accurate atomic physics theory?

Overview of reactive heavy-particle processes we are interested in this CRP Special stress on molecules Challenging in the environment of reduced funding

REMINDER:

( )p H n Excitation, Ionization, Charge transfer

ION-ATOM

2 ( )H H H H H v

2 ( )H H v

Three body diatomic association

( )p H H n H

p H p H e

2 ( )

H p e

H v e

Negative ions (atomic)

Exc

Ion

Recombination by capture

With protons

2 2

2 2

2

2

2 2

( ) ( ')

( ) ( ')

( )

( )

( ) ( , ')

p H v p H v

p H v H H v

p H v H H H

p H v H H H e

p H v p H n v

Proton impact of molecule

Exc elec vib

Dissoc Double ion

Charge transfer

2 2

2 2

2

( ) ( ')

( ) ( ')

( )

H H v H H v

H H v p H v

H H v p H H

Processes with molecular ion

2 2

2 2

2

2 2 2 2

2 2 2

( ) ( ')

( ) ( ')

( )

( ') ( ") ( ''') ( "")

( )

H H v H H v e

H H v H H v

H H v H H H

H v H v H v H v

H H v H H H

Numerous other processes with molecules

2 2 3( ') ( ) ( ")H v H v H v H

DE, DR, branching ratios with electrons D, DCT with H

Creation of H3+

3H Series of interesting reactions:

p He H He *

( )

p He

p He n e

( )p He p He n *p He

p He e

Processes with He

Processes with vibrationally and rotationally excited hydrogen molecules What can we do here

Vibrational done in good extent!

7/17/2013 18

2 2 ,

2 2

2

,2 2

2 2

2

2

( ) ( ), 0 -14

( ) (1 ) ( ), 0 -14, 0 -19

( ) , 0 -14.

( ) ( ), 0 -19

( ) ( ), 0 -19, 0 -14

( ) , 0 -19.

,( )

i f i f

i f i f

i i

i f i f

i f i f

i i

f

H H H H

H H v H s H

H H v H H H

H H H H

H H v H H

H H v H H H

H H H H H

2

0 -14.

, 0 -19( )f

ffH H H H H

WHAT HAS BEEN DONE WITH VIBRATIONAL RESOLUTION?

•Comprehensive QM calculations of cross sections,

•on the “same footing”

•0.5-100 eV collision energy

EXC

CT

DISS

EXC

CT

DISS

ASSOC

ASSOC

+ENERGY&ANGULAR SPECTRA (DISS)

7/17/2013 19

Fragments of H3+: (H2,H2

+,H,H+)

g

R R 1

R 2

H +

H

H

IOSA : g "frozen"

r

Geometry

The approximation: Sudden approximation for target rotations (IOSA): g frozen

Cross sections averaged over g

By understanding the underlying physics FIRST (What to expect?)

R (a.u.)

0 2 4 6 8 10

Po

ten

tial

en

erg

y (

eV)

-5

-4

-3

-2

-1

0

1

2

0

40

H2+ (1sg) +H(1s)

H2(X1g

+)

mixed diss. continuum

H2+(2pu) +H(1s)

and, similarly,

for H+H2+

Place of events: H3+

Two lowest electronic surfaces

HOW? NOT ROTATIONAL DYNAMICS INCLUDED?

Angular average of the cross section!!!

7/17/2013 20

“Battle field of hydrogen molecule:

Two-electronic, strongly coupled potential-surfaces of H3+; Reactive

Physics highly dependent on projectile-diatom angle; Reactive at small γ

Reactive at very large r for large γ

Need large config space (40 a.u.)

Violent coupling (CT)

Need trans to diabatic

representation

R

r

WA

02468

012345-1.36

-1.22

-1.09

-0.95

g=90o

R r

|<1|d/d|2>|

0 2 4 6 810 0 1 2 3 4 50.0

0.5

1.0

1.5

2.0

R

r

0 2 4 6 8 100

2

4

6

8

10

R r

WA

02468

02

46

8

-1.30

-1.12

-0.95

g=8.11o

R r

|<1|d/d|2>|

24

68

10

024680.0

0.5

1.0

R

r

0 2 4 6 8 100

2

4

6

8

10

config 1

config 2

H3+ -> H + H2

+

H3+ -> H

+ + H2

g=850

1

0

4

2

3

5

1 4 1 8

210

I II III V VIIV

-10.0

-8.0

-6.0

-4.0

-2.0

0.0

Wa

(eV

)

H3+: ADIABATIC VIBRATIONAL "TERMS"

0 1 2 3 4 5 6 7 8 9 10

R (a.u.)

II IV

3

=0

1

2

'=1

=5

HC HC Demkov

=0

LZ

0.0 2.0 4.0 6.0 8.0 10.0

R (a.u.)

0

2

4

6

8

< |d

/dR

| '>

Dissociation

Charge transfer

g =85 0

Physics in direct channel

Dissociative continuum discretized

Extensively rich

•We describe both electronic and nuclear motion quantum- mechanically •Solve resulting Schrödinger equation by expanding in diabatic vibrational basis •Several hundreds states to converge

VIBRONIC REPRESENTATION:

7/17/2013 22

How did we approach for E< 10 eV?

Fully QM!!

•Diabatic representation for two electronic surfaces

•Large configuration space in r and R (40 a.u.)

•Dissociative continuum discretized in more than 800 states;

•Solve resulting Schrödinger equation by expanding in diabatic

vibrational basis (bound + continuum)

0 0

2 2 2 2

1 ( 1) ( 1)( , , ) ( , , ) 0

2 2 2l

l l j jI I I W R r EI R r

R r R rg g

Resulting equation is a system of ordinary differential equations : Variable is R

ISSI, Bern, 09/2009

Collisionally assisted diatomic association

(also known as three-body recombination)

Two atoms (or ion-atom) associate in presence of a third

particle which “relaxes” the excess energy and momentum.

H++(H+H) -> H++H2 direct association

-> H+H2+ charge transfer association

H+(H++H) -> H++H2 charge transfer association

-> H+H2+ direct association

Possible processes:

T (K)

102

103

104

Recom

bin

ati

on r

ate

(10

-31 c

m6/s

)

10-4

10-3

10-2

10-1

100 H

++(H+H) H+H2

+()

Tot. H+H2+

=1817161311

9

42

0

10-4

10-3

10-2

10-1

100 H

++(H+H) H

++H2

Tot. H++H2

=14131210

11

9

420

7

0 2 4 6 8 10 12 14 16 18

Recom

bin

ati

on r

ate

(10

-32 c

m6/s

)

0.0

0.2

0.4

0.6H

++(H+H)

H++H2()

H+H 2+()

T=1000 K

(a)

(b)

(c)

T (K)

102

103

104

Rec

om

bin

atio

n r

ate

(10

-31 c

m6/s

)

10-2

10-1

100

H2

H2+

Tot. (H2, H2+)

Classical theory,

Orel (1987)

(H+H+H)

Exp., H+H+H

Jacobs (1967)

Krstic et al, JPBL 36, L249 (2003)

Dominance of the H2+ creation in both cases

Range of values:

5x10-32-6x10-34

(200-20,000K)

7/17/2013 24

“Interplay” of transport and inelastic processes

Cro

ss S

ection (

a.u

.)

10-1

100

101

102 H

++H2(=0)

mtvib

dis

vi

=4

mt

vib

ct

dis

vi

ct

ECM (eV)

0 1 2 3 4 5 6 7 8

Cro

ss S

ection (

a.u

.)

10-1

100

101

102

=7

mt

vib

ct

dis

vi

ECM (eV)

1 2 3 4 5 6 7 8

mt

vib

ctdis

vi

=12

a) b)

c) d)

H+H2+

ν=0

v=4

ν=7

v=12

7/17/2013 25

Cro

ss S

ecti

on (

a.u.

)

10-1

100

101

102 H+H2

+(=0)

mtvib

dis

vi

=4

mt

vib

ct

disvi

ct

ECM (eV)

0 1 2 3 4 5 6 7 8

Cro

ss S

ecti

on (

a.u.

)

10-1

100

101

102 =7

mt

vib

ct

dis

vi

ECM (eV)

1 2 3 4 5 6 7 8

mt

vib

ct

dis

vi

=15

a) b)

c) d)

v=0

v=4

v=7 v=14

3

Present

2

1

4

5

6

12

7

3

4

6,7

i=0

H++H2(i) -> H(1s)+H2

+

a)

i=0, Holiday et al (1971)

i=0

5

TSH (Ichihara et al, 2000)

0 2 4 6 8 10

CM Energy (eV)

10-17

10-16

10-15

10-14

Char

ge

tran

sfer

cro

ss s

ecti

on (

cm2) Total charge transfer

Fig.1a)

14

b)

TSH (Ichihara et al, 2000)

Present

89

1011

12

13

H++H2(i) -> H(1s)+H2

+

Fig. 1b)

14

14

13

12

11

10

9

8

0 2 4 6 8 10

CM Energy (eV)

10-15

Char

ge

tran

sfer

cro

ss s

ecti

on (

cm2)

Comparison with Ichihara is shown above for the charge transfer. Comparison as predicted by the general correspondence principle Good agreement for v>3, and larger energies. For large v’s cross section decreases – Classical wrong.

COMPARISON OF QUANTUM AND CLASSICAL APPROACHES

Weaknesses of both approaches (classical Ichihara and quantal Krstic) (example of vibrationally resolved H++H2(v) charge transfer) • It is not fully clear what is the lower limit of energy in Ichihara work. For lower v’s, the

lowest energy is limited by the threshold, which is ~1.8 ev for v=1. • In case of Krstic, the lowest state depends on v, and is about 0.1 eV for v=4, and goes

down to 0.05 eV for v=14. This gives inconsistent integrals for the rate coefficients. • The problem of integration limits is present in Krstic’s work also for higher energies.

• Ichihara calculation considers motion of atoms (c.m. of H2, H+as well as rotational and vibrational) as classical. This is problematic at low energies, i.e. when deBroglie wavelength is of the order of characteristics dimensions : already a case for 1 eV motion.

•Ichihara calculation threat the charge transfer transition of electron by an approximate trajectory surface hoping, assuming that the transition is strictly localized. As is well known, the accuracy of the LZ model is accidental.

•There is a barrier between two particle exchange configurations (reactions). Classical approach of Ichihara cannot treat correctly the tunneling transitions corresponding to the particle exchange.

Comparison of quantal and classical II:

•Krstic’s calculation (PRA) is fully quantum-mechanical, for both electron transitions and for atomic/molecular motion in vibrational dimension. However, a frozen rotational approximation is used (IOSA), and the rotational dynamics is not considered simultaneously with electronics and vibrational ones.

•The averaging over various diatom angles is done at the level of the cross sections. IOSA is correct if the characteristic time scale of rotational motion is (“much”) smaller than the vib and translational scales. Since energy of a rotational quant is about 0.07 eV, obviously only translational energies larger than (at least, but possibly higher then) fraction of eV are possibly acceptable.

•This approach becomes increasingly difficult and numerically instable for tens of eV energy. Unlike Ichikara, Krstic’s quantal calculations stop at about 10 eV.

•Krstic’c quntum-classical calculation for higher energies (< 100eV) is based on a straight line classical approximation of the translational motion, while electronic transition and vibrational motions are treated fully quantally. The straight line approximation may induce overestimates of the transitions. The transition between the two approaches of Krstic is not smooth.

29

Electronically excited : *Huge increase of the cross sections (as n4 for CT)

*For a complete H/H2 CR model, Hα diagnostics,

*Fulcher-band diagnostics for H2.

Vibrationally excited: *Infrared emission plasma diagnostics.

*CR models of H2/D2 plasma.

*Lack of quantitative analysis in molecular spectr.

Rotationally : High rotational temperatures of H2 indicated?

Isotopic constitution : *D2,T2, HD, HT and DT, Sensitive on vib. energy levels.

and excitation *Wherever internal energy plays role

(“ion conversion”).

*No data for excited molecules.

*Ex.:σpex(D++H2→HD+H+) » 10 σpex(D

++HD→D2+H+).

WHAT IS NEEDED?

1) Atom + a rigid rotator (Dalgarno) • Structureless particles + two-particle entity with internal angular momentum 5 coordinates Atom with reduced mass • Alternatively, BC angles can be defined with respect to the coordinate system In which the Z-axis coincides with MA, Z-axis rotate in the course of collision: Body fixed system (potential nice V(R,theta’) Appearance of Coriolis + centrifugal forces) The treatment of the system is formaly the same as e+H scattering, as defined by Percival & Seaton.

'

R

' M

C

B

z

Z

x

y Jacobi coordinates

We are working on the rotationally resolved dynamics in ion/atom-molecule collisions

SF against BF

• Wave function of the rotor can be expressed in terms of a full set of angular functions in either system, • Angular momentum of the rotor, j, is invariant to the coordinate system (its projection m in SF and Ω (in BF) will be different) • So the wave function expand in or in

, ( , )j mY , ( ', ')jY

• Relationship between two sets expressible in terms of the rotation matrices • The total angular momentum of the system J=j+L is conserved in both systems (L of the atom relative to the rotor)

2 22

2 2

1[ 2 ( , ') ] 0j

LR V R k

R R R

2 2 [ ( 1)]jk E Bj j

Partial differential equation of the system

Can be solved directly or obtain various forms, depending on a chosen coordinate system Jacobi coordinate theta can be frozen during the collision : IOSA or kept through the operator L and potential (multi-D partial equations)

However, conventionally : In SF:

22

2 2

' 'p' ' '

( 1)[ ] ( | )

2 | ( , ') | ' 'p' ' ' F(j'l'p'J'M' | R)

j

j l J M

d l lk F jlpJM R

dR R

jlJM V R j l J M

In BF:

22

2

2

2' 'p' ' '

[ ]G( | )

2 | ( , ') | ' 'p' ' ' (j' 'p'J'M' | R)2

j

j J M

dk j pJM R

dR

Ij pJM V R j J M G

R

• Only approximations lead to the different solutions with SF and BF • The centrifugal pot decreases as while in neutral molecules pot energy falls as for collision of neutral particles • Therefore, SF better when the collision is long range, i.e. at large values of impact parameter. Pot energy expansion can be truncated in just a few terms. • For short range transitions, and small b, BF is the choice. • Rotational transitions with neutral particles are better suited at short range

2R

6R

2 2 2 2

' '

' '

1 ( 1) ( 1)( , )

2 2 2

| ( , , ') | ' ' ( , )

ˆ ˆcos

JM

lj

JM

l j

l j

l l j jE G R r

R r R r

lj V R r j l G R r

R r

g

We have developed so far a full set of potentials (using CC (S,D,T,Q) on Titan, NWChem) for:

2H H 2H H

2Li H

!!!!

Thank you!