Upload
others
View
7
Download
0
Embed Size (px)
Citation preview
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!