Vibrationally resolved ion-molecule collisions

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1 Vibrationally resolved ion-molecule collisions CRP: Atomic and Molecular Data for State-Resolved Modelling of Hydrogen and Helium and Their Isotopes in Fusion plasma Predrag Krstic Physics Division, Oak Ridge National Laboratory Support of US DOE (OFES and OBES) for the Department of Energy

2 Atomic physics for magnetically confined fusion - 17 Mev per dt fusion in plasma core (> 50 mil. K) ; 80% transferred by n to Li blanket which fuel t; 0% carried by a, 1/4 supports the plasma, rest needs to be exhausted by e, p, a via atomic inelastic processes: - SOL plasma ( ev), absence of neutrals and molecules, electron-impurity ion processes, radiative plasma cooling - Divertor region, 50-1 ev, cm 3, H, H dominant, He, He,, impurities; neutral particle transport, helium removal, recombination, collision with surfaces: Key for thermal power exhaust problem

3 In fusion plasma 1. Typical for the divertor region is formation of the molecules, particularly H, H, hydrocarbons (with carbon facing plasma), vib-rot excited. Huge increase of the cross sections (as n 4 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 infrared emission plasma diagnostics; For CR models of H/D plasma. 4. High rotational temperatures of hydrogen molecules indicated 5. Tritium codeposition in tokamaks (with carbon) closely linked with the plasma chemistry of hydrocarbons in plasma.

4 Why does fusion/plasma need accurate atomic physics theory? Also: D. Coster et al, AIP Conf. Proc. 115(1), 11 (009) D. Reiter et al, Phys. Scr. T138, (009) Hydrocarbon sens analysis

5 And because : For these kind of data (vib-rot-elec excit.,isotop.): *Experiments difficult: Impossible? Missing! *Quality theoretical data: Sparse! And: It is 1 st century H H is the most fundamental ion-molecule system We should know all about it Do not know well this only (3)-body system? 8/1/ 5

6 Collisional term is a contact with reality in kinetics and fluid modeling Sources and sinks Because: Many critical data not accessible by experiments. Understanding underlying physics brings quality evaluation and predictive power Benchmarking data are foundation stones for possible scaling relations Krstic (003) <= [a bad example from astrophysical modeling community: Savin et al, ApJ 607, L147 (004)] CT in H H(v=0) To avoid arbitrariness: Standardization of data needed!!: Evaluation and recommendation Close collaboration of data users and producers is a must!! Validation by experiment a must!!!! ISSI, Bern, 09/009

7 Overview of reactive processes we are interested in this CRP CRP has to bring to attention particularly important blocks of processes Define the blocks

8 Here : main attention at Processes with vibrationally excited hydrogen molecules What can we do here

9 WHAT? Comprehensive QM calculations of cross sections, on the same footing ev collision energy H H ( ) H H ( ), 0-14 i f i, f H H ( v ) H (1 s) H ( ), 0-14, 0-19 i f i f H H ( v ) H H H, i i H H ( ) H H ( ), 0-19 i f i, f H H ( v ) H H ( ), 0-19, 0-14 i f i f H H ( v ) H H H, i H H H H H ( f ), f H H H H H ( ), 0-19 i f ENERGY&ANGULAR SPECTRA (DISS) f EXC CT DISS EXC CT DISS ASSOC ASSOC 8/1/ 9

10 Potential energy (ev) HOW? By understanding the underlying physics FIRST (What to expect?) Place of events: H 3 Two lowest electronic surfaces Fragments of H 3 : (H,H,H,H ) H (X 1 g ) H (pu ) H(1s) H (1sg ) H(1s) R (a.u.) 8/1/ 10 mixed diss. continuum IOSA g : "frozen" The approximation: Sudden approximation for target rotations (IOSA): g frozen H R r g R H Geometry R 1 Cross sections averaged over g H and, similarly, for HH

11 r r Two-electronic, strongly coupled potential-surfaces of H 3 ; Reactive Physics highly dependent on projectile-diatom angle; Reactive at small γ 8 R Reactive at very large r for large γ Need large config space (40 a.u.) 3 8/1/ 11 r W A 1 g=90 o R.0 <1 d/d > R r 0 4 g=8.11 o r R R <1 d/d > r 0 R W A config config 1 Violent coupling (CT) Need trans to diabatic representation

12 < d/dr '> H 3 : ADIABATIC VIBRATIONAL "TERMS" Physics in direct channel Wa (ev) Extensively rich g=85 0 H 3 -> H H H 3 -> H H Dissociative continuum discretized I II III IV V VI R (a.u.) Dissociation g = LZ 6 3 =5 Charge transfer 1 4 We describe both electronic and nuclear motion quantummechanically Solve resulting Schrödinger equation by expanding in diabatic vibrational basis =0 HC II HC IV R (a.u.) '=1 Demkov = Several hundreds states to converge

13 Collision dynamics extensively rich (within both bound states and continuum) Red line: Dynamically changing continuum edge H H o g=90-8 HH 0.10 (a) Coupling (a.u.) Energy (ev) Energy (ev) ' 14 17' ' o g=90 (b) R (a.u.) 10 1 Adiabatic vibronic states and nonadiabatic couplings 8/1/ for the Department of Energy R (a.u.) Dynamics in the dissociative continuum mimics discrete states dynamics OFES

14 How do 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) 1 l( l 1) j0( j0 1) I I I W ( R, r, g) EI (,, ) 0 l R r g R r R r 8/1/ 14

15 Probability density Probability density The full wave function vector (of r) at t, evolving from some initial φ i of either H or H (r), H H( i =0) ( ) ( r) M( r) ( r) i i (r), H H( i =6) (r), H (r), H r (a.u.) γ=90 o r (a.u.) 8/1/ 15

16 Charge transfer cross section (cm ) Charge transfer from excited H, summed over final states H H ( ) H H H H ( i ) -> H(1s)H 4 i Total charge transfer 10 6, SClass (Krstic 04) 5,6, Fully QM (Krstic 0) i =0 FQ 1 i =0, rec. (Linder et al, 1985) TSH (Ichihara et al, 000) i =0, Holiday et al (1971) i = CM Energy (ev) 8/1/ 16

17 Charge transfer cross section (cm ) II.Charge transfer from H ( i ) to H Summed over all final bound vib. states H H ( i ) -> H(1s)H b) TSH (Ichihara et al, 000) Present CM Energy (ev)

18 Charge transfer cross section (cm ) HH system: Charge transfer summed over final vib. states HH (i ) -> H(1s)H i = i = i = i = CM Energy (ev) CM Energy (ev)

19 Total dissociation cross cection (cm ) Dissociation from various υ H H i =0 SClass, Krstic 04 QM, Krstic& Janev 03 TSH, (Ichihara et al, 000) i = i =0 H H -> H HH CM Energy (ev) E CM =.61 ev 3.11 ev 4.11 ev 5.61 ev 7.61 ev Total dissociation from vibrationally excited target Direct; CT dissociation Differential cross section (angular, momentum) ISSI, Bern, 09/009

20 Quality control H H HH E CM =10 ev 0-1 a) More on comparisons with sparse experiments ev Herman et al. (1978) 0- b) sin d el /d (a.u.) ev 0-3 c) ev CM (rad) 1.58 ev 1 ev d) DCS for excitation to the first three vibrationally states from the ground state. ISSI, Bern, 09/009

21 Recombination rate (10 Collisionally assisted diatomic association (also known as three-body recombination) Recombination rate (10-31 cm 6 /s) Two atoms (or ion-atom) associate in presence of a third particle which relaxes the excess energy and momentum. Possible processes: H (HH) -> H H direct association -> HH charge transfer association H(H H) -> H H charge transfer association -> HH direct association Range of values: 5x x10-34 (00-0,000K) Krstic et al, JPBL 36, L49 (003) -3 cm 6 /s) H (HH) { T=1000 K H H () HH () (a) 10 0 H H Classical theory, Orel (1987) (HHH) Tot. (H, H ) Exp., HHH Jacobs (1967) Dominance of the H creation in both cases 10 0 H (HH) H H ISSI, Bern, 09/009 Managed by 10UT-Battelle -1 = for the Department of Energy Tot. H H (b) OFES T (K)

22 Cross Section (a.u.) Cross Section (a.u.) Interplay of transport and inelastic processes HH 10 H H (=0) ct =4 v= vib mt vi mt vib vi ν=0 mt ν=7 =7 E CM (ev) dis ct ct vib dis vi dis a) b) vib vi E CM (ev) dis ct mt v=1 =1 c) d) 8/1/

23 Cross Section (a.u.) Cross Section (a.u.) 10 ct HH (=0) vi vib ct =4 v= vib mt mt 10 0 v=0 dis dis vi ct = vib mt vi dis a) b) vi dis vib ct mt =15 v=7 v= c) d) E CM (ev) E CM (ev) 8/1/ 3

24 ALL DATA AND RELEVANT PUBLICATIONS AT WWW-CFADC.PHY.ORNL.GOV (several thousands vib resolved cross sections in tabular and graphical form) CFADC=Controlled Fusion Atomic Data Center Also in ALADDIN 8/1/ 4

25 REFERENCES: [1] R. K. Janev, D. Reiter, and U. Samm, Collision Processes in Low-temperature Hydrogen Plasmas ( or 003). [] P. S. Krstic, Inelastic Processes from Vibrationally Excited States in Slow H H and H H Collisions: Excitations and Charge Transfer, Phys. Rev. A 66, (00). [3] P. S. Krstic and R. K. Janev, Inelastic Processes from Vibrationally Excited States in Slow H H and H H Colliesions. II. Dissociation, Phys. Rev. A 67, 0708 (003). [4] Krstic, PS; Janev, RK; Schultz, DR, Three-body, diatomic association in cold hydrogen plasmas, J. Phys. B 36 (16), L49-L55 (003). [5] P. S. Krstic and D. R. Schultz, "Elastic Processes Involving Vibrationally Excited Molecules in Cold Hydrogen Plasmas," J. Phys. B 36, (003). [6] D.W. Savin, P.S. Krstić, Z. Haiman, and P.C. Stancil, Rate coefficient for H H (X 1 Σ g, ν=0, J=0) H(1s) H charge transfer and some cosmological implications, Astrophys. J. 606, L167 (004). [7] A. Ichihara, O. Iwamoto, and R. K. Janev, "Cross Sections for the Reaction H H(v=0-14) H H at Low Collision Energies," J. Phys. B. 33, (000). [8] P.S. Krstić, Vibrationally resolved collisions in cold hydrogen plasma, Nucl. Instrum. Methods Phys. Res. B 41, 58 (005).

26 CT Rate Coefficient (cm 3 /s) New Results: Fully quantum-mechanical treatment (vib, rot, electronic) at low energies! 1 l( l 1) j( j 1) JM E G (, ) lj R r R r R r lj V ( R, r, g ) j ' l ' G ( R, r) l' j' cosg Rr ˆ ˆ JM l' j' R=reactive, r =vibrational coordinates v= v=0 (normalized to the threshold energy) v= H H (v) -> H(1s) H T(K)

27 Relevant references for ALADDIN database 1980, 1983, 1987, 1989, 1990, 1993, 1998, 00, , 006 Need to come by the end of CRP with evaluation and recommendation for the state-of-the-art H, He database that will carry the quality of the nd decade of 1 st century