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Rescattering ionization of D 2 + in intense laser pulses

Rescattering ionization of D 2 + in intense laser pulses. M.Benis, A.Alnaser, T.Osipov, A.Wech, C.Wyant, J.Stuhlman, Erge Edgu-Fry, Z.Chang, B.Shan, C.Wang, M.Wells, A.Rankin, C.L.Cocke Purpose: To reveal rescattering ionization of a molecule in an intense laser pulse or

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Rescattering ionization of D 2 + in intense laser pulses

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  1. Rescattering ionization of D2+ in intense laser pulses M.Benis, A.Alnaser, T.Osipov, A.Wech, C.Wyant, J.Stuhlman, Erge Edgu-Fry, Z.Chang, B.Shan, C.Wang, M.Wells, A.Rankin, C.L.Cocke Purpose: To reveal rescattering ionization of a molecule in an intense laser pulse or To explain the confusing results we got two years ago in a precursor experiment at Berleley. Questions: What experiment was that? What is rescattering? What do these have to do with each other? How to stimulate theoretical attention?

  2. What experiment was that? Observation of a nearly isotropic, high-energy Coulomb explosion group in the fragmentation of D2 by short laser pulses A. Staudte,1 C. L. Cocke,2 M. H. Prior,3 A. Belkacem,3 C. Ray,3 H. W. Chong,3 T. E. Glover,3 R. W. Schoenlein,3 and U. Saalmann4 1Institut fu¨r Kernphysik, University of Frankfurt, Frankfurt, Germany 2Physics Department, Kansas State University, Manhattan, Kansas 66506-2601 3Lawrence Berkeley Laboratory, Berkeley, California 94720 4Max-Planck-Institut fu¨r Physik Komplexer Systeme, No¨thnitzer Strasse 38, 01187 Dresden, Germany ~Received 12 September 2001; published 18 January 2002 We have used momentum spectroscopy to examine the production of deuteron pairs in the double ionization of D2 molecules by a fast (200 fs), moderately intense (0.65– 8.0)x1014 W/cm2laser pulses. By measuring in coincidence the momentum vectors of both deuterons, we have isolated, at the lowest laser power density, a weak ionization channel characterized by Coulomb-explosion deuterons with a sum energy near 10 eV. This is much higher than has been seen in previous studies. The angular distribution of these deuterons is nearly isotropic, in contrast to previous observations that the deuterons are strongly peaked along the laser polarization. These new observations suggest a previously unobserved ionization mechanism. PHYSICAL REVIEW A, VOLUME 65, 020703~R!

  3. :the apparatus

  4. Time of flight spectra of d+ ions counts counts time of flight [ns] time of flight [ns] 1.5 x 1014 W/cm2 t=100 fs 8 x 1014 W/cm2 t=100 fs

  5. The data: d+ spectra I.Reiser, Ph.D.thesis Second step CREI Dissociation to d and d+: BS and ATI First step Double ionization to d+ and d+: CREI (or CE) Frazinski et al, PRL 83, 3625 HD+ protons BS/ATI

  6. CREI

  7. Staudte et al.:the energy distributions ??? CREI

  8. Staudte et al.:angular distributions What is this? CREI

  9. Meanwhile , in atoms, non-sequential… Non sequential

  10. Rescattering:the electron returns with energy Maximum return energy 3.17 Up at phase of 0.32

  11. The NS can be interpreted as due to rescattering

  12. The KSU experiment

  13. New parameters THE KSU LIGHT SOURCE Zenghu Chang and gang… Pulse length 25 fs-50 fs (?) Intensity 0.8-3 x 10 14 w/cm2 Polarization variable Cold gas jet

  14. The data: d+ d+ ion coincidences 20 Ion pair energy (eV) 0

  15. Look at polarization effect on CREI 100 a.u. 25 a.u. Sum Energy (eV) 0 20 4 Sum Energy (eV) 0 20 Py Py Ptotal Px Ptotal Px Pz Pz Pz Pz Py Px Py Px Circular polarization Linear polarization y y x x z z CREI

  16. The effect of circular polarization Linear polarization Circular polarization KER (units of 0.1 eV) Ptot (units of 0.1 a.u.) Energy (units of 0.1 eV)

  17. Linear polarization Circular polarization KER (units of 0.1 eV) Ptot (units of 0.1 a.u.) Energy (units of 0.1 eV)

  18. Or another presentation…

  19. The ellipticity dependence

  20. General character of results Spectra at various peak laser intensities (in units of 10 14 w/cm2 ) 1.5 1.1 Rescattering 20 0 1.2 1.6 Coulomb explosion: CREI Ion sum energy (eV) 20 0 2.5 1.3 20 0 cos(q) 1 -1 cos(q) -1 1

  21. Two ways to separate the rescattering contribution Linear polarization Circular polarization Relative intensity Difference Angle selected 40 0 40 0 20 20 Ion sum energy (eV)

  22. The real energy spectra

  23. Probabilities What is the probability for a rescattering event? How does the rescattering ionization compete with CREI?

  24. Can we build a model? • Idea: • The electron is created at around 17 degrees of phase in the ionization of D2 • A vibrational wave packet is created in the 1sg potential curve of the D2+ molecule starting at 1.4 a.u. • Meanwhile the electron returns to the molecule after 1.35 fs (times an integer) and reionizes the molecule into d+ and d+. • Problem: At 1 x 10 14 w/cm 2 the Up is only 6eV; FC ionization energy is 26 eV.

  25. Nikura et al., Nature 417,917(2002)

  26. Nikura et al., Nature 417,917 (2002)a

  27. Can we build model for double ionization? • Idea: • The electron is created at around 17 degrees of phase in the ionization of D2 • A vibrational wave packet is created in the 1sg potential curve of the D2+ molecule starting at 1.4 a.u. • Meanwhile the electron returns to the molecule after 1.35 fs (times an integer) and reionizes the molecule into d+ and d+. • Problem: At 1 x 10 14 w/cm2 the Up is only 6eV; FC ionization energy is 26 eV. • -Solution: the returning electron does not directly ionize the D2+, it just excites it to a state from which the laser field immediately removes it.

  28. Schematic 20 eV 10 eV Laser/res? Rescattering Tunneling

  29. How to evaluate model -The returning electron has a maximal energy of 3.17 Up -The cross section for ionization is given by an analytic expression which fits e + H(1s) -> e’ + H(2p) and which is an analytic function of Ip, the excitation energy. In this case Ip is a function of R and is the 1sg-2pu energy separation. - The vibrational wave packet is taken to be a delta function at the classical position of a classical particle moving in the 1sg potential curve. -The returning electron wave packet spreads according to a transverse velocity imparted to the electron in the initial step. -At each return, the excitation probability is given by the product of the excitation cross section for the R times the inverse square of the radius of the returning electron wave packet. -If the D2+ is excited, it immediately goes further into the d+ d+ continuum.

  30. How to evaluate model1 -The returning electron has a maximal energy of 3.17 Up 3.17 Up

  31. How to evaluate model2 -The cross section for ionization is given by an analytic expression which fits e + H(1s) -> e’ + H(2p) and which is an analytic function of Ip, the excitation energy. In this case Ip is a function of R and is the 1sg-2pu energy separation. . Long discussion about dielectronic resonances and electron energy in internal region and inelastic scattering from an ion!

  32. How to evaluate model3 . - The vibrational wave packet is taken to be a delta function at the classical position of a classical particle moving in the 1sg potential curve. Well, not really, because in the end I folded the resulting energy spectrum Into a Gaussian to take into account the finite width of the wave packet. See Several nice movies batting about , such as at http://www.mpipks-dresden.mpg.de/~us/h2+/

  33. How to evaluate model4 -The returning electron wave packet spreads according to a transverse velocity imparted to the electron in the initial step. y= a+ v(transverse)t v(transverse) = .08 a.u. -At each return, the excitation probability is given by the product of the excitation cross section for the R times the inverse square of the radius of the returning electron wave packet. P= n (electrons/area) * sigma for excitation (area) Where n = 1/y2

  34. Results Not averaged over Interaction volume!

  35. Oops, the most recent results Stay tuned…..

  36. Summary -The rescattering mechanism for double ionization of D2 is clearly identified. -It is quite competitive with CREI at low intensities, but grows less rapidly than CREI. It cannot be seen in singles spectra because of competing processes. -The general characteristics: Energy distributions Order of magnitude of probability Angular behaviour are consistent with a simple model of rescattering process. -We need a solution to the two electron Schroedinger equation for this process.

  37. Energy and angular density plots and projections Laser power: Low Medium High 20 E1+E2 [eV] 10 0 High energy Medium energy Low energy cos()

  38. Vibrational wave packet (Ulf Saalman)

  39. Some basic parameters Collisions: Bohr parameter k = Z1Z2 e2 / hv Small k : Perturbative Large k : Classical (Decorated) Born approximation Over-barrier,CTMC, tunnelling,… Pulsed Laser: Keldysh parameter g= [Ub/2 Up] ½ Large g : Perturbative Small g : Classical High order perturbation, Tunnelling,Over-barrier, Multiphoton Rescattering,…

  40. Better .prn postscript figures of some of these are Available in laserpapers.zip archive.

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