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Dynamics and Radiation in Ultra-intense Laser-Ion Interactions

Dynamics and Radiation in Ultra-intense Laser-Ion Interactions. Suxing Hu Department of Physics & Astronomy, University of Nebraska-Lincoln, NE 68588-0111. Work done in cooperation with. Anthony F. Starace ( University of Nebraska-Lincoln ), Supported by DOE and NSF .

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Dynamics and Radiation in Ultra-intense Laser-Ion Interactions

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  1. Dynamics and Radiation in Ultra-intense Laser-Ion Interactions Suxing Hu Department of Physics & Astronomy, University of Nebraska-Lincoln, NE 68588-0111 Kansas State University

  2. Work done in cooperation with • Anthony F. Starace (University of Nebraska-Lincoln), Supported by DOE and NSF. • Wilhelm Becker & Wolfgang Sandner (Max-Born-Institut, Berlin), Supported by The Alexander von Humboldt Foundation. • Christoph H. Keitel( University of Freiburg, Germany), Supported by German SFB-276. Kansas State University

  3. Outline • Introduction • Numerical & Analytical Methods • Relativistic Effects in Intense Laser Interaction with Multiply-Charged Ions • “Nontunnelling” High-order Harmonic Generation • Ultra-energetic GeV Electrons from Super-strong Laser Interactions with Highly-Charged Ions • Conclusion Kansas State University

  4. Introduction • From Terawatt (TW) to even Petawatt (1015 W) laser systems become available recently in labs. Focused laser intensity may be high up to ~ 1022 W/cm2 (E ~500 atomic units) ! • Tens of electrons can be stripped from neutral atoms under the irradiation of such ultra-intense laser pulse! • Highly-charged ions (HCIs) may be produced in a variety of ways: i.e., EBIT, Intense laser-cluster interactions. • What happens to super-strong laser interactions with highly-charged ions ? Kansas State University

  5. Motivations of our research • Exploring relativistic dynamics of intense laser-ion interactions: Lorentz force; Spin effects; Relativistic Stark shift ..…. • Extending the short wavelength limit of coherent radiations: Ultra-high harmonic generation & Nontunnelling harmonics… • Studying the laser acceleration of charged particle: Table-top laser accelerator (HCIs targets) ? Kansas State University

  6. Numerical &Analytical Methods • Quantum-Mechanical Calculations • Using the Foldy-Wouthuysen expansion of the Dirac equation. • Using the weakly relativistic Schrödinger equation • Fully Dirac equation…… • Analytical Approach: Relativistic strong-field approximation (RSFA) • 3D relativistic classical Monte-Carlo method Kansas State University

  7. The Foldy-Wouthuysen Expansion of the Dirac Equation • The Hamiltonian (up to ~1/c2 terms; neglect O(1/c4)) • Split-operator algorithm is applied to solve the time-dependent • equation of motion. Kansas State University

  8. The Weakly Relativistic Schrödinger Equation • Expanding the Klein-Gordon Hamiltonian up to the order of 1/c2 by neglecting electron spin. • Split-operator algorithm: • Ψ(x,z,t+Δt)=exp[-iH1Δt/2] exp[-iH3Δt/2] exp[-iH2Δt/2] •  exp[-iH3Δt/2] exp[-iH1Δt/2]  Ψ(x,z,t) • H1 = H1(px ,pz); H2 = H2(x,z,t); H3 =H3(px ,z,t) Kansas State University

  9. 3D Relativistic Classical Monte-Carlo Method • Preparing a so-called “micro-canonical ensemble” (mimics the initial quantum state). • Numerically integrate the relativistic Newton’s equation with initial condition randomly chosen from the ensemble. dr /dt = p/ dp /dt = - (EL+EC +pBL/c) • Repeat the second step until a statistically • unchanged result is obtained. Kansas State University

  10. Relativistic Effects: Lorentz force H0=[p+A(z,t)/c]2/2 +V(x,z) • The laser Lorentz force (v/c) induces a “light pressure” along its propagating direction. 1017W/cm2; 248nm; Be3+ S.X.Hu & C.H. Keitel, Europhys. Lett. 47, 318 (1999) Kansas State University

  11. Relativistic Effects: Spin-flipping H=H0+.B/2c • Laser-induced spin flipping was observed. 7×1016W/cm2 527nm model Al12+ H=H0+HP+Hkin+HD+Hso Kansas State University

  12. Relativistic Effects: Spin-orbit splitting H=H0+ HP • Enhanced spin-orbit coupling can be measured from the radiation spectrum. 7×1016W/cm2 527nm model Al12+ H=H0+HP+Hkin+HD+Hso S.X.Hu & C.H. Keitel, Phys. Rev. Lett. 83, 4709 (1999) Kansas State University

  13. “Relativistic Stark Shift” of Radiations 7×1016W/cm2 ; 527nm; a model ion of Mg11+ H=H0+Hkin H=H0 |1e>  |g> Kansas State University

  14. “Relativistic Stark Shift” of Radiations |2e>  |g> Kansas State University

  15. “Relativistic Stark Shift” of Radiations |4e>  |g> S.X.Hu & C.H. Keitel, Phys. Rev. A.63, 053402 (2001) Kansas State University

  16. Relativistic Correction to Kinetic Energy: “the mass increase term” • This second order correction causes energy-levels a further shift---“relativistic Stark shift”. For a model ion of Mg11+ in an intense laser field. Kansas State University

  17. High-order Harmonic Generation (HHG) from Ions Tunnelling - Recombination Ip+3.17Up The ponderomotive energy Up=E2/42 Kansas State University

  18. Analytical Study of Ultrahigh Harmonics (tunnelling) • With the relativistic strong-field approach, the transition matrix for high-harmonic emission is: where, the interaction potentials are And the Klein-Gordon Volkov-type Green function is D.B.Milosevic, S.X.Hu, & W.Becker, Laser Phys. 12, 389 (2002) Kansas State University

  19. Relativistic Ultrahigh Harmonics D.B.Milosevic, S.X.Hu, & W.Becker, Phys. Rev. A 63, 011403(R) (2001) Kansas State University

  20. “Nontunnelling” High-order Harmonics Due to the large Ip of ions, there may be hundreds of harmonics below Ip/. May some structures develop in this regime ? ? Kansas State University

  21. New Plateau in Nontunneling Harmonics H=V(x,z)+[p+A(z,t)/c]2/2 -[p+A(z,t)/c]4/8c2 • The weakly relativistic Schrödinger equation is applied to numerically study radiations from intense laser-driven ions. 1.31018 W/cm2 =248nm Model ion of N6+ S.X.Hu et.al., Phys. Rev. A 64, 013410 (2001) Kansas State University

  22. Plateau Behavior of Nontunneling Harmonics 1. 91018 W/cm2 ; =248nm ; Model ion O7+ Kansas State University

  23. Temporal Information of Nontunneling HHG 1.91018 W/cm2 ; =248nm ; Model ion of O7+ Kansas State University

  24. “Surfing Mechanism” of Nontunneling HHG S.X.Hu, A. F. Starace, W. Becker et. al., J. Phys. B 35, 627 (2002) Kansas State University

  25. Low orders of Nontunneling Harmonics Starting inside the potential barrier, the electron gains small energy !! Kansas State University

  26. “Surfing Mechanism” for |1e> electrons • The first excited state |1e> is • below the barrier. Harmonic order • Electron on state |1e> may also • “surf” the effective potential !! Kansas State University

  27. High-Efficiency of Nontunneling HHG • High efficiency: Inner-atomic dynamics Kansas State University

  28. “Tabletop Laser Accelerator” ? Petawatt (1015 W) laser: M.D. Perry et al., Opt. Lett. 24, 160 (1999). In the laser focus, the electric field is high up to~ 1012 V/cm !! And the magnetic field is of the order of~ 1010 Gauss !!! Kansas State University

  29. Free electrons as targets Laser intensity 8×1021W/cm2; =1054nm; ~50fs pulse duration; beam waist 10m. Free electrons leave the laser focus area before it “sees” the peak intensity ! Kansas State University

  30. How to make electrons “see” the peak intensity Shooting electrons into the tightly focused laser beam ? Electrons need initially high-energy (~10MeV) to overcome the potential ! Tightly bound electron may survive the pulse turn-on !! There will be big problems for “timing” ultra-short (less than 100fs) laser pulses !! How about highly-charged ions as targets ? Kansas State University

  31. Highly charged ions (V22+) as targets [ Note: “ Any charge state of any atom can be produced” ---- J.D. Gillaspy J. Phys. B34, R93 (2001) ] Kansas State University

  32. Laser field EL “felt” by the electron Kansas State University

  33. Electron energy vs. interaction time Kansas State University

  34. 3D Monte-Carlo results for V22+ 12,000 trajectories are considered, of which ~4000 are ionized. Nearly 60% ionized electrons have an energy  1GeV !! S.X. Hu & A.F. Starace, Phys. Rev. Lett. 88, 245003 (2002) Kansas State University

  35. Conclusions • Relativistic effects are shown in our calculations. B-field-induced “hole” enhanced spin-orbit splitting “relativistic Stark shift” • We characterized radiations from laser-ion interactions. New plateau in nontunnelling HHG Relativistic effects on ultra-high tunnelling HHG The “surfing” mechanism for NHHG • We predicted GeV electrons for HCIs targets. • Ionized electrons can • “surf” on the laser wave thereby being • accelerated to GeV energy. • Tightly bound electrons of HCIs • may survive the pulse turn-on. Kansas State University

  36. Kansas State University

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