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1Kansas State UniversityApril 2nd, 2003
Dynamics and Radiation in Dynamics and Radiation in Ultra-intense Laser-Ion Ultra-intense Laser-Ion
InteractionsInteractions
Suxing HuSuxing Hu
Department of Physics & Astronomy, University of Department of Physics & Astronomy, University of Nebraska-Lincoln, NE 68588-0111Nebraska-Lincoln, NE 68588-0111
April 2nd, 2003 Kansas State University 2
Work done in cooperation withWork done in cooperation with
• Anthony F. Starace (University of Nebraska-University of Nebraska-
LincolnLincoln), ), Supported by DOE and NSFSupported 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.
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OutlineOutline
• 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
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IntroductionIntroduction
• 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 ?
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Motivations of our researchMotivations of our research
• Exploring relativistic dynamics of intense laser-ion interactions: Lorentz forceLorentz force; Spin Spin effectseffects; Relativistic Stark shiftRelativistic Stark shift ..….
• Extending the short wavelength limit of coherent radiations: Ultra-high harmonic Ultra-high harmonic generationgeneration & Nontunnelling harmonicsNontunnelling harmonics…
• Studying the laser acceleration of charged particle: Table-top laser acceleratorTable-top laser accelerator (HCIs targets) ?
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Numerical &Analytical MethodsNumerical &Analytical Methods
1. Quantum-Mechanical Calculations• Using the Foldy-Wouthuysen expansion of the
Dirac equation.• Using the weakly relativistic Schrödinger
equation• Fully Dirac equation……
2. Analytical Approach: Relativistic strong-field approximation (RSFA)
3. 3D relativistic classical Monte-Carlo method
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The Foldy-Wouthuysen Expansion of The Foldy-Wouthuysen Expansion of the Dirac Equationthe 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.
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The Weakly Relativistic SchrThe Weakly Relativistic Schrödinger Equationödinger 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)
HH1 1 = H= H11(p(px x ,p,pzz); H); H2 2 = H= H22(x,z,t); H(x,z,t); H3 3 == HH33(p(px x ,z,t),z,t)
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3D Relativistic Classical Monte-Carlo Method3D 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 +pBL/c)• Repeat the second step until a statistically unchanged result is obtained.
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Relativistic Effects: Lorentz forceRelativistic Effects: Lorentz force• The laser Lorentz force (v/c) induces a “light pressure” along
its propagating direction.
S.X.Hu & C.H. Keitel, Europhys. Lett. 47, 318 (1999)
1017W/cm2; 248nm; Be3+
H0=[p+A(z,t)/c]2/2 +V(x,z)
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Relativistic Effects: Spin-flippingRelativistic Effects: Spin-flipping• Laser-induced spin flipping was observed.
7×1016W/cm2
527nm model Al12+
H=H0+.B/2c
H=H0+HP+Hkin+HD+Hso
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Relativistic Effects: Spin-orbit splittingRelativistic Effects: Spin-orbit splitting• Enhanced spin-orbit coupling can be measured from
the radiation spectrum.
7×1016W/cm2
527nm model Al12+
S.X.Hu & C.H. Keitel, Phys. Rev. Lett. 83, 4709 (1999)
H=H0+ HP
H=H0+HP+Hkin+HD+Hso
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““Relativistic Stark Shift” of RadiationsRelativistic Stark Shift” of Radiations7×1016W/cm2 ; 527nm; a model ion of Mg11+
|1e> |g>
H=H0H=H0+Hkin
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““Relativistic Stark Shift” of RadiationsRelativistic Stark Shift” of Radiations
|2e> |g>
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““Relativistic Stark Shift” of RadiationsRelativistic Stark Shift” of Radiations
|4e> |g>
S.X.Hu & C.H. Keitel, Phys. Rev. A.63, 053402 (2001)
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Relativistic Correction to Kinetic Energy: Relativistic Correction to Kinetic Energy: “the mass increase term”“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.
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High-order Harmonic Generation (HHG) High-order Harmonic Generation (HHG) from Ionsfrom Ions
Tunnelling - Recombination
Ip+3.17Up
The ponderomotive energy
Up=E2/42
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Analytical Study of Ultrahigh Harmonics Analytical Study of Ultrahigh Harmonics (tunnelling)(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)
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Relativistic Ultrahigh HarmonicsRelativistic Ultrahigh Harmonics
D.B.Milosevic, S.X.Hu, & W.Becker, Phys. Rev. A 63, 011403(R) (2001)
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““Nontunnelling” High-order HarmonicsNontunnelling” 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 ?
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New Plateau in Nontunneling HarmonicsNew Plateau in Nontunneling Harmonics • The weakly relativistic Schrödinger equation is applied to
numerically study radiations from intense laser-driven ions.
1.31018 W/cm2
=248nmModel ion of N6+
S.X.Hu et.al., Phys. Rev. A 64, 013410 (2001)
H=V(x,z)+[p+A(z,t)/c]2/2 -[p+A(z,t)/c]4/8c2
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Plateau Behavior of Nontunneling HarmonicsPlateau Behavior of Nontunneling Harmonics
1. 91018 W/cm2 ; =248nm ; Model ion O7+
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Temporal Information of Nontunneling HHGTemporal Information of Nontunneling HHG
1.91018 W/cm2 ; =248nm ; Model ion of O7+
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““Surfing Mechanism” of Nontunneling HHGSurfing Mechanism” of Nontunneling HHG
S.X.Hu, A. F. Starace, W. Becker et. al., J. Phys. B 35, 627 (2002)
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Low orders of Nontunneling HarmonicsLow orders of Nontunneling Harmonics
Starting inside the potential barrier, the electron gains small energy !!
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““Surfing Mechanism” for |1e> electronsSurfing Mechanism” for |1e> electrons
Harmonic order
•Electron on state |1e> may also “surf” the effective potential !!
•The first excited state |1e> is below the barrier.
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High-Efficiency of Nontunneling HHGHigh-Efficiency of Nontunneling HHG• High efficiency: Inner-atomic dynamics
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““Tabletop Laser Accelerator” ?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 toIn the laser focus, the electric field is high up to ~ 10~ 101212 V/cm V/cm !! !! And the magnetic field is of the order ofAnd the magnetic field is of the order of ~ 10~ 101010 Gauss Gauss !!! !!!
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Free electrons as targetsFree electrons as targets
Laser intensity 8×1021W/cm2; =1054nm; ~50fs pulse duration;
beam waist 10m.
Free electrons leave the laser focusarea before it “sees” the peak intensity !
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How to make electrons “see” the peak intensityHow 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 !
There will be big problems for “timing” ultra-short (less than 100fs) laser pulses !!
How about highly-charged ions as targets ?How about highly-charged ions as targets ?
Tightly bound
electron may
survive the
pulse turn-on
!!
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[ Note: “ Any charge state of any atom can be produced” ---- J.D. Gillaspy J. Phys. B34, R93 (2001) ]
Highly charged ions (VHighly charged ions (V22+22+) as targets) as targets
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Laser field ELaser field EL L “felt” by the electron“felt” by the electron
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Electron energy vs. interaction timeElectron energy vs. interaction time
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3D Monte-Carlo results for V3D Monte-Carlo results for V22+22+
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)
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ConclusionsConclusions•Relativistic effects are shown in our calculations.
• We characterized radiations from laser-ion interactions.
B-field-induced “hole” enhanced spin-orbit splitting
“relativistic Stark shift”
Relativistic effects on ultra-high tunnelling HHG
New plateau in nontunnelling 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.
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