Dynamics and Radiation in Ultraintense LaserIon Interactions

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Dynamics and Radiation in Ultra-intense Laser-Ion
Interactions

• Suxing Hu
• Department of Physics Astronomy, University of
  Nebraska-Lincoln, NE 68588-0111

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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.

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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

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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 ?

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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) ?

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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

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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.

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The Weakly Relativistic Schrödinger Equation

• Expanding the Klein-Gordon Hamiltonian up to the
  order of 1/c2 by neglecting electron spin.

• Split-operator algorithm
• ?(x,z,t?t)exp-iH1?t/2? exp-iH3?t/2?
  exp-iH2?t/2
• ? exp-iH3?t/2?
  exp-iH1?t/2 ? ?(x,z,t)
• H1 H1(px ,pz) H2 H2(x,z,t) H3 H3(px
  ,z,t)

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3D Relativistic Classical Monte-Carlo Method

• Preparing a so-called micro-canonical ensemble
  (mimics the initial quantum state).
• Numerically integrate the relativistic Newtons
  equation with initial condition randomly chosen
  from the ensemble.

dr /dt p/?
dp /dt - (ELEC p?BL/?c)

• Repeat the second step until a statistically
• unchanged result is obtained.

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Relativistic Effects Lorentz force

• The laser Lorentz force (v??/c) induces a light
  pressure along its propagating direction.

H0pA(z,t)/c2/2 V(x,z)
1017W/cm2 248nm Be3
S.X.Hu C.H. Keitel, Europhys. Lett. 47, 318
(1999)
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Relativistic Effects Spin-flipping

• Laser-induced spin flipping was observed.

HH0?.B/2c
71016W/cm2 527nm model Al12
HH0HPHkinHDHso
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Relativistic Effects Spin-orbit splitting

• Enhanced spin-orbit coupling can be measured from
  the radiation spectrum.

HH0 HP
71016W/cm2 527nm model Al12
HH0HPHkinHDHso
S.X.Hu C.H. Keitel, Phys. Rev. Lett. 83, 4709
(1999)
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Relativistic Stark Shift of Radiations
71016W/cm2 527nm a model ion of Mg11
HH0
HH0Hkin
1egt ? ggt
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Relativistic Stark Shift of Radiations
2egt ? ggt
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Relativistic Stark Shift of Radiations
4egt ? ggt
S.X.Hu C.H. Keitel, Phys. Rev. A.63, 053402
(2001)
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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.
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High-order Harmonic Generation (HHG) from Ions
Tunnelling - Recombination
Ip3.17Up
The ponderomotive energy UpE2/4?2
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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)
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Relativistic Ultrahigh Harmonics
D.B.Milosevic, S.X.Hu, W.Becker, Phys. Rev. A
63, 011403(R) (2001)
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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 ?
?
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New Plateau in Nontunneling Harmonics

• The weakly relativistic Schrödinger equation is
  applied to numerically study radiations from
  intense laser-driven ions.

HV(x,z)pA(z,t)/c2/2 -pA(z,t)/c4/8c2
1.3?1018 W/cm2 ?248nm Model ion of N6
S.X.Hu et.al., Phys. Rev. A 64, 013410 (2001)
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Plateau Behavior of Nontunneling Harmonics
1. 9?1018 W/cm2 ?248nm Model ion O7
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Temporal Information of Nontunneling HHG
1.9?1018 W/cm2 ?248nm Model ion of O7
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Surfing 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 Harmonics

Starting inside the potential barrier, the
electron gains small energy !!
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Surfing Mechanism for 1egt electrons

• The first excited state 1egt is
• below the barrier.

Harmonic order

• Electron on state 1egt may also
• surf the effective potential !!

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High-Efficiency of Nontunneling HHG

• High efficiency Inner-atomic dynamics

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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 !!!
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Free electrons as targets
Laser intensity 81021W/cm2 ?1054nm 50fs
pulse duration beam waist 10?m.
Free electrons leave the laser focus area before
it sees the peak intensity !
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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 ?
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Highly charged ions (V22) as targets

• Note Any charge state of any atom can be
  produced ---- J.D. Gillaspy J.
  Phys. B34, R93 (2001)

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Laser field EL felt by the electron
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Electron energy vs. interaction time
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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)
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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.
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