Dynamics and Radiation in Ultra-intense Laser-Ion Interactions

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.


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


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 ?


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) ?


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


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.


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)


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.


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)


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


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


““Relativistic Stark Shift” of RadiationsRelativistic Stark Shift” of Radiations7×1016W/cm2 ; 527nm; a model ion of Mg11+

|1e> |g>

H=H0H=H0+Hkin


““Relativistic Stark Shift” of RadiationsRelativistic Stark Shift” of Radiations

|2e> |g>


““Relativistic Stark Shift” of RadiationsRelativistic Stark Shift” of Radiations

|4e> |g>

S.X.Hu & C.H. Keitel, Phys. Rev. A.63, 053402 (2001)


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.


High-order Harmonic Generation (HHG) High-order Harmonic Generation (HHG) from Ionsfrom Ions

Tunnelling - Recombination

Ip+3.17Up

The ponderomotive energy

Up=E2/42


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)


Relativistic Ultrahigh HarmonicsRelativistic Ultrahigh Harmonics

D.B.Milosevic, S.X.Hu, & W.Becker, Phys. Rev. A 63, 011403(R) (2001)


““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 ?


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


Plateau Behavior of Nontunneling HarmonicsPlateau Behavior of Nontunneling Harmonics

1. 91018 W/cm2 ; =248nm ; Model ion O7+


Temporal Information of Nontunneling HHGTemporal Information of Nontunneling HHG

1.91018 W/cm2 ; =248nm ; Model ion of O7+


““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)


Low orders of Nontunneling HarmonicsLow orders of Nontunneling Harmonics

Starting inside the potential barrier, the electron gains small energy !!


““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.


High-Efficiency of Nontunneling HHGHigh-Efficiency of Nontunneling HHG• High efficiency: Inner-atomic dynamics


““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 !!! !!!


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 !


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

!!


[ 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


Laser field ELaser field EL L “felt” by the electron“felt” by the electron


Electron energy vs. interaction timeElectron energy vs. interaction time


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)


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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Dynamics and Radiation in Ultra-intense Laser-Ion Interactions