diffraction of the xfel femtosecond pulse in a crystal belarusian state university a.benediktovich,...
TRANSCRIPT
Diffraction of the XFEL femtosecond pulse in a crystal
BELARUSIANSTATE
UNIVERSITY
A.Benediktovich, I.Feranchuk, A.Leonov, D.Ksenzov, U.Pietsch
The Actual Problems of Microworld PhysicsGomel, July 22-August 2
Contents
1.Motivation2.Basic assumptions and approximations3.Master equations for electron density dynamics4.Numerical results5.Discussion & outlook
Contents
1.Motivation2.Basic assumptions and approximations3.Master equations for electron density dynamics4.Numerical results5.Discussion & outlook
Irradiation of a crystal with XFEL pulse
1 (23)
X-ray Free Electron Laser (XFEL) – the perfect tool to study ultrafast dynamics with Ångström resolution
Recording of the complete diffraction pattern by a single shot is possible
Interaction of the XFEL fs-pulses with a crystal CAN NOT be described in the
framework of the linear response theory because of the time evolution of the
electron density is comparable with the time formation of the diffracted wave!
The time scale we consider
We consider the processes that take place during the passing of the XFEL pulse
through the crystal ( t < 100 fs )
Contents
1.Motivation2.Basic assumptions and approximations3.Master equations for electron density dynamics4.Numerical results5.Discussion & outlook
Energy spectrum of a crystal
Ground state Excited states
IONIZATION ENERGY IN CRYSTAL IS SMALLER THAN THE PHOTON ENERGY
2 (23)
Features of ionization dynamics
Characteristic photoelectron energy:
The mean free path of electrons:
Percentage of remaining free electrons:
THE ROLE OF FREE ELECTRONS SHOULD BE ESSENTIAL
3 (23)
General dynamics scheme
4 (23)
Contents
1.Motivation2.Basic assumptions and approximations3.Master equations for electron density dynamics4.Numerical results5.Discussion & outlook
5 (23)
Model to be considered
Totalsystem
Freeelectrons
EMfield
Beyond the present consideration
Boundelectrons
Atomic state population dynamics
General form of rate equations:
Constituting processes:
- photoionization
- Auger decay
- electron-impact ionization
- three-body recombination
6 (23)
probability of transitionfrom λ to μ configuration
in unit time:
Free electron gas dynamics
The Boltzmann kinetic equation:
Set of simplifications:
- lateral homogeneity:
- anisotropy parameter: =>
- diffusion term:
Reduced Boltzmann equation:
- net force:
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System of master equations
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coupled toONE HAS TO SOLVE THE SYSTEM OF TWO INTEGRO-DIFFERENTIAL EQUATIONS
SIMULTANEOUSLY
Effective charge model
Hydrogen-like wave functions:
Energy of a configuration:ALL CROSS-SECTIONS AND RATES CAN BE CALCULATED ANALYTICALLY
1
9 (23)
Contents
1.Motivation2.Basic assumptions and approximations3.Master equations for electron density dynamics4.Numerical results5.Discussion & outlook
Atomic population probabilities Pλ(t)
10 (23)
Atomic population probabilities Pλ(t)
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Evolution of the atomic scattering factor
12(23)
Evolution of the atomic scattering factor
13 (23)
Evolution of the atomic scattering factor
14 (23)
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Pulse parameters: duration: 40 fs; photon energy: 8 keV; shape: Gaussian; fluence: 104 phs/Å2.
Evolution of the free electron density
Contribution of different channels
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Intensity of the XFEL pulse diffraction
17 (23)
Contents
1.Motivation2.Basic assumptions and approximations3.Master equations for electron density dynamics4.Numerical results5.Discussion & outlook
Discussion and outlook
- the role of free electrons is essential
- three-body recombination rate is extremely low
Numerical algorithm and software are developed
Simulation for the example of Si crystal is carried out
Outlook
- investigation of X-ray optics in the extremely intensive regime- similar calculations are required for description of interaction of
relativistic dense electron bunches with the crystal (in order to use parametric X-ray radiation for compact XFEL sources1)
19(23)
- non-expensive based on basic principles
- rates and cross-sections are fully analytical
Acknowledgements
This work was supported by the BMBF under 05K10PSA
20 (23)
Belarusian State University
• Prof. Dr. Ilya Feranchuk• Dr. Andrei Benediktovitch
Siegen University
• Prof. Dr. Ullrich Pietsch• Dr. Dmitry Ksenzov
Discussions
• Prof. Dr. Robin Santra and members of his group (CFEL, DESY)• Dr. Ivan Vartaniants and members of his group (HASYLAB, DESY)
Collaborators
THANK FOR YOUR ATTENTION !