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

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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

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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

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General dynamics scheme

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Contents

1.Motivation2.Basic assumptions and approximations3.Master equations for electron density dynamics4.Numerical results5.Discussion & outlook

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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

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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

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Contents

1.Motivation2.Basic assumptions and approximations3.Master equations for electron density dynamics4.Numerical results5.Discussion & outlook

Atomic population probabilities Pλ(t)

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Atomic population probabilities Pλ(t)

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Evolution of the atomic scattering factor

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Evolution of the atomic scattering factor

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Evolution of the atomic scattering factor

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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

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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)

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- non-expensive based on basic principles

- rates and cross-sections are fully analytical

Acknowledgements

This work was supported by the BMBF under 05K10PSA

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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 !