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Relativistic Modeling of Ultra-Short Electron Pulse Propagation

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Miller,  R. J. D.
Miller Group, Atomically Resolved Dynamics Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Hamburg Centre for Ultrafast Imaging;
Departments of Chemistry and Physics, University of Toronto;

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Citation

Kochikov, I. V., Miller, R. J. D., & Ischenko, A. A. (2019). Relativistic Modeling of Ultra-Short Electron Pulse Propagation. Journal of Experimental and Theoretical Physics - JETP, 128(3), 333-340. doi:10.1134/S1063776119020201.


Cite as: http://hdl.handle.net/21.11116/0000-0003-BD3C-6
Abstract
The ultrafast electron microscopy, electron diffraction, electron crystallography, and nanocrystallography methods opened the possibility of studying the coherent structural dynamics of matter. The time resolution of the ultrafast electron microscopy and electron diffraction methods determined by the duration of electron pulses is the key parameter of experimental setups. This paper treats electron pulse dynamics in the field free drift region specifically for applications in atomic imaging. The electron beam is modeled as a system of particles (N) with N = 1000 and N = 10 000 electrons. The beam propagates for a certain period of time (1–4 ns); during its propagation, electron distribution parameters (over coordinates and velocities) are calculated to characterize the temporal profile and uncertainty in the electron wavelength at the sample. The results of applying relativistic dynamic equations show that nonrelativistic results are satisfactorily applicable (with 15 per cent or better accuracy) for modeling short electron pulse elongation and broadening at 30 keV and lower energies. However, the results of such modeling may be significantly in error for intermediate energies (300 keV), and for the fast relativistic beams (3 MeV) they become completely wrong. The relative reduction in Coulomb repulsion effects at higher energies is known, however; we give a comprehensive treatment that allows a quantitative picture. Using high-energy electron pulses results in almost complete elimination of the repulsive Coulomb effect. Dispersion of electron velocities becomes much lower at higher energies. For 3 MeV electrons, electron pulse duration as well as its radius does not noticeably change even after traveling for 4 ns (1.2 m). Even at 300 keV, the pulse duration increase is negligible until 1 ns (0.2 m). A simple mean-field model suggested in [13] has been extended to arbitrarily fast relativistic electron pulses with good correspondence to direct dynamic modeling.