Relativistic Modeling of Ultra-Short Electron Pulse Propagation
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Relativistic Modeling of Ultra-Short Electron Pulse Propagation1 I. V. Kochikova, R. J. Dwayne Millerb,c, and A. A. Ischenkod,* a
b
Moscow State University, Research Computing Center, Moscow, 119991 Russia The Max Planck Institute for the Structure and Dynamics of Matter, Hamburg Centre for Ultrafast Imaging, Hamburg, 22761 Germany c Departments of Chemistry and Physics, University of Toronto, M5S 3H6 Toronto, Canada d Russian Technological University MIREA, Moscow, 119571 Russia * e-mail: [email protected] Received June 29, 2018; revised September 14, 2018; accepted September 17, 2018
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 = 10000 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 meanfield model suggested in [13] has been extended to arbitrarily fast relativistic electron pulses with good correspondence to direct dynamic modeling. DOI: 10.1134/S1063776119020201
1. INTRODUCTION The determination of the characteristics of the structural dynamics of matter with a high space-time resolution opens a new understanding of the triad “structure-dynamics-function” in physics, chemistry, biology, and materials science (see reviews [1–4]). The ultrafast electron microscopy, electron diffraction, electron crystallography and nanocrystallography methods opened the possibility of stud
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