Electron vortex beams in nonuniform magnetic fields

Melkani, Abhijeet; Enk, S. J. van

doi:10.1103/physrevresearch.3.033060

Cited by 6 publications

(2 citation statements)

References 55 publications

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“…The natural framework to study the intrinsic OAM of the electron beam is, however, not the Schrödinger but the Dirac equation. The first vortex-like solution of this equation for freely moving electrons in the form of the non-diffractive Bessel beam was obtained in [44], followed by those in various external fields [45][46][47][48][49][50][51].…”

Section: Introductionmentioning

confidence: 99%

Paraxial Dirac equation

Radożycki

2023

Proc. R. Soc. A.

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In this work, the paraxial approximation of the free Dirac equation is examined. The results are first obtained by constructing superpositions of exact solutions with suitable profiles, which are borrowed from paraxial optics. In this manner, the paraxial Dirac beams are obtained in four cases: as Gaussian, Bessel-Gaussian, modified Bessel-Gaussian and elegant Laguerre-Gaussian beams. In the second part of the work, the paraxial Dirac equation is derived, and then its solutions in the aforementioned cases are directly obtained. All the resulting wave functions conform to those derived formerly by virtue of superpositions, except for terms that are negligible upon the assumption that the paraxial functions along the propagation axis vary only slightly over a distance equal to the de Broglie wavelength, which is the standard paraxial requirement.

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Section: Introductionmentioning

confidence: 99%

Paraxial Dirac equation

Radożycki

2023

Proc. R. Soc. A.

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“…However, the dynamics of charged particles with the phase vortices in a lattice that consists of a set of drifts and magnetic lenses have not been investigated previously in detail. The problem was studied excessively in the paraxial approximation for the homogeneous [15][16][17][18][19] as well as for the case of inhomogeneous fields [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Evolution of the accelerated charged vortex particle in an inhomogeneous magnetic lens

Baturin¹,

Grosman²,

Sizykh³

et al. 2022

Preprint

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We present a detailed analysis of the capture and acceleration of a non-relativistic charged vortex particle (electron, positron, proton, etc.) with an orbital angular momentum in a field of an axisymmetric electromagnetic lens, typical for a linear accelerator. We account for the acceleration as well as for the inhomogeneity of both electric and magnetic fields that may arise from some reallife imperfections. We establish conditions when the wave packet can be captured and successfully transported through the lens. We describe the transition process and explain how a free Laguerre-Gaussian packet could be captured into the Landau state of the lens preserving its structure for all moments in time. Several representative examples are provided to illustrate developed formalism.

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Nonstationary Laguerre–Gaussian states in a Magnetic Field

Sizykh,

Chaikovskaia,

Grosman

et al. 2024

Progress of Theoretical and Experimental Physics

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The Landau states of electrons with orbital angular momentum in magnetic fields are important in the quantum theories of metals and of synchrotron radiation at storage rings, in relativistic astrophysics of neutron stars, and in many other areas. In realistic scenarios, electrons are often born inside the field or injected from a field-free region, requiring nonstationary quantum states to account for boundary or initial conditions. This study presents nonstationary Laguerre-Gaussian (NSLG) states in a longitudinal magnetic field, characterizing vortex electrons after their transfer from vacuum to the field. Comparisons with Landau states and calculations of observables such as mean energy and r.m.s. radius show that the r.m.s. radius of the electron packet in the NSLG state oscillates in time around a significantly larger value than that of the Landau state. This quantum effect of oscillations is due to boundary conditions and can potentially be observed in various problems, particularly when using magnetic lenses of electron microscopes and linear accelerators. Analogies are drawn between a quantum wave packet and a classical beam of many particles in phase space, including the calculation of mean emittance of the NSLG state as a measure of their quantum nature.

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Electron vortex beams in nonuniform magnetic fields

Cited by 6 publications

References 55 publications

Paraxial Dirac equation

Paraxial Dirac equation

Evolution of the accelerated charged vortex particle in an inhomogeneous magnetic lens

Nonstationary Laguerre–Gaussian states in a Magnetic Field

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