Paraxial wave function and Gouy phase for a relativistic electron in a uniform magnetic field

Zou, L.; Zhang, P. M.; Silenko, Alexander J.

doi:10.1088/1361-6471/ab7a88

Cited by 13 publications

(20 citation statements)

References 59 publications

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“…One can also derive this phase from a wave function, which is a solution to the paraxial wave equation in the magnetic field [22]. We see that the condition of paraxiality,…”

Section: Entering the Solenoidmentioning

confidence: 92%

“…In many of these applications, relativistic energies are needed, which are much higher than the current upper limit of ε c ≈ 300 keV achieved with electron microscopes [26][27][28]. Although quantum dynamics of the vortex electrons in electromagnetic fields has been extensively studied in recent years [5][6][7][8][9][10][20][21][22], there is still no clear understanding of whether the OAM is conserved in electric and magnetic lenses, employed in accelerators and electron microscopes for focusing and phase-space manipulations. Here we address this question by pointing out that the OAM of a vortex particle is conserved in a wide class of azimuthally symmetric electric and magnetic fields, while a transverse emittance of the packet is also conserved on average in weakly inhomogeneous -that is, linear -fields, analogously to that of a classical beam [29].…”

Section: Introductionmentioning

confidence: 99%

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Vortex particles in axially symmetric fields and applications of the quantum Busch theorem

Karlovets

2020

Preprint

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The possibilities to accelerate vortex electrons with orbital angular momentum (OAM) to relativistic energies and to produce vortex ions, protons, and other charged particles crucially depend on whether the OAM is conserved during the acceleration and on how phase space of the wave packet evolves. We show that both the OAM and a mean emittance of the packet, the latter obeying the Schrödinger uncertainty relation, are conserved in axially symmetric fields of electric and magnetic lenses, typical for accelerators and electron microscopes, as well as in Penning traps, while a linear approximation of weakly inhomogeneous fields works much better for single packets than for classical beams. We analyze quantum dynamics of the packet's rms radius ρ 2 , relate this dynamics to a generalized form of the van Cittert-Zernike theorem, applicable at arbitrary distances from a source and for non-Gaussian packets, and adapt the Courant-Snyder formalism to describe the evolution of the wave packet's phase space. The vortex particles can therefore be accelerated, focused, steered, trapped, and even stored in azimuthally symmetric fields and traps, somewhat analogously to the classical angular-momentum-dominated beams. Moreover, we give a quantum version of the Busch theorem, which states how one can produce vortex electrons with a magnetized cathode during either field-or photoemission, as well as vortex ions and protons by using a magnetized stripping foil employed to change a charge state of ions. Spatial coherence of the packets plays a crucial role in these applications and we provide the necessary estimates for particles of different masses.

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“…One can also derive this phase from a wave function, which is a solution to the paraxial wave equation in the magnetic field [22]. We see that the condition of paraxiality,…”

Section: Entering the Solenoidmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Vortex particles in axially symmetric fields and applications of the quantum Busch theorem

Karlovets

2020

Preprint

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“…In Ref. [11], the paraxial equation has been determined for relativistic electrons in a uniform magnetic field.…”

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confidence: 99%

Exact quantum-mechanical equations for particle beams

Silenko

2022

Preprint

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The exact quantum-mechanical equations for beams of free particles including photons and for beams of Dirac and spin-1 particles in a uniform magnetic field have been derived. These equations present the exact generalizations of the well-known paraxial equations in optics (exact Helmholtz equation for light beams) and particle physics and of the previously obtained paraxial equation for a Dirac particle in a uniform magnetic field. Some basic properties of exact wave eigenfunctions of particle beams have been determined.

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“…Relativistic wave functions in the FW representation defining the Landau states are based on the nonrelativistic solution [46,47] and are presented, e.g., in Refs. [48,56]. For relativistic particles with a negative charge, the Landau energy levels are defined by (see Ref.…”

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confidence: 99%

Twisted particles in heavy-ion collisions

Silenko¹,

Zhang²,

Zou³

2021

Proceedings of 40th International Conference on High Energy Physics — PoS(ICHEP2020)

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The importance of twisted (vortex) particles in heavy-ion collisions is analyzed. Free twisted particles can possess giant intrinsic orbital angular momenta. Twisted particles are spatially localized and can be rather ubiquitous in laboratories and nature. Twisted photons have nonzero effective masses. Charged twisted particles can be recognized by their dynamics, magnetic moments, and specific effects in external fields.

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Paraxial wave function and Gouy phase for a relativistic electron in a uniform magnetic field

Cited by 13 publications

References 59 publications

Vortex particles in axially symmetric fields and applications of the quantum Busch theorem

Vortex particles in axially symmetric fields and applications of the quantum Busch theorem

Exact quantum-mechanical equations for particle beams

Twisted particles in heavy-ion collisions

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