Siberian snake-like behavior for an orbital polarization of a beam of twisted (vortex) electrons

TL;DR

This paper demonstrates that twisted electrons with orbital angular momentum exhibit Siberian snake-like behavior, maintaining their orbital polarization in magnetic fields, which simplifies their acceleration in cyclotrons for high-energy physics.

Contribution

It introduces the concept of Siberian snake-like behavior for orbital polarization of twisted electrons, enabling stable polarization during acceleration in cyclotrons.

Findings

Orbital polarization of twisted electrons is unaffected by magnetic field perturbations.

Siberian snake-like behavior enables stable orbital polarization in cyclotrons.

Simplifies the acceleration process of twisted electron beams in high-energy physics applications.

Abstract

The orbital polarization of twisted electrons carrying an intrinsic orbital angular momentum is not influenced by field perturbations in arbitrary magnetic fields. This property means an existence of the Siberian snake-like behavior for an orbital polarization of a beam of twisted electrons in cyclotrons with the main magnetic field and magnetic focusing. As a result, the acceleration of twisted electron beams in cyclotrons necessary for their applications in high-energy-physics experiments considerably simplifies.

Equations

$$\begin{array}[]{c}\frac{d\bm{L}}{dt}=\bm{\Omega}\times\bm{L},\qquad\bm{\Omega}=-\frac{e}{2mc\gamma}\left(\bm{B}-\bm{\beta}\times\bm{E}\right),\end{array}$$

$$\begin{array}[]{c}\frac{d\bm{N}}{dt}=\bm{\omega}\times\bm{N},\qquad\bm{\omega}=-\frac{e}{mc\gamma}\left(\bm{B}-\frac{\bm{\beta}\times\bm{E}}{\beta}\right),\end{array}$$

$$\mathbf{\omega }=2\mathbf{\Omega }$$

Full text

Twisted (vortex) electrons which existence has been predicted in Ref. Bliokh2007 are Dirac particles carrying an intrinsic orbital angular momentum (OAM). They have been discovered in 2010 UTV . Since such electrons possess large magnetic moments, this discovery has opened new possibilities in the electron microscopy and investigations of magnetic phenomena (see Refs. BliokhSOI ; Lloyd ; LloydPhysRevLett2012 ; Rusz ; Edstrom ; imaging ; Observation ; OriginDemonstration and references therein). Twisted electron beams with large intrinsic OAMs (up to 1000$\displaystyle\hbar$) have been recently obtained VGRILLO . Main properties of twisted electrons have been expounded in the reviews BliokhSOI ; Lloyd . In Refs. Manipulating ; ResonanceTwistedElectrons , the general form of relativistic classical and quantum-mechanical equations of motion has been obtained for an intrinsic OAM of twisted electrons in electric and magnetic fields. The orbital polarization (the fixed direction of intrinsic OAMs) of twisted electrons obtained experimentally is parallel or antiparallel to their momenta.

It is known that the acceleration of particles may be accompanied by their passing through spin resonances. These resonances may lead to a depolarization of particle beams. In particular, the beam depolarization is very important for polarized protons. To pass them through spin resonances, one uses Siberian snakes. It has been proposed in Refs. Manipulating ; ResonanceTwistedElectrons to accelerate polarized (and unpolarized) beams of twisted electrons for their applications in high-energy-physics experiments. The natural question can be put: are there any resonances depolarizing a beam with an orbital polarization?

We answer this question in the present work. The system of units $\displaystyle\hbar=1,c=1$ is used.

The equation of motion of the intrinsic OAMs ($\displaystyle\bm{L}$) of twisted electrons or other twisted particles in electric and magnetic fields has the form Manipulating ; ResonanceTwistedElectrons

[TABLE]

where $\displaystyle\gamma$ is the Lorentz factor and $\displaystyle\bm{\beta}=\bm{V}/c$. The motion of the intrinsic OAMs is the Larmor precession. Otherwise, the angular velocity of their cyclotron motion is defined by

[TABLE]

where $\displaystyle\bm{N}=\bm{p}/p$ is the unit vector along the momentum direction. One usually applies cyclotrons with the main vertical magnetic field and magnetic focusing. Evidently, the accelerating longitudinal electric field does not influence the quantities $\displaystyle\bm{\omega}$ and $\displaystyle\bm{\Omega}$. In this case, $\displaystyle\bm{\beta}\times\bm{E}$. As a result,

[TABLE]

for any beam energy.

Equation (3) means that any perturbation of the intrinsic-OAM motion (originated from a horizontal magnetic field at any path section) twice affects the electron during the period of the intrinsic-OAM rotation. It is important that the phases of the intrinsic-OAM oscillation at the moments of the twofold action of the perturbation are opposite and the deflections of the intrinsic OAM caused by this perturbation are also opposite. Thus, the acceleration of twisted electrons in usual cyclotrons with the main vertical magnetic field and magnetic focusing does not lead to the resonant orbital depolarization.

The result presented means an existence of the Siberian snake-like behavior for an orbital polarization of a beam of twisted electrons. This is the wonderful property of orbitally polarized twisted electron beams significantly simplifying their acceleration in cyclotrons.

The work was supported in part by the Belarusian Republican Foundation for Fundamental Research (Grant No. $\displaystyle\Phi$18D-002), by the Heisenberg-Landau program of the Federal Ministry of Education and Research of Germany (Bundesministerium für Bildung und Forschung), and by the Russian Foundation for Basic Research (Grant No. 16-02-00844-A).