Pinning and transport of cyclotron/Landau orbits by electromagnetic vortices

Abstract

Electromagnetic waves with phase defects in the form of vortex lines combined with a constant magnetic field are shown to pin down cyclotron orbits (Landau orbits in the quantum mechanical setting) of charged particles at the location of the vortex. This effect manifests itself in classical theory as a trapping of trajectories and in quantum theory as a Gaussian shape of the localized wave functions. Analytic solutions of the Lorentz equation in the classical case and of the Schrödinger or Dirac equations in the quantum case are exhibited that give precise criteria for the localization of the orbits. There is a range of parameters where the localization is destroyed by the parametric resonance. Pinning of orbits allows for their controlled positioning -- they can be transported by the motion of the vortex lines.

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References in corpus (5)

• Vortex lines of the electromagnetic field
• Particle beams guided by electromagnetic vortices: New solutions of the Lorentz, Schrödinger, Klein-Gordon, and Dirac equations
• Electromagnetic vortex lines riding atop null solutions of the Maxwell equations
• Trojan states of electrons guided by Bessel beams
• Gravity-induced resonances in a rotating trap

Cited by in corpus (5)

• Nonuniform currents and spins of relativistic electron vortices in a magnetic field
• From polarized gravitational waves to analytically solvable electromagnetic beams
• Trapping neutral particles endowed with a magnetic moment by an electromagnetic wave carrying orbital angular momentum: Semiclassical theory
• Guiding neutral particles endowed with a magnetic moment by an electromagnetic wave carrying orbital angular momentum. II. Quantum mechanics
• Guiding neutral polar molecules by electromagnetic vortex field --- a classical approach