Propagation of charged particle waves in a uniform magnetic field

TL;DR

This paper investigates the spatial distribution of charged particles emitted in a magnetic field, comparing quantum and semiclassical approaches, revealing complex interference patterns and the effectiveness of semiclassical methods.

Contribution

It provides a detailed analysis of charge and current distributions in a magnetic field using both quantum and semiclassical models, highlighting the semiclassical approach's accuracy.

Findings

Semiclassical method reproduces quantum interference patterns.

Spatial charge and current distributions depend on a single physical parameter.

Complex patterns emerge in the charge and current profiles.

Abstract

This paper considers the probability density and current distributions generated by a point-like, isotropic source of monoenergetic charges embedded into a uniform magnetic field environment. Electron sources of this kind have been realized in recent photodetachment microscopy experiments. Unlike the total photocurrent cross section, which is largely understood, the spatial profiles of charge and current emitted by the source display an unexpected hierarchy of complex patterns, even though the distributions, apart from scaling, depend only on a single physical parameter. We examine the electron dynamics both by solving the quantum problem, i. e., finding the energy Green function, and from a semiclassical perspective based on the simple cyclotron orbits followed by the electron. Simulations suggest that the semiclassical method, which involves here interference between an infinite set of paths, faithfully reproduces the features observed in the quantum solution, even in extreme circumstances, and lends itself to an interpretation of some (though not all) of the rich structure exhibited in this simple problem.