Doppler effect in vacuum and medium in X-ray range

TL;DR

This paper explores the Doppler effect in X-ray radiation emitted by relativistic oscillators and charged particles in vacuum and media, analyzing spectral and angular properties across various phenomena.

Contribution

It provides a unified geometric and physical framework for understanding Doppler effects in diverse relativistic X-ray radiation processes.

Findings

Spectral and angular properties of Doppler X-ray radiation are characterized.

Doppler effect interpretation applies to multiple radiation phenomena.

Relativistic oscillator and particle interactions with media are analyzed.

Abstract

This paper discusses the Doppler effect for radiation emitted by a relativistic oscillator in vacuum described geometrically as an ellipsoid in momentum space. Spectral and angular properties of the Doppler X-ray radiation emitted by a relativistic oscillator moving through a homogeneous medium are considered. Additionally, we show that radiation from an elementary relativistic charged particle interacting with periodic medium can be interpreted as a manifestation of the Doppler effect. Examples include parametric X-ray radiation, coherent bremsstrahlung, undulator radiation in crystalline or vacuum undulators, transition radiation from stacked foils, and Smith-Purcell radiation.