On the peculiar features of the instantaneous angular distribution of synchrotron radiation

TL;DR

This paper analyzes the angular distribution of synchrotron radiation, revealing that in the ultrarelativistic limit, all radiation is confined within a specific conical region aligned with the charge's velocity.

Contribution

It provides a detailed investigation of the instantaneous angular distribution, showing that in the ultrarelativistic limit, radiation is confined within a cone and the rest vanishes.

Findings

Radiation is contained within a cone of angle 2α₀ in the ultrarelativistic limit.

Outside the cone, the radiation vanishes when α₀ is non-zero.

The space is divided into two parts: inside the cone and outside, with distinct radiation behaviors.

Abstract

The instantaneous angular distribution of synchrotron radiation is investigated. The radiation space is divided into two parts. The first part of the space is the interior of a cone with the apex located at the point of a radiating charge, the angular span being $2\alpha_0$ and the central axis oriented along the instantaneous velocity of the charge. The second part of the space is the complement of the first part in the entire space. It is shown that the radiation in the ultrarelativistic limit is entirely contained in the first part of the space, and the radiation in the second part (with a non-zero $\alpha_0$) vanishes.