Conditions for Existence of Compact Stationary Relativistic Beam Torus

TL;DR

This paper investigates the feasibility of creating a stable magnetic trap for controlled fusion using high-power relativistic charged beams, concluding that such traps cannot be formed by external fields and that strict stationarity is impossible under certain conditions.

Contribution

It demonstrates the limitations of external electromagnetic fields in forming absolute magnetic traps and applies the virial theorem to show the non-existence of strict stationary states in this context.

Findings

AMT cannot be created by external electromagnetic fields

Strict stationary states do not exist with positive beam pressure and electromagnetic energy density

Virial theorem implies fundamental limitations on stable relativistic beam configurations

Abstract

Conditions for obtaining the absolute magnetic trap (AMT) to be used for the controlled fusion by means of high power relativistic charged beam have been considered. It is shown that AMT can not be created by external electromagnetic fields. Also the virial theorem implies that strict stationary state of the system does not exist in empty flat Minkowski space-time in case of positive beam pressure and positive electromagnetic field energy density.