Maximum attainable energy at a fixed frequency cyclotron

TL;DR

This paper explores the theoretical maximum energy achievable in a cyclotron at a fixed frequency, highlighting key relativistic considerations and subtle points in the solution process.

Contribution

It provides a detailed analysis of the maximum energy limit in a cyclotron within a relativistic framework, clarifying subtle aspects of the problem.

Findings

Derived the maximum energy formula for a fixed frequency cyclotron

Identified relativistic effects that limit particle acceleration

Clarified subtle points in the relativistic solution process

Abstract

We consider a problem of finding the maximum attainable energy at a cyclotron as an exercise in the introductory relativity course and comment on some subtle points of the solution.