Scale invariance of electrodynamics in radio-frequency linear accelerators

TL;DR

This paper explores the conditions under which electromagnetic fields and ion trajectories in radio-frequency linear accelerators exhibit scale invariance, potentially enabling the design of high-current beam accelerators.

Contribution

It derives a condition for mechanical similarity in RF accelerators, including space charge effects, facilitating the development of high-current beam accelerators.

Findings

Derived a scale transformation condition for electromagnetic fields and ion trajectories.

Demonstrated the invariance of Maxwell's equations with sources under this scale transformation.

Discussed implications for designing linear accelerators with extremely high current beams.

Abstract

This study discusses the scale transformation of electromagnetic fields and trajectories of ions in radio-frequency linear accelerators. We will obtain a condition for mechanical similarity, where Maxwell equations with source terms and the equation of motion under Lorentz force remain invariant, including space charge fields, while the trajectories of ions are accordingly scaled. The possibility of linear accelerators for extremely high current beams will be considered based on this condition.