Scale invariance of electrodynamics in radio-frequency linear accelerators

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.