Understanding superconducting cavities through the least action principle

Superconducting cavities are indispensable elements in modern particle accelerators, utilizing the ultra-low sur-face resistance of superconductors to achieve exceptionally high quality factors. In this work, we apply the least action principle to derive an equivalent RLC circuit model, offering a unified theoretical framework to describe the electromagnetic behavior of superconducting cavities. Beyond the classical model, we examine the underlying heat dissipation mechanisms and identify quantized physical quantities that influence cavity performance. Particular attention is given to the quantum aspects of the quality factor, including its manifestation in decay time measurements. By bridging classical electrodynamics and quantum dissipation, this study provides a deeper under-standing of the fundamental principles governing super-conducting cavity dynamics.