Simulating beam loading in radiofrequency accelerating structures is criticalfor understanding higher-order mode effects on beam dynamics, such as beambreak-up instability in energy recovery linacs. Full wave simulations of beamloading in radiofrequency structures are computationally expensive, whilereduced models can ignore essential physics and can be difficult to generalize.We present a self-consistent algorithm derived from the least-action principlewhich can model an arbitrary number of cavity eigenmodes and with a genericbeam distribution.
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