Simulating beam loading in radio frequency accelerating structures is critical for understanding higher-order mode effects on beam dynamics, such as beam break-up instability in energy recovery linacs. Full wave simulations of beam loading in radio frequency structures are computationally expensive, while reduced models can ignore essential physics and can be difficult to generalize. We present a self-consistent algorithm derived from the least-action principle which can model an arbitrary number of cavity eigenmodes and with a generic beam distribution. It has been implemented in our new Open Library for Invesitigating Vacuum Electronics (OLIVE).
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