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Description
F-divergence can be used to precisely quantify the differences between beam distributions in high-dimensional phase space, as it comprehensively captures the total contribution of discrepancies from all points in phase space. Current applications of f-divergence are primarily confined to the static comparison of distributions. This paper aims to investigate its evolution during beam transport. We mathematically prove that f-divergence remains invariant in both linear and nonlinear transport processes, and validate this conclusion through beam transport simulations. Further research indicates that space charge forces can break this conservation. We show how this property of f-divergence can be used as a tool to help us understand, predict, or control beam degradation caused by space charge effects.
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