Beam emittance is a fundamental property in accelerator physics and related fields, describing the spread of particles in a beam with respect to their position and momentum. It quantifies how "focused" or "spread out" the beam is in both spatial and momentum dimensions, and it plays a crucial role in determining the quality and performance of particle beams in accelerators, such as those used in synchrotrons and colliders. Emittance is often expressed in units of area (e.g.
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