The positive function and the displayed associated parameters describe a stable linear beam ellipse. A trajectory with invariant obeys and has phase advance . Writing gives ; the coefficient of is , not one.
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The Courant–Snyder parameters are a set of four parameters used in the field of accelerator physics to describe the transverse motion of charged particles in a beam as they travel through a magnetic or electric field. They are particularly useful in the context of beam dynamics and are central to the analysis of particle accelerators and storage rings.