Momentum compaction

Momentum compaction is a parameter that is derived in orbital motions, such as in a particle accelerator or in a gravitational bound orbit.

For two close orbits it is defined as the fractional deviation of the path length to the fractional deviation of the momentum^[1]:

$\alpha_p = \frac {\frac {dL} {L} } {\frac {dp} {p} } = \frac {dL} {dp} \frac {p} {L}$

Orbits to be compared must be similar, with similar eccentricity etc.

References

1. ^ Conte, Mario; William W MacKay (Oct 1991). An Introduction to the Physics of Particle Accelerators. World Scientific Publishing Company. pp. 14–18. ISBN 981020812X. https://www.worldscibooks.com/physics/1527.html.