Existence of a twist angle intrinsic to the reference orbit in circular accelerators

Abstract

In a circular accelerator, a horizontal-vertical coupling can occur as a purely geometrical effect, in the absence of any coupling device (skew-quadrupole magnets, etc.). The coupling between horizontal and vertical coordinates (and momenta) is represented by a rotation [SO(2)]. The rotation angle is called the twist angle. It comes from the geometry of the reference orbit, and is related to the possible nonintegrability of parallel transport on it. We give an analytic expression of the twist and discuss some simple dynamical consequences of the twist on betatron tune.