Analysis of continuously rotating quadrupole focusing channels using generalized Courant-Snyder theory

Abstract

By extending the recently developed generalized Courant-Snyder theory for coupled transverse beam dynamics, we have constructed the Gaussian beam distribution and its projections with arbitrary mode emittance ratios. The new formulation has been applied to a continuously rotating quadrupole focusing channel because the basic properties of this channel are known theoretically and could also be investigated experimentally in a compact setup such as the linear Paul trap configuration. The new formulation retains a remarkably similar mathematical structure to the original Courant-Snyder theory, and thus, provides a powerful theoretical tool to investigate coupled transverse beam dynamics in general and more complex linear focusing channels.