Circular accelerators: Transverse

Intended as an introduction to the theory of transverse beam dynamics in circular accelerators, this contribution to the 1985 US Accelerator School deals mainly with linear theory. After establishing the physical concept of alternating gradient focusing for those new to the field, the classical matrix theory and betatron functions are derived from a Hamiltonian. Imperfections which cause closed orbit distortion are examined and the effect of momentum defect described in terms of dispersion and chromaticity. The theory of gradient errors is extended to point the way to more mathematical treatments of non‐linear effects in other contributions to the School.