Perturbations in Beam Dynamics

Abstract

The study of beam dynamics under ideal conditions is the first basic step toward the design of a beam transport system. In the previous sections we have followed this path and have allowed only the particle energy to deviate from its ideal value. In a real particle beam line or accelerator we may, however, not assume ideal and linear conditions. More sophisticated beam transport systems require the incorporation of nonlinear sextupole fields to correct for chromatic aberrations. Deviations from the desired field configurations can be caused by transverse or longitudinal misplacements of magnets with respect to the ideal beam path. Of similar concern are errors in the magnetic field strength, undesirable field effects caused in the field configurations at magnet ends, or higher order multipole fields resulting from design, construction, and assembly tolerances. Still other sources of errors may be beam-beam perturbations, insertion devices in beam transport systems or accelerating sections which are not part of the magnetic lattice configurations. Such systems may be magnetic detectors for high energy physics experiments, wiggler and undulator magnets for the production of synchrotron radiation, a gas jet or immaterial field sources like that of a free electron laser interacting with the particle beam to name just a few examples. The impact of such errors is magnified in strong focusing beam transport systems as has been recognized soon after the invention of the strong focusing principle. Early overviews and references can be found for example in [7.1— 12].