Mapping chaos in particle revolutions

Over the past decade the technique of frequency map analysis, developed to study astronomical systems, has shown its value in an increasing number of areas, including the analysis of particle orbits in accelerators. In a circular accelerator, focusing magnetic fields cause particles to oscillate transversely about the closed, central trajectory. The number of oscillations in one turn around the ring is called the betatron tune and can be different in the horizontal and vertical directions. Additionally, the oscillations are nonlinear and the oscillation frequencies change with the transverse amplitude of the particles. In this context the fundamental frequencies extracted from the frequency map analysis correspond to the tunes for each trajectory. The amplitude of the transverse particle motion is mapped into frequency space by associating a pair of fundamental frequencies with the horizontal and vertical transverse amplitudes. This frequency map is displayed in a coordinate system with the horizontal and vertical tunes as the axes. From the nominal working point corresponding to small transverse amplitude oscillations, the frequencies shift over a wide area as the amplitudes of the betatron oscillations increase. The motion of electrons with large transverse amplitudes may be influenced by resonances. Damaging resonances show as distortions in the map. The goal of investigating this new application of frequency map analysis is to the study of ALS dynamics. (5 refs).