A study of nonlinear dynamics in the Fermilab Tevatron.

Abstract

This thesis describes an accelerator physics experiment (E778) performed in the Fermilab Tevatron to study the nonlinear dynamics of transverse particle oscillations. Nonlinearities were introduced by sixteen special sextupole magnets. The various characteristics of the phase space were studied experimentally. The results were compared with calculations performed by numerical tracking of particles through an accurate representation of the Tevatron. Canonical Hamiltonian theory was used to derive the quantities of interest which were in turn compared with both experimental and simulated results. 'Smear' was one of the parameters used to quantify the degree of nonlinearity. It is the fractional root mean square deviation of the particle oscillation amplitude. After confirming that the Tevatron was essentially linear with the sextupoles turned off, smear measurements were performed and compared with calculation over a wide range of conditions. The agreement is excellent to the degree of experimental accuracy. The correlation between smear and other measures of accelerator performance such as injection efficiency and particle lifetime was studied. The conclusion is that it is still possible to diagnose and correct injection problems in the presence of strong nonlinearities. Capture of particles into stable nonlinear resonance islands was directly observed. The tune, defined as the number of oscillation periods in one revolution, is about 19.4 for the Tevatron. The fractional part of the tunes of the captured particles corresponds exactly to the particular resonance. In E778 systematic data taking was restricted to the 2/5 resonance, although particle trapping was observed on other resonance islands. Precision measurement of the tune of trapped particles yielded a value of.4000 as expected. The 'island tune', defined as the frequency of rotation of a particle around the center of the island, and the 'capture efficiency', used to quantify the fraction of beam actually trapped in one of the islands, were calculated and compared with experimental results. The agreement is generally good and reasonable explanations are offered for any discrepancy. Finally, the maximum stable amplitude, sometimes called the 'dynamic aperture' of the accelerator, was determined experimentally. The measurements were compared with the prediction from tracking calculations. The outcome is satisfactory.