This thesis examines the evolution of beams in synchrotrons. Following an introduction to accelerator physics in Chapter 1, in Chapter 2 I describe the Fermilab E778 'diffusion' experiment. Families of sextupoles were powered to drive the 2/5 resonance, and a beam was then kicked to populate a nonlinear region of the transverse phase space. The beam was then observed over periods of approximately 30 minutes for a variety of kick amplitudes and physical apertures. In Chapter 3 comments about the analytic treatment of such systems are discussed, including the assumptions inherent in the conventional treatment. I motivate my use of a simplified model in Chapter 4 after examining common computational methods. Deriving the model from the formalism of traditional accelerator physics, I discuss its implementation on a massively parallel computer, the Intel iPSC/860 hypercube, and examine the performance of this algorithm in detail. Using the simple model to perform the numerical experiment equivalent to E778 is the subject of Chapter 5. I derive the parameters needed for the simple model based upon the physical experiment. Both three dimensional cases and cases with reduced dimensionality are run. From power supply ripple data and an electrical model of the magnet string, I compute tune modulation depths, and a subset of these are run. I conclude that tune modulation from power supply ripple is not a significant source of transport for this system. In Chapter 6, the intensities of the beams are used to compare the experimental and numerical runs, using both exponential and algebraic decays, and the algebraic form is seen to provide a better fit. The agreement between numerical and experimental results is best for fully three-dimensional runs, but the numerical results show slower decay than the experimental. Individual particles are examined, whose motion consists of stochastic motion interspersed with regular motion, suggestive of a Continuous Time Random Walk process. A pausing time distribution is extracted which is algebraic in time, which is consistent with dispersive transport observed elsewhere.

N.H. Frank and R.Q. Twiss. / "February 9, 1948." / Bibliography: p. 27. / Army Signal Corps Contract No. W-36-039 sc-32037.

by R.Q. Twiss. / "June 2, 1947." / Bibliography: p. 16.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 304-307). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 98-103). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 98-103). Also available on the Internet.

Thesis (Ph.D.)--University of California, Berkeley, 1963. / "UC-28 Particle Accel. and High Volt. Mach." -t.p. "TID-4500 (19th Ed.)" -t.p. Includes bibliographical references (p. 302-303).

Thesis (M.S. in Physics)--United States Naval Postgraduate School, California. / "Unclassified Physics." Includes bibliographical references (p. 20). 8

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 304-307). Also available on the Internet.

Thesis (Electronic Engineering)--University of California, Berkeley. / Errata sheet at end. Includes bibliographical references (p. 55). 4