Steven M. Lund, John J. Barnard (Lawrence Livermore National Laboratory Lawrence Berkeley National Laboratory)
Real beams are expected to have some degree of space-charge nonuniformity and rms envelope mismatch in any accelerator system. For intense beams, such perturbations will evolve and can become thermalized as the distribution relaxes to a more thermal-like distribution characterized by uniform density and temperature. Past studies  have employed a continuous focusing model and energy conservation to estimate emittance increases from the thermalization of initial rms mismatches in the beam envelope and initial space-charge nonuniformities. Here we extend these studies to analyze the emittance growth of an initial beam composed of a space-charge dominated beam equilibrium with an azimuthally symmetric normal mode perturbation. These normal modes were derived in an earlier study using a fluid theory  and are expected to be characteristic of beams with flat density profiles -- a general feature of smooth equilbrium distributions in a space-charge dominated regime. The initially perturbed beam is taken to have the nonuniform space-charge profile and self-consistent envelope mismatch characteristic of a single normal mode perturbation. Since an arbitrarily perturbed beam will evolve as a superposition of normal modes, this formulation helps characterize possible emittance increases associated with classes of nonuniformities in a self-consistent manner.
 Martin Reiser, Theory and Design of Charged Particle Beams (Wiley, New York, 1994).
 Steven M. Lund and Ronald C. Davidson, Physics of Plasmas 5, 3028, (1998).
*This work was performed under the auspices of the U.S. Department of Energy by University of California at Lawrence Livermore National Laboratory and Lawrence Berkeley National Laboratory under contract Nos. W-7405-Eng-48 and DE-AC03-76SF00098.
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