U.S. Particle Accelerator School
U.S. Particle Accelerator School
Education in Beam Physics and Accelerator Technology

Space-Charge Effects in Beam Transport course

Sponsoring University:

University of Colorado at Boulder

Course:

Space-Charge Effects in Beam Transport

Instructors:

John Barnard and Steven Lund, Lawrence Livermore National Laboratory

This course will be an introduction to the role of space charge in particle beam transport. The topics include: the Vlasov equation; 4-D equilibrium distribution functions (such as the Kapchinski-Vladimirski and thermal equilibrium), reduced moment and envelope equation formulations of beam evolution; transport limits; the concept of emittance and the calculation of its growth from mismatches in beam envelope and space-charge non-uniformities using system conservation constraints; space-charge and dispersion effects in rings; the role of space-charge in producing beam halos; longitudinal space-charge effects including small amplitude and rarefaction waves; stable and unstable oscillation modes of beams (including envelope modes, kinetic modes, and fluid modes); the role of space-charge in the injector; and algorithms to calculate space-charge effects in particle codes. Examples of space-charge effects will be given primarily from the ion and proton accelerator communities with applications from heavy-ion fusion, tritium production, and/or spallation neutron sources. Prerequisites: Undergraduate Electromagnetism and Mechanics.