U.S. Particle Accelerator School

Space-Charge Effects in Beam Transport course

Sponsoring University:

University of Colorado at Boulder


Space-Charge Effects in Beam Transport


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.