U.S. Particle Accelerator School

Intense Beam Physics: Space-Charge, Halo and Related Topics course

Sponsoring University:

College of William and Mary


Intense Beam Physics: Space-Charge, Halo and Related Topics


John Barnard and Steven Lund, LLNL

This course will be an introduction to the physics of intense charged particle beams, focusing on the role of space charge. The topics include: particle equations of motion, the paraxial ray equation, and the Vlasov equation; 4-D and 2-D equilibrium distribution functions (such as the Kapchinskij-Vladimirskij, thermal equilibrium, and Neuffer distributions), reduced moment and envelope equation formulations of beam evolution; transport limits and focusing methods; the concept of emittance and the calculation of its growth from mismatches in beam envelope and from space-charge non-uniformities using system conservation constraints; 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 and kinetic modes); the role of space-charge in the injector; and algorithms to calculate space-charge effects in particle codes. Examples of intense beams will be given primarily from the ion and proton accelerator communities with applications from heavy-ion fusion, spallation neutron sources, and/or tritium production. Prerequisites: Undergraduate Electromagnetism and Mechanics. Some familiarity with basic accelerator concepts and plasma physics is recommended but not required.
Course outline can be found here.