U.S. Particle Accelerator School

Accelerator Physics

Sponsoring University:

Northern Illinois University

Course Name:

Beam Physics with Intense Space Charge


Steven Lund, Michigan State University and John Barnard, Lawrence Livermore National Laboratory

Purpose and Audience
The purpose of this course is to provide a comprehensive introduction to the physics of beams with intense space charge. This course is suitable for graduate students and researchers interested in accelerator systems that require sufficiently high intensity where mutual particle interactions in the beam can no longer be neglected.

Undergraduate level Electricity and Magnetism, Classical Mechanics, Special Relativity, and Accelerator Physics. Some familiarity with plasma physics is strongly recommended.

It is the responsibility of the student to ensure that he or she meets the course prerequisites or has equivalent experience.

This course is intended to give the student a broad overview of the dynamics of beams with strong space charge. The emphasis is on theoretical and analytical methods of describing the acceleration and transport of beams. Some aspects of numerical and experimental methods will also be covered. Students will become familiar with standard methods employed to understand the transverse and longitudinal evolution of beams with strong space charge. The material covered will provide a foundation to design practical architectures.

Instructional Method
Lectures will be given during morning and early afternoon sessions, followed by an afternoon discussion/recitation session, which will engage the student on the materials covered. Daily problem sets will be assigned that will be completed outside of scheduled class sessions. Problem sets will generally be due the morning of the next lecture session. A comprehensive final take-home exam will be given on the second Thursday. The instructors and the recitation session leader/grader will be available for guidance during evening homework sessions.

Course Content
In this course, we will introduce you to the physics of intense charged particle beams, focusing on the role of space charge. 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 sources and front ends, heavy-ion fusion and beam-driven facilities to explore high energy density physics, spallation neutron sources, nuclear waste transmutation, etc.

Reading Requirements
Extensive class notes will be provided that will serve as the primary reference. Course materials will also be archived on a course web site.  A supplemental text is provided (by the USPAS): "The Theory and Design of Charged Particle Beams" Second Edition, Updated and Expanded by Martin Reiser, Wiley & Sons 2008.

Credit Requirements
Students will be evaluated based on performance: homework assignments (80% of course grade), final exam (20% of course grade).

Northern Illinois University course number:
PHYS 790D - Special Topics in Physics - Beam Physics
Indiana University course number: Physics 571 "Special Topics in Physics of Beams"
Michigan State University course number: PHY 963 
MIT course number: 8.790 "Accelerator Physics"