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

Beam Physics with Intense Space Charge


Michigan State University (ONLINE)

Course Name:

Beam Physics with Intense Space Charge
This class is limited to 20 students

Steven Lund, Michigan State University and USPAS; John Barnard, Lawrence Livermore National Laboratory; Arun Persaud, Lawrence Berkeley National Laboratory; Daniel Winklehner, Massachusetts Institute of Technology

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.

Required: Senior undergraduate level Electricity and Magnetism, Classical Mechanics covering the Hamiltonian formulation and classical electrodynamics, Special Relativity and relativistic kinematics, and Accelerator Physics at the level of USPAS Fundamentals of Accelerator Physics and Technology with Simulations and Measurements Lab or USPAS graduate Accelerator Physics.

Recommended: Familiarity with elementary Plasma Physics, graduate-level Electromagnetic Theory and Classical Mechanics

It is the responsibility of the student to ensure that they meet the course prerequisites or have 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 analyze a broad range of collective effects and access impact on design choices for intense beam transport and acceleration systems.   

Instructional Method
Daily lectures will be given. There will be regular discussion/recitation sessions, which will engage the student on the materials covered. Regular problem sets will be assigned that will be completed outside of scheduled class sessions. A comprehensive final take-home exam will be given. 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. Limited aspects of diagnostic measurements will the reviewed at the end of the course. 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 on a course web site that will serve as the primary reference. It is recommended that students bring a laptop computer or tablet to access these notes. Course materials will also be posted and 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.

Perspective students evaluate the fit of the course and/or prepare for the course in advance by reviewing the materials in the last version of the course given in the winter 2020 USPAS session: https://people.nscl.msu.edu/~lund/uspas/bpisc_2020/

Credit Requirements

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

Michigan State University course number: PHY 963 - 703
Indiana University course number: Physics 571 Special Topics in Physics of Beams
MIT course number: 8.790 Accelerator Physics