U.S. Particle Accelerator School

U.S. Particle Accelerator School

Education in Beam Physics and Accelerator Technology

University of Maryland

Beam Physics with Intense Space Charge

John Barnard and Steven Lund, 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 sufficient high intensity where mutual particle interactions in the beam can no longer be neglected.

**Prerequisites
**Undergraduate level Electricity and Magnetism and Classical Mechanics. Some familiarity with plasma physics, special relativity, and basic accelerator physics is recommended but not required.

**Objectives**

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 sessions, followed by afternoon discussion sessions, which will engage the student on the material covered in lecture. Daily problem sets will be assigned that will be expected to be completed outside of scheduled class sessions. Problem sets will generally be due the morning of the next lecture session. A final take home exam will be given on the second Thursday, and will cover the contents of the entire course. Two instructors 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. 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, for example, heavy-ion fusion, spallation neutron sources, nuclear waste transmutation, etc.

**Reading Requirements**

Extensive class notes will be provided that will serve as the primary reference. *(To be 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: final exam (20 % of course grade), homework assignments (80 % of course grade).