U.S. Particle Accelerator School

Space-Charge Dominated Beam Transport and Acceleration course

Sponsoring University:

Massachusetts Institute of Technology (MIT)


Space-Charge Dominated Beam Transport and Acceleration


Yuri Batygin, Los Alamos National Lab

Purpose and Audience
The purpose of this course is to provide a comprehensive introduction to high brightness particle beam physics with strong space charge forces. This course is suitable for graduate students and researchers who want to get a better understanding of high-current beam dynamics.

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

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 self-consistent beam dynamics with strong space charge forces in beamlines and in Radio Frequency (RF) accelerators. Special emphasis is on the physics of high brightness beams in phase space. After taking the course students will be able to design beam optics with space charge, find optimal conditions for particle dynamics to minimize particle losses and to provide minimal beam sizes in beamlines, determine limited values of beam current in beamlines and in RF accelerators, solve Poisson's equation for beam field, determine nonlinear distortion of the beam due to space charge.

Instructional Method
The course will consist of 23 hours of lectures during the morning and afternoon, focusing on the theoretical understanding of the course content, as well as sessions on how to solve practical problems. Daily homework will be given that lets the student review basic concepts introduced in class.

Course Content
The course provides description of the beam dynamics with strong space charge forces in beamlines and RF accelerators. The topics include: Hamiltonian self-consistent dynamics of particles, equations of motion, emittance and brightness of the beam, beam transport in quadrupole focusing channel and in longitudinal magnetic field, averaging method in particle dynamics, Kapchinsky-Vladimirsky beam envelope equations, beam current limit in beamlines, nonlinear effects in beam transport, beam emittance growth due to space charge forces, halo formation in particle beams, beam equilibrium in focusing channels, space charge dominated beam in RF linacs, numerical methods in high brightness beam physics.
Reading Requirements
Instructor-provided handouts.

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

IU/USPAS course number P671