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

Plasma-Based Acceleration course

Sponsoring University:

Michigan State University (ONLINE)


Plasma-Based Acceleration


Alec Thomas and Qian Qian, University of Michigan; Navid Vafaei-Najafabadi and Jiayang Yan, Stony Brook University; Warren Mori, UCLA

Purpose and Audience
This is an introductory course on plasma-based acceleration, including laser wakefield and plasma wakefield acceleration.  The course will introduce students to the physics of how lasers and charged particle beams propagate through plasmas, how they excite plasma wave wakefields, and how particles are loaded into and are accelerated in these wakefields. The nomenclature of the subject will be introduced and why this topic is currently of great interest will be explained.  This course is suitable for graduate students or upper division undergraduate students with an interest in this promising multi-disciplinary field. The course is also appropriate for physicists or engineers working in accelerator-related fields who wish to familiarize themselves with plasma-based accelerator concepts.

Upper division Electromagnetism and Classical Mechanics are required. An introductory course in Plasma Physics and some knowledge of Accelerator Physics at the level of USPAS Fundamentals of Accelerator Physics and Technology with Simulations and Measurements Lab or USPAS graduate Accelerator Physics is recommended. 

It is the responsibility of the student to ensure that they meet the course prerequisites or have equivalent experience.

This course will provide the fundamentals needed to understand plasma-based acceleration and the interaction of high intensity lasers and particle beams with plasmas. It will also introduce the computational and experimental tools needed to explore the physical phenomena involved. The course will also introduce the student to fundamental concepts and directions of present research so that they will be able to read and understand past and current literature. 

Instructional Method
This course includes a series of lectures and computational laboratory sessions using Jupyter Notebooks highlighting subject matter covered. Regular problem sets, to be completed outside of scheduled class time, will be assigned in the lecture sessions. The instructors and teaching assistants will be available for guidance during evening homework sessions. There will be an open-book final exam at the conclusion of the course.

Course Content
The course will cover a variety of topics with varying degrees of detail. The course will begin with an analysis of phase-space trajectories of charged particles in the fields of lasers and particle beams. This will be used to identify an intensity parameter for a laser or particle beam that defines when the trajectories are nonlinear. The course will cover plasma waves in one dimension, including when they are nonlinear which will introduce the concept of wavebreaking and particle trapping. This will show that plasmas can support accelerating fields more than three orders of magnitude larger than conventional accelerators. Next, nonlinear wake fields in multi-dimensions (called the blowout regime) will be described including a general description of particle trapping. We will describe how lasers propagate and evolve in a plasma as they excite plasma wave wakefields through the ponderomotive force. The concepts of photon or action conservation, photon acceleration, longitudinal bunching, and transverse focusing will be introduced with an eye towards how they cause the laser to evolve. Analogous concepts for a particle beam and the concepts of pump depletion and dephasing will be introduced. Linear wakefield theory for how lasers and particle beams will illustrate the differences and similarities between laser and beam wakefield excitation (by either electrons or positrons). Techniques for analyzing beam loading may also be discussed. The concepts of emittance and emittance preservation will be introduced, including the Panofsky-Wenzel theorem for plasma wakefields. Computational and experimental techniques, the generation of radiation by charged particle beams, and the current status of using plasma-based acceleration for a future collider or compact XFEL will also be covered.

Reading Requirements
Extensive class notes will be provided on a course web site that will serve as the primary reference. Course materials will also be archived on a course web site.

Students may also benefit from reviewing in advance:
- A. Seryi, Unifying Physics of Accelerators, Lasers and Plasma, CRC Press, 2015. 
- C.  Joshi, Plasma Acceleration, Scientific American V. 294, (February 2006), pp. 40-47
- F. Chen, Introduction to Plasma Physics, Springer, 2012.

Credit Requirements:
Students will be evaluated based on performance in the homework and computer assignments (70 % of course grade) and a comprehensive final exam (30% of course grade).

Michigan State University course number: PHY 963
Indiana University course number: Physics 671, Advanced Topics in Accelerator Physics
MIT course number: 8.790, Accelerator Physics