# PHY 694 spring 2022

## Syllabus

PHY 694: Plasma and Wakefield Accelerators, Spring 2022

Date of this version of the Syllabus: 1/25/2022

**Course Description:**

This course provides an introduction to the physics of laser-driven and beam-driven plasma wakefield accelerators. Topics include the description of the motion of a single particle in the fields of a laser or relativistic particle beam, coupling of intense drivers to plasma waves, description of linear and nonlinear plasma waves in 1D and 3D, injection of particles into plasma waves and beam loading, as well as other advanced topics such as the directions of present research as time permits. In addition to the theoretical concepts, the students will also be introduced to the computational and experimental tools used to explore the relevant physical phenomena.

1-3 credits, Letter graded (A, A-, B+, etc.)

**Course Material:**

Class Notes: Class notes on each topic will be posted on Blackboard ahead of the class.

**Topics & Approximate Timeline:**

The focus of the class will be on the study of coupling high-energy-density sources (i.e. laser and particle beams) to plasma and how the resulting fields can be used to accelerate particles. The topics and the approximate time devoted to each during the semester is as follows:

1. Single particle motion in fields of intense laser and particle beams (2.5 weeks)

2. Introduction to plasma and fluid equations in plasma (2 weeks)

3. Nonlinear plasma waves in 1D and 3D (2 weeks)

4. Plasma wake excitation by laser and particle beams (2.5 weeks)

5. Electron trapping conditions and mechanisms (1.5 week)

6. Beam loading and emittance preservation (1.5 weeks)

7. Paraxial wave solutions in vacuum and ponderomotive guiding center approximation (2 weeks)

8. Status of experiments in LWFA and PWFA (1 week)

**Learning Objectives:**

Upon completing this course, students will be able to • Predict the motion of a charged particle inside the fields of an intense laser or e-beam

• Explain the physical interpretation of Vlasov equation and plasma fluid equations

• Summarize & explain the properties of the fields in nonlinear plasma waves

• Predict the properties of a plasma wave excited by a particular laser or beam

• Identify trapping conditions to determine whether a particular situation would lead to particle trapping

• Describe examples of trapping mechanism in plasma waves

• Explain the pondermotive guiding center approximation

• Describe the status of the LWFA and PWFA research

## Course Notes

Nine topics were covered in the class. The prepared lecture documents associated with each topic are presented below:

Lec Set 1 - Single Particle Motion in the Fields of Lasers and Particle Beams(File:Single Particle Motion in the Fields of Lasers and Particle Beams v2022.pdf)

Lec Set 2 - Introduction To Plasma(File:Introduction To Plasma.pdf)

Lec Set 3 - Collective Behavior in Plasma, Fluid Equations (File:Collective Behavior in Plasma, Fluid Equations.pdf)

Lec Set 4 - Linear and Nonlinear 1D Plasma Wakefields (File:Linear and Nonlinear 1D Plasma Wakefields.pdf)

Lec Set 5 - 3D Blowout Wakefields (File:3D Blowout Wakefields.pdf)

Lec Set 6 - Laser and Beam Coupling to Plasma (File:Laser and Beam Coupling to Plasma.pdf)

Lec Set 7 - Beam loading (File:Beam loading.pdf)

Lec Set 8 - Particle Orbits and Trapping Physics (File:Particle Orbits and Trapping Physics.pdf)

Lec Set 9 - Transverse beam dynamics and emittance preservation (File:Transverse beam dynamics and emittance preservation.pdf)

## Homework

Homework 1 File:Phy 694 Homework 1.pdf

Homework 2 File:Phy 694 Homework 2.pdf

Homework 3 File:Phy 694 Homework 3.pdf

Homework 4 File:Phy 694 Homework 4.pdf

Homework 5 File:Phy 694 Homework 5.pdf

Homework 6 File:Phy 694 Homework 6.pdf

Homework 7 File:Phy 694 Homework 7.pdf

Homework 8 File:Phy 694 Homework 8.pdf