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

Simulation of Beam and Plasma Systems

Sponsoring University:

Old Dominion University

Course Name:

Simulation of Beam and Plasma Systems


Steven Lund, Michigan State University and USPAS; David Bruhwiler, RadiaSoft LLC; Remi Lehe and Jean-Luc Vay, Lawrence Berkeley National Laboratory; Daniel Winklehner, MIT

Purpose and Audience
The purpose of this course is to provide a comprehensive introduction to numerical modeling techniques used to analyze beam and plasma systems in the context of accelerator technology. This course is suitable for upper level graduate students and scientists in physics and engineering interested in numerical modeling of beams and plasmas. Emphasis is placed on self-consistent modeling of systems where beam intensities are considered to be high enough that self-fields cannot be neglected and collective effects can be important and in “plasma accelerators” where particles are accelerated in an ionized gas using resonant plasma waves. Classic accelerator formulations of collections of non-interacting particles evolving in applied fields are also covered and serve to connect to standard, highly developed tools to model lower intensity accelerator systems. Simulation methodologies are presented in a top-down hierarchy of particle, distribution, and moment methods. In the self-consistent context, emphasis is given to Vlasov model descriptions of evolution, and motivating the particle-in-cell (PIC) method of solving the Vlasov equation. More advanced refinements of the PIC method are also surveyed including mesh refinement, advanced movers, and optimal Lorentz frame simulations. Issues associated with numerical resolution and convergence are addressed. Practical issues including code organization, diagnostics, benchmarking, parallel computing, and collaborations are also covered. Although the course is not on any specific code, we employ the Elegant and Warp codes for single particle and self-consistent illustrations and exercises.  The course can also serve as an introduction to Elegant and Warp. Elegant is a tracking and design code with many features. Students will run Elegant in the cloud using a browser-based graphical user interface (GUI), http://beta.sirepo.com/. The Warp code is a highly developed open-source PIC code with a large hierarchy of self-consistent models integrated under a common Python-based interpreter. More information on the Warp code can be found http://warp.lbl.gov/ .

Undergraduate level Electricity and Magnetism, Classical Mechanics, and Accelerator Physics required. Basic knowledge of elementary numerical methods (finite differencing, quadrature, solution of ODEs, etc.) and the Python Programming Language (can meet by studying sections 1.1 to 1.4 of the Python Scientific Lecture Notes : https://scipy-lectures.github.io/) are required.  Some familiarity with Plasma and Fluid Physics, Linux and/or OSX operating systems, and a compiled programming language (FORTRAN, C, C++, etc.) is recommended.

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 modeling accelerator systems with emphasis on strong space charge and beam-plasma (as in plasma accelerator) systems. The level is sufficient to provide a solid foundation for contemporary numerical modeling of accelerator systems where intensities are sufficiently high that mutual interactions of the particles in the beam/plasma cannot be neglected. In such regimes of strong space-charge, the system can be dominated by collective effects, leading to rich wave and stability properties beyond characteristic single-particle oscillations in conventional accelerator systems. Emphasis is given on motivating methods employed in particle-in-cell simulations of beams and plasmas within a Vlasov model. Both linear (linac) and circular (ring) machine architectures, injectors and front-ends, transfer/transport lines, and beam/plasma interactions will be covered. Aspects of comparisons/benchmarking with experiments will be discussed, but details of laboratory implementations will not be covered. The material covered will provide a foundation to provide numerical modeling support for a wide range of accelerator and plasma systems. 

Instructional Method
Lectures will be given during morning and early afternoon sessions, followed by afternoon simulation/recitation sessions, which will engage the students on the material covered in lecture. Lectures also include interactive simulation exercises. Daily problem sets/simulation exercises 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 Thursday of the 2nd week, and will cover the contents of the entire course. Duties for lecturing, interactive sessions, recitations and grading will be divided among the instructors. Instructors will be available for guidance during the evening homework sessions. Cooperation among students is encouraged to enhance learning. 

Course Content
This course will provide an overview of when and why simulations are useful. We will cover a wide range of basic numerical methods relevant to both single particle and self-consistent PIC simulations in both linear and circular architectures. Topics include: particle movers, field solvers (both electrostatic and electromagnetic), and deposition of particle charges and currents on the simulation mesh. Simulation diagnostics, code initialization, and numerical convergence issues are discussed and illustrated with examples. Advanced topics including injector modeling, mesh refinement in field solvers, map based particle moving, and optimal Lorentz frame simulations are overviewed. Code infrastructure issues including the Python interpreter and object-oriented computing, GUIs, parallel computing, GPUs, and code maintenance are discussed. Hands-on simulation exercises with the Elegant and Warp codes illustrate concepts covered in the lectures and also serve as an introduction to the codes. Linux based workstations with Warp installed will be provided for the simulation exercises and Elegant exercises will be carried out with an online GUI interface. Assistance will be provided for those wishing to build Warp on Linux and OSX laptops (Windows not supported).

Reading Requirements
Class notes will be provided that will serve as the primary reference. A paper copy will be provided by the USPAS.  Notes will be archived and updated on the course web site    https://people.nscl.msu.edu/~lund/uspas/sbp_2018/

Supplemental text to be provided: “Computer Simulation Using Particles,” R.W. Hockney and J.W. Eastwood, (Taylor & Francis, NY) 1988.

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

Old Dominion University course number:
Phys 851, "Simulation of Beam and Plasma Systems"
Indiana University course number: Physics 571, "Special Topics in Physics of Beams"
Michigan State University course number: PHY 963, "U.S. Particle Accelerator School"
MIT course number: 8.790, "Accelerator Physics"