U.S. Particle Accelerator School

Self-Consistent Simulation of Beam and Plasma Systems course

Sponsoring University:

Colorado State University


Self-Consistent Simulation of Beam and Plasma Systems
This course is limited to 20 students.


Steven Lund, Michigan State University/Facility for Rare Isotope Beams; Jean-Luc Vay, Rémi Lehe and David Grote, Lawrence Berkeley National Laboratory; Daniel Winklehner, MIT

Purpose and Audience
The purpose of this course is to provide a comprehensive introduction to self-consistent 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 numerically modeling systems where beam intensities are considered to be high enough that self-fields cannot be neglected and collective effects can be important and/or in “plasma accelerators” where particles are accelerated in an ionized gas using resonant plasma waves. Self-consistent simulation methodologies are presented in a top-down hierarchy of particle, distribution, and moment methods. Emphasis is given to Vlasov model descriptions of evolution, and motivating the particle-in-cell (PIC) method of solving the Vlasov model.  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, and parallel computing are also covered. Although the course is not on any specific code, we employ the Warp particle-in-cell code for many illustrations and exercises and the course can also serve as an introduction to Warp. The Warp code is a highly developed open-source PIC code with a large hierarchy of models integrated under a common Python-based interpreter making it ideal for the course. More information on the Warp code can be found at: 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 be met by reading 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 he or she meets the course prerequisites or has equivalent experience.

This course is intended to give the student a broad overview of modeling accelerator systems with 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 so that mutual interactions of the particles in the beam/plasma can not 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 model numerical 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 student on the material covered in lecture. 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, and will cover the contents of the entire course. Instructors as well as the simulation exercise leader and grader will be available for guidance during the evening homework sessions.

Course Content
In this course we will overview why numerical simulations are useful, classes of self-consistent simulations, basic numerical methods, and build-up the components of PIC simulations, including 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 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, parallel computing, GPUs, and code maintenance are discussed.  Hands on simulation exercises with the Warp code illustrate concepts covered in the lectures and also serve as an introduction to the code. Linux based workstations with Warp installed will be provided for the simulation exercises.  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/scs_2016/

Supplemental text to be provided by the USPAS: “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 (40 % of course grade), homework assignments (60 % of course grade).

Colorado State University course number: ENGR 697 Group Study: Special Topics in Accelerator Physics and Engineering: Self-Consistent Simulations of Beam and Plasma Systems
Indiana University course number: Physics 671
Michigan State University course number: PHY 963
MIT course number: 8.790 "Accelerator Physics"