Fundamentals of the Particle In Cell Method

Student Area: access here
Upcoming Class Schedule: May 21 to July 30, 2024
Lecture Time: Tuesdays 8am to 10am US Pacific Time (tentative)
Registration Fee: $275 regular, $210 student until May 3rd (then $320/$250)
20% discount to former students!
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This eight-week online course will teach you how develop electrostatic plasma simulation codes using the Particle In Cell (PIC) method. PIC is a popular numerical approach used to simulate plasmas, rarefied gases, and other processes marked by departure from continuum. It represents the gas as a collection of simulation macroparticles, allowing the method to resolve the local velocity distribution function self-consistently. These particles move in a domain covered by a computational mesh, and the mesh is used to compute self-induced forces and inter-particle interactions. In the course, we will develop 1D, 3D, and 2D axisymmetric ES-PIC codes operating on Cartesian meshes. We will also learn about handling surface interactions, modeling ion-neutral collisions, and data post-processing. The more complex electromagnetic and finite element, unstructured mesh PIC codes are covered in the follow-on Advanced PIC course. Material from this course covers material from chapters 1 through 4 in Plasma Simulations by Example. The class will run from May 21st to July 30th, 2024, with a 3 week break between classes 4 and 5 due to conference travel. This should give you time to catch up on homework assignments!

Course Objectives

At the end of the course, you should have a solid understanding of the PIC method and be able to develop your own 1D, 2D, and 3D plasma simulation codes for modeling cases in which the magnetic field is either not present, or does not change with time. You should also be able to: 1) write a solver for plasma potential, 2) model electrons using a simple fluid model, 3) include surface interactions, and 4) model multi-species gases including neutral interactions. The course will also cover post-processing and data visualization.

Course Format

The course consists of online lessons conducted through GoToMeeting. The lessons are recorded and the videos, along with pdf slides and code examples, are posted online shortly after each lesson. The course also includes optional homework assignments, which need to be completed in order to receive a certificate of completion.

Class Schedule


Below are some examples of course materials from 2015:

pic fundamentals slide plasma flow past a sphere visualized in paraview
Figure 1. Example of a lecture material and data visualization in Paraview



The instructor, Dr. Lubos Brieda, is the founder and president of Particle In Cell Consulting, LLC, a Los Angeles-based company specializing in providing tools and services for the plasma physics and rarefied gas communities. Dr. Brieda has over 10 years of experience developing PIC codes for a wide range of applications, including electric propulsion, space environment interactions, surface processing, and plasma medicine. In addition to his work through PIC-C, Dr. Brieda also teaches scientific computing and computational plasma physics at the Department of Astronautical Engineering at the University of Southern California. He is the author of two textbooks: Plasma Simulations by Example, and Introduction to Modern Scientific Programming and Numerical Methods.


All students are expected to have a basic understanding of numerical techniques, plasma and gas dynamics, and computer programming. The lectures and demonstration programs will utilize C++ and Python programming languages. Students need to have access to a computer with a compiler of choice. Computer with Internet access will be needed to access the lectures and course material. The course will be conducted in English.

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