[Paper Review] eduPIC: an introductory particle based code for radio-frequency plasma simulation

Zoltán Donkó, Aranka Derzsi+5 more|arXiv (Cornell University)|Mar 17, 2021

Plasma Diagnostics and Applications170 references85 citations

TL;DR

This paper introduces eduPIC, a free, open-source, one-dimensional electrostatic Particle-In-Cell/Monte Carlo Collisions (PIC/MCC) simulation code designed for educational and research use in radio-frequency capacitive plasma simulations. It provides a tutorial on PIC/MCC theory and algorithms, along with ready-to-use C++, C, and Rust implementations, enabling users to simulate ion flux-energy distributions and electron energy probability functions in argon plasmas under single- and dual-frequency excitation.

ABSTRACT

For the self-consistent description of various plasma sources operated in the low-pressure (nonlocal, kinetic) regime, the Particle-In-Cell simulation approach, combined with the Monte Carlo treatment of collision processes (PIC/MCC), has become an important tool during the past decades. PIC/MCC simulation codes have been developed and maintained by many research groups, some of these codes are available to the community as freeware resources. While this computational approach has already been present for a number of decades, the rapid evolution of the computing infrastructure makes it increasingly more popular and accessible, as simulations of simple systems can be executed now on personal computers or laptops. During the past few years we have experienced an increasing interest in lectures and courses dealing with the basics of particle simulations, including the PIC/MCC technique. In a response to this, this paper (i) provides a tutorial on the physical basis and the algorithms of the PIC/MCC technique and (ii) presents a basic (spatially one-dimensional) electrostatic PIC/MCC simulation code for Capacitively Coupled Plasmas, whose source is made freely available in various programming languages. We share the code in C/C++ versions, as well as in a version written in Rust, which is a rapidly emerging computational language. Our code intends to be a "starting tool" for those who are interested in learning the details of the PIC/MCC technique and would like to develop the "skeleton" code further, for their research purposes.

Motivation & Objective

• To provide a pedagogical introduction to the physics and algorithms of the PIC/MCC method for low-temperature plasma simulations.
• To offer a minimal, extensible, and freely available simulation code for beginners in plasma physics and computational physics.
• To support the learning and development of custom plasma simulation codes by providing a modular, well-documented starting point.
• To enable simulation of key plasma phenomena such as non-Maxwellian electron energy distributions and ion flux-energy distributions in RF capacitive discharges.
• To promote accessibility of advanced plasma simulation techniques by providing implementations in modern and traditional programming languages.

Proposed method

• Employs the electrostatic PIC/MCC method to simulate charged particle dynamics in a 1D domain with periodic boundary conditions.
• Uses a structured grid to solve the Poisson equation for self-consistent electric potential and field calculations.
• Applies Monte Carlo collision modeling to simulate electron-neutral and ion-neutral interactions using differential cross sections.
• Implements particle push and charge deposition algorithms to update particle positions, velocities, and charge densities on the grid.
• Supports voltage-driven simulations with time-dependent electric fields and includes sheath edge detection via density profile analysis.
• Provides modular code structure in C++, C, and Rust, with clear comments and extensibility for advanced features like circuit coupling or parallelization.

Experimental results

Research questions

• RQ1 How can a beginner learn the fundamentals of PIC/MCC simulation for low-temperature plasmas in a practical, code-based way?
• RQ2 What are the core algorithmic components of a 1D electrostatic PIC/MCC code for RF capacitive discharges?
• RQ3 How do non-Maxwellian electron energy distributions and ion flux-energy distributions emerge in single- and dual-frequency argon plasmas?
• RQ4 What are the key implementation considerations for making a PIC/MCC code both educational and extensible?
• RQ5 How can the code be extended to simulate advanced plasma phenomena such as sheath dynamics, external circuits, or magnetic fields?

Key findings

• The eduPIC code successfully simulates the formation of non-Maxwellian electron energy probability functions (EEPFs) in argon plasmas under single- and dual-frequency excitation.
• Ion flux-energy distributions (IFEDFs) are accurately captured, showing distinct features such as ion energy modulation and harmonic content consistent with known physics.
• The code reproduces the development of self-bias voltage in asymmetric electrode configurations due to unequal ion fluxes.
• Sheath edge positions are reliably determined from time-dependent electron and ion density profiles, enabling calculation of sheath voltage and charge.
• The modular design allows for straightforward extension to include external circuits, null-collision methods, and power control loops.
• The availability of code in multiple languages, including modern Rust, enhances accessibility and performance portability for educational and research use.