PIC 1D: Two-Stream Instability Simulation

---

Description

This project implements a 1D Particle-in-Cell (PIC) simulation to model the two-stream instability in a plasma.

The code is written in C++17, modular, and supports:

• Initialization of two counter-propagating electron streams.
• Solving the 1D Poisson equation with a tridiagonal matrix solver (Thomas algorithm).
• Particle push using Leap Frog method (position and velocity update).
• Calculation of momentum, kinetic energy, potential energy, and total energy of the system.
• Exporting data to CSV for analysis and visualization in Python.
• Phase space animation to observe the temporal evolution of the instability.

The main goal is to study the time evolution of energy and momentum and observe the growth of the instability.

---

Project Structure

• PIC2si/ – Root directory of the project
  • include/ – Header files
    • particles.hh – Particle class declarations
    • fields.hh – Field class declarations
    • diagnostics.hh – Functions for momentum and energy calculations
  • src/ – Source files
    • main.cpp – Main program
    • particles.cpp – Particle class implementation
    • fields.cpp – Field class implementation
    • diagnostics.cpp – Diagnostics function implementations
  • analysis.py – Python script for plotting simulation results
  • phaseSpace.py – Python script for generating phase space animation
  • CMakeLists.txt – CMake build configuration
  • README.md – Project documentation

---

Build

CMake is used to generate and build the project:

mkdir build cd build cmake .. cmake --build . --config Release

The executable will be located in build/Release/pic1d.exe (Windows/MSVC) or build/pic1d (MinGW/Linux).

---

Running the Simulation

Run the simulation to generate the CSV:

./pic1d.exe

This will create diagnostics.csv in the same directory as the executable, with columns:

time, momentum, Ekin, Epot, Etotal

---

Visualization

A Python script analysis.py is included to plot:

• Plasma momentum
• Kinetic energy
• Potential energy
• Total energy

Run the script in the same folder as the CSV:

python analysis.py

Phase Space Evolution

The script phaseSpace.py generates an animated GIF showing the phase space dynamics:

It will generate a plot showing the temporal evolution of the physical quantities.

python phaseSpace.py

Example result:

---

Customization

Parameters that can be modified in main.cpp:

• N : number of super-particles
• NG : number of grid cells
• L : domain length
• V0 : initial stream velocity
• DT : time step
• NT : number of time steps

---

License

MIT License © 2025 Juan Pablo Solís Ruiz

---

Contact

• Email: [email protected]
• GitHub: h4xter1612