⚡ 2D Plasma — Particle-in-Cell Charged Gas

How this particle-in-cell simulation works

This is a genuine, if small-scale, particle-in-cell (PIC) plasma solver — not a decorative N-body glow effect. Every step: (1) each charged particle's charge is deposited onto a 64×40 grid using bilinear (cloud-in-cell) weighting; (2) the resulting charge density feeds a real Poisson equation −∇²φ = ρ/ε₀, solved with 20 Gauss–Seidel relaxation iterations per frame on a periodic domain; (3) the electric field E = −∇φ is computed on the grid by finite differences and interpolated back to each particle's position; (4) particles are pushed by F = qE with a real electron/ion mass ratio of 1 : 1836.

In Plasma Oscillation mode, electrons move against a stationary, uniform positive ion background. A single-wavelength density perturbation is seeded at start, and the resulting restoring electric field makes the electron gas oscillate at the real electron plasma frequency ω_p = √(ne²/ε₀m_e) — the readout panel measures the oscillation period directly from the simulated motion and compares it to the theoretical value from the formula.

In Debye Shielding mode, both ions and electrons are mobile and thermalised. A fixed test charge is inserted into the plasma, and the mobile charges rearrange around it, screening its field beyond roughly one Debye length λ_D — the same real length scale that limits how far an electrostatic disturbance in a real plasma can be felt.