⚡ Plasma Oscillations — Langmuir Waves

The plasma frequency ω_p = √(n·e²/(ε₀·mₑ)) is the natural rate at which displaced electrons oscillate about the neutralising ion background. It depends only on the electron density n, not on wavelength, so in a cold plasma every Langmuir wave rings at the same frequency. It is also a cut-off: electromagnetic waves with frequency below ω_p cannot propagate through the plasma and are reflected instead.

The Plasma density n slider scales ω_p directly, since in the simulation's normalised units ω_p = √n. Increasing n raises the plasma frequency and speeds up the visible oscillation of the density wave, exactly as higher electron density does in a real plasma.

For a warm plasma, thermal electron motion modifies the oscillation frequency according to ω² = ω_p² + 3k²v_th², where v_th is the thermal velocity and k is the wavenumber. Raising the Temperature slider increases v_th, which raises the displayed ω above ω_p and adds a slow envelope decay to the wave, echoing how Landau damping attenuates real warm-plasma oscillations.

When electrons shift away from the fixed positive ions, the exposed ion charge creates a restoring electric field pulling the electrons back, much like a spring. Because the ions are far more massive than the electrons, they stay essentially fixed on the electron oscillation timescale, so this restoring force keeps pulling the electron cloud back and forth rather than letting it disperse.

This visualisation is a real-time WebGL shader that reproduces the correct physical relationships — the plasma frequency formula and the Bohm-Gross dispersion relation both drive the animation directly — rather than a full N-particle particle-in-cell code integrating individual electron trajectories. It is designed to build intuition for how density, wavenumber and temperature control the oscillation, using the same governing equations a PIC solver would obey.