Langmuir electron density waves in 1D plasma with real particle-in-cell dynamics.
Langmuir waves: electrons displaced from uniform background → restoring electrostatic force → oscillation at plasma frequency ωₚ = √(ne²/mε₀). The dispersion relation is ω² = ωₚ² + 3k²v_th² (Bohm-Gross). These electrostatic oscillations don't propagate at ωₚ alone; thermal effects create the traveling wave. Upper panel: electron positions. Lower: density n(x) and E-field E(x).