time ωpet
measured growth rate γ
cold-fluid theory γ for this k
fastest-growing mode (cold theory)
total energy drift

A real 1-D electrostatic particle-in-cell simulation: CIC deposition, a spectral Poisson solve, and a leapfrog push. Two counter-streaming electron beams on a fixed ion background. Watch the phase space: ripples → exponential growth → the beams roll into cat's-eye vortices → thermalisation. Nothing here is scripted; the vortices form because the equations say so.