Home▸Physics & Mechanics▸Two-Stream Instability — Counter-Streaming Plasma Beams

⚡ Two-Stream Instability — Counter-Streaming Plasma Beams

Two counter-streaming electron beams in a plasma spontaneously grow an electrostatic wave. Watch phase space roll up into 'cat's eye' vortices while the field energy climbs exponentially, then saturates.

Physics & Mechanics3DAdvanced60 FPS⚡ Plasma

How this works

A 1D electrostatic particle-in-cell (PIC) solver tracks thousands of macro-particles split into two counter-streaming beams over a uniform neutralizing ion background. Each step: charge is deposited to a grid, the field is found from Gauss's law by direct integration, the field is gathered back to each particle, and particles are pushed with their charge-to-mass ratio.

The left panel is phase space — position on the horizontal axis, velocity on the vertical axis. The two beams start as flat horizontal bands; a resonant ripple grows and the bands fold into the characteristic "cat's eye" vortex of the nonlinear two-stream instability. The right panel plots total electrostatic field energy on a log scale, which should rise in a straight line during the linear growth phase before saturating once the beams trap each other.

⚙ Under the hood

A 1D electrostatic particle-in-cell solver tracks two counter-streaming electron beams: watch phase space roll up into 'cat's eye' vortices as a resonant ripple grows exponentially, then plot the field energy on a log scale against the theoretical growth rate.

plasma physicstwo-stream instabilityparticle-in-cellPIC simulationphase spaceelectrostatic wavesLangmuir wavesplasma instability

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install