Kinetic theory (particle-in-cell)#
An electrostatic particle-in-cell (PIC) solution of the 1D1V
Vlasov-Poisson system: particles stream along exact single-particle
orbits and the self-consistent field is recovered by depositing their
charge onto a grid and solving Poisson’s equation each step
(pic_simulate()). The same
deposit-solve-gather-push pipeline reproduces collisionless Landau
damping (landau_damping_ic(),
landau_damping_rate()), its
mirror-image growth mechanism, the two-stream instability
(two_stream_ic()), and a Langmuir wave
ringing in place at the plasma frequency
(langmuir_wave_ic()), all without ever
assuming a collision operator. The Weibel/filamentation instability
(weibel_growth_rate(),
simulate_weibel_filamentation())
is treated as a reduced quasi-linear model of the same current-driven
physics, at the opposite (temperature-anisotropy) end of the kinetic
spectrum from a beam-driven instability.
Landau damping from first principles with particle-in-cell
The two-stream instability: exponential growth and phase-space vortices
Weibel filamentation: growing current filaments from temperature anisotropy
Langmuir waves: electron density ringing at the plasma frequency