collisionless

Collisionless describes a regime in which binary interactions between particles occur so rarely that they can be neglected. In such systems, the evolution is governed by collective fields and the phase-space distribution changes mainly through streaming along orbits, mixing, and wave-particle interactions rather than direct collisions. The collisionless approximation is appropriate when the collision time is long compared to the dynamical time and the mean free path exceeds the system size.

In plasma physics and space plasmas, the collisionless regime is common. The kinetic description uses the Vlasov equation for the distribution function f(r,v,t), coupled to Maxwell's equations. The collision term in the Boltzmann equation is omitted, as long-range electromagnetic forces and shielding (Debye length) govern dynamics. Phenomena include Landau damping and collisionless shocks; collisions become important only when the mean free path is reduced by high density or turbulence.

In astrophysics, gravity is also long-range and, for many systems, two-body encounters are infrequent. The relevant equation is the collisionless Boltzmann equation, often paired with Poisson's equation. Jeans theorem implies that equilibrium distributions depend on integrals of motion. The two-body relaxation time in galaxies and dark matter halos typically exceeds the age of the universe, so these systems are treated as collisionless. Numerical simulations use N-body methods to model self-gravitating, collisionless ensembles while suppressing artificial collisions.

Limitations: When densities are high or collisional processes become non-negligible, kinetic theories with collision terms or fluid models (magnetohydrodynamics) are required.