Plasmadispersion

Plasmadispersion refers to the frequency-dependent propagation of electromagnetic waves in a plasma, arising from the medium's dispersive dielectric response. In a cold, collisionless plasma the free electrons collectively respond to oscillating fields, producing a plasma frequency below which waves cannot propagate. In magnetized plasmas, the dispersion also depends on direction relative to the magnetic field, giving multiple propagation modes.

Key quantities include the plasma frequency ω_p = sqrt(n_e e^2/(ε0 m_e)). In an unmagnetized cold plasma, the dispersion relation is ω^2 = ω_p^2 + c^2 k^2, implying a refractive index n = sqrt(1 - ω_p^2/ω^2) for ω > ω_p. The phase velocity is v_p = c / sqrt(1 - ω_p^2/ω^2) and the group velocity is v_g = dω/dk = c sqrt(1 - ω_p^2/ω^2). Waves with ω ≤ ω_p are evanescent and do not propagate.

In magnetized plasmas the Appleton–Hartree relation describes the dielectric response, yielding distinct propagation for the ordinary (O) and extraordinary (X) modes when the wave vector is aligned with the magnetic field, and more complex behavior otherwise. Left- and right-circularly polarized waves generally experience different indices, leading birefringence and phenomena such as Faraday rotation of the polarization plane.

Plasmadispersion has wide-ranging implications. In astrophysics it causes frequency-dependent delays of radio signals, enabling measurements of electron column density in the interstellar and intergalactic media. In laboratory and space communications, it affects signal timing and wave coupling; in fusion and laser-plasma experiments, it informs diagnostics and heating schemes. The topic is treated in the cold plasma model and extended with kinetic and magnetohydrodynamic descriptions for more accurate modeling.