Plasma oscillation

A plasma oscillation is a collective oscillation of charge density and its restoring electric field. In a three-dimensional bulk charged superfluid, long-range Coulomb forces give the longitudinal collective mode a nonzero long-wave plasma frequency. Different geometry and electromagnetic boundary conditions can change that limit.

A low-frequency electrostatic plasma wave with ion inertia and a pressure restoring force, usually dominated by electron pressure. Weak ion Landau damping requires the phase velocity to exceed typical ion speeds. Electron Landau damping depends on the electron parallel marginal distribution and need not vanish even when ion damping is absent.

For equal densities of singly charged ions and electrons, a completely degenerate electron equation of state gives $d{P}_e/d{n}_e=m_e{v}_{Fe}^2/3$. Coupling this restoring force to ion inertia yields the sound speed in the title. If both species are degenerate and $m_e\ll m_i$, then $v_{Fi}\ll c_s\ll v_{Fe}$. Ion resonances are absent, while the electron parallel marginal distribution has a small slope at the phase velocity, producing relative Landau damping of order $\sqrt{m_e/m_i}$.

An electron-supported electrostatic branch with approximately linear small-wavenumber dispersion relation $\omega \simeq k{u}_a$. A velocity plateau can support such a completely undamped mode even when ion response is neglected. A single Maxwellian electron population generally damps the corresponding acoustic response strongly. Distinct electron populations provide another setting for electron acoustic behavior, with different assumptions and damping properties.

A longitudinal electron plasma oscillation whose long-wavelength frequency approaches the electron plasma frequency when ions can be treated as stationary. Its dispersion relation and Landau damping depend on the electron phase-space distribution function. Compact velocity support can permit exactly undamped branches outside the support.

The long-wavelength root of the degenerate-plasma dielectric response. Expanding its logarithm at large $s=\omega /(k{v}_F)$ gives $ϵ=1-{\omega }_p^2/{\omega }^2-3{\omega }_p^2{k}^2{v}_F^2/(5{\omega }^4)+\cdots$. The occupied Fermi sphere has $⟨v_{\parallel }^2⟩=v_F^2/5$, accounting for the dispersive coefficient. The static electron response instead defines the Thomas-Fermi screening length $v_F/(\sqrt{3}{\omega }_p)$.