Langmuir Plasma Waves — Electron Dispersion Relation

ω(k) dispersion — Langmuir (blue), light (gray), Landau damping rate (red)

Electron density wave oscillation in real space

Plasma Parameters

Electron density n₀: 1.0 ×10¹⁷ m⁻³ Electron temperature Te: 1.0 eV Wave number k: 1.00 ×λ_D⁻¹ Amplitude δn/n₀: 0.10

Frequencies & Lengths

ω_pe (plasma freq)—

λ_D (Debye length)—

ω(k) [Bohm-Gross]—

Phase velocity—

Group velocity—

Landau damping γ—

ω² = ω_pe² + 3k²v_th²

ω_pe² = n₀e²/(ε₀mₑ)

λ_D = √(ε₀kT/n₀e²)

Langmuir waves are longitudinal electron oscillations at ω ≥ ω_pe. Ions are too heavy to respond.

Landau damping: resonant electrons with v ≈ ω/k absorb energy — exponential decay without collisions (kinetic effect).