Plasma Wave Dispersion

Langmuir waves, ion-acoustic waves, Bohm-Gross dispersion & Landau damping

Plasma Parameters

Dispersion

ωₚ:
ω_Langmuir(k):
ω_ion-acoustic(k):
Landau damp γ:
Phase vel vφ:
Group vel vg:

Theory

Bohm-Gross (Langmuir):
ω² = ωₚ² + 3k²vₜₕ²
Ion-acoustic:
ω = k·cs, cs = vₜₕ/√(m_i/m_e)
Landau damping (weak damping):
γ/ωₚ ≈ −√(π/8)(ωₚ/kvₜₕ)³ e^{−ω²/2k²vₜₕ²}
Wave-particle resonance at v_res = ω/k — particles near resonance drain wave energy.