Dispersion relation ω² = ωₚ² + 3k²v_th² for electrostatic waves in plasma
Plasma Parameters
Wave Properties
ωₚ = —
ω(k) = —
v_ph = ω/k = —
v_g = dω/dk = —
Theory
Plasma frequency:
ωₚ = √(n_e e²/ε₀m_e)
Bohm-Gross dispersion:
ω² = ωₚ² + 3k²v_th²
Below ωₚ: no wave propagation (evanescent). Above ωₚ: electron plasma waves (Langmuir waves). At k→0: pure plasma oscillation (purely temporal, zero group velocity).