Plasma Waves & Dispersion Relations

Langmuir, ion-acoustic, whistler, and Alfvén modes — ω-k diagram with cutoffs and resonances

Dispersion Diagram ω vs k

Plasma frequency ω_pe: 1.5

B-field Ω_ce (cyclotron): 0.8

Ion-electron mass ratio: 50

EM (R-wave)

EM (L-wave)

Langmuir

Ion-acoustic

Whistler

Alfvén

Light cone

Wave Properties at cursor

Hover over the dispersion diagram to see ω, k, phase velocity, group velocity.

Wave Animation

Mode:

Phase & Group Velocity vs k

Phase velocity v_ph = ω/k (dashed). Group velocity v_gr = dω/dk (solid). At cutoffs (ω = ω_pe, ω_R, ω_L), k→0 so v_ph→∞. At resonances (ω = Ω_ce, ω_LH), k→∞ so v_gr→0.