frequency ω of that wave and is given by (SI units) If the critical density is exceeded, the plasma is called over-dense. In a magnetized plasma, except for the O wave, the cut-off relationships are more complex. O wave The O wave is the "ordinary" wave in the sense that its dispersion relation is the same as that in an unmagnetized plasma, that is, . It is plane polarized with E1 || B0. It has a cut-off at the plasma frequency. X wave The X wave is the "extraordinary" wave because it has a more complicated dispersion relation: Where . It is partly transverse (with E1⊥B0) and partly longitudinal; the E-field is of the form Where refer to the Stix notation. As the density is increased, the phase velocity rises from c until the cut-off at is reached. As the density is further increased, the wave is evanescent until the resonance at the upper hybrid frequency . Then it can propagate again until the second cut-off at . The cut-off frequencies are given by where is the electron cyclotron resonance frequency, and is the electron plasma frequency. The resonant frequencies for the X-wave are: where and . R wave and L wave The R wave and the L wave are right-hand and left-hand circularly polarized, respectively. The R wave has a cut-off at ωR (hence the designation of this frequency) and a resonance at ωc. The L wave has a cut-off at ωL and no resonance. R waves at frequencies below ωc/2 are also known as whistler modes. Dispersion relations The dispersion relation can be written as an expression for the frequency (squared), but it is also common to write it as an expression for the index of refraction ck/ω (squared). See also Appleton-Hartree equation List of plasma (physics) articles References Waves in plasmas