2.5 Dispersion relation

In order to obtain non-trivial solutions to the Eq. ??, the determinant of the dispersion tensor must be zero,

(18)

which defines the dispersion relation. This relation gives the local electromagnetic eigenmodes that can be excited independently in the homogenous plasma. By cylindrical symmetry about the direction of the magnetic field = B₀∕B₀, depends only upon the components of N parallel and perpendicular to the magnetic field, defined respectively as N_∥ = N ⋅ and N_⊥ = . Thus, the dispersion relation (??) can be solved for either ω, N_∥ or N_⊥. The polarization of any eigenmode resulting from equation (??) is determined by the corresponding eigenvector of the wave equation (??).

Explicit expressions of the dispersion relation are given in Appendix A1.