defined such that the background magnetic field is
In a cartesian system defined such that the background magnetic field is
 | (88) |
and the wave index of refraction is
 | (89) |
the permittivity tensor can be expressed explicitly as
 | (90) |
such that the dispersion tensor is
 | (91) |
and the dispersion relation becomes
is rearranged in powers of N⊥ as
 | (93) |
with
 | (94) |
The dispersion relation (??) can be further expanded as
In preparation for calculating the derivatives, it is useful to split the dispersion relation in a sum of products
 | (96) |
where
 | (97) |
 | (98) |
 | (99) |
 | (100) |
 | (101) |