Footnotes:
1They are therefore sometimes called `Moment
Equations.'
2This is often, for historical reasons,
written an the equivalent form (called the Appleton-Hartree
dispersion relation) that can be considered to be
N2 = 1 − [(2(A−B+C))/(2A−B±F)].
The benefit of the earlier Appleton Hartree formulation is not this trivial
reorganization, however. It is that in it the coefficients A, B, and C
are effectively multiplied by a factor
r=(Ωe2−ω2)(ω2−Ωi2). That has the considerable
benefit of avoiding the necessity to flip the sign of F in order to
get continuous behavior of the solutions through the cyclotron
frequencies. The benefit can also be obtained by writing the solution as
N2=[B±sign(R)F]/2A.
HEAD
File translated from
TEX
by
TTH,
version 4.12.