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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
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On 14 Nov 2017, 10:06.