Eigenfrequencies of geomagnetic field lines and implications for plasma‐density modeling

Abstract

Toroidal eigenfrequencies ωn/2π (with harmonic numbers n ≥ 1) of dipolar magnetospheric B field lines are well approximated (within a few percent at most for L ≥ 2) by the linear expression , if the plasma density ρ is proportional to (La/r)m along the magnetic field line of interest (r being the geocentric distance, a being the planetary radius, and subscript 0 signifying evaluation at the magnetic equator). The spacings Δω/2π between consecutive eigenfrequencies are nearly equal and well approximated by the reciprocal of ∮ (ds/cA), where cA is the local Alfvén speed and s is the coordinate that measures arc length along the field line. Poloidal eigenfrequencies ωn/2π with harmonic numbers n ≥ 2 are equally well approximated by the same expression for ωn. This means that observed pulsation periodicities can be identified with their respective harmonic numbers by plotting the corresponding frequencies on a rectangular grid against possible harmonic numbers to see which reasonable identifications produce the best straight line. (Identification could alternatively be achieved, without plotting, through a modified form of linear regression.) Extrapolated to n = 3/4, the linear fit to an observed eigenfrequency spectrum (toroidal with n ≥ 1 and/or poloidal with n ≥ 2) would then yield a good estimate for the equatorial plasma density ρ0. The slope of this same linear fit would lead (when divided by ω0.75/2π) to a good estimate for the corresponding value of m, which is the exponent of La/r in the modeled plasma density distribution.