Determining the mass density along magnetic field lines from toroidal eigenfrequencies

Toroidal eigenfrequencies can be used to remotely sense the equatorial mass density ρ_eq and the density dependence along a magnetic field line. Here we present improvements to the method of Schulz [1996], which allows ρ_eq and the power law index α (for mass density along a field line ∝ R^-α, where R is the radial distance from the center of the Earth) to be-determined from the y intercept and slope of a plot of toroidal frequency versus toroidal harmonic number n. Our modifications include a model form for eigenfrequencies with a fractional precision of 0.0005 for -6 ≤ α ≤ 6 and 2 ≤ L ≤ 8 (accuracy is doubtful beyond L = 5) and an iterative procedure for getting more accurate results than those found using Schulz's method. In addition, we do an analysis of the effect of random measurement errors. Observed frequencies need to be accurate to ∼6% (3%) of the fundamental frequency in order to determine ρ_eq (α) to a precision of 30% (unity). We then apply our method to data generated using the Global Core Plasma Model for plasmaspheric mass density; our analysis demonstrates clearly how the a index represents the mass density dependence on the outer part of the field line (R/(LR_E) ≳ 2/3).