Determining the mass density along magnetic field lines from toroidal eigenfrequencies

Toroidal eigenfrequencies can be used to remotely sense the equatorial mass density rho (eq) and the density dependence along a magnetic field line. H ere we present improvements to the method of Schulz [1996], which allows rh o (eq) and the power law index alpha (for mass density along a field line a lpha R-alpha, 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 frequ ency versus toroidal harmonic number n. Our modifications include a model f orm for eigenfrequencies with a fractional precision of 0.0005 for -6 less than or equal to alpha less than or equal to 6 and 2 less than or equal to L less than or equal to 8 (accuracy is doubtful beyond L = 5) and an iterat ive procedure for getting more accurate results than those found using Schu lz's method. In addition, we do an analysis of the effect of random measure ment errors. Observed frequencies need to be accurate to similar to6% (3%) of the fundamental frequency in order to determine rho (eq) (alpha) to a pr ecision of 30% (unity). We then apply our method to data generated using th e Global Core Plasma Model for plasmaspheric mass density; our analysis dem onstrates clearly how the alpha index represents the mass density dependenc e on the outer part of the held line (R/(LRE) greater than or similar to 2/ 3).