Because the harmonics of toroidal Alfvén wave eigenmodes have a different response to mass density at different points along a magnetic field line, the frequencies of these harmonics can, in principal, be used to infer the distribution of mass density along the field line. Here we present several improvements to the methodology and test our method using magnetic and plasma wave data from the CRRES spacecraft. Our method includes the calculation of toroidal frequencies in a Tsyganenko magnetic field assuming a polynomial expansion for the logarithm of the mass density with respect to a coordinate related to distance along the field line. We use a Monte Carlo distribution of frequencies about the observed peaks in order to infer an uncertainty for the mass density. The method only works well if the frequencies of the fundamental and second harmonic are known. We compare the inferred mass density at the spacecraft location with the electron density determined from the plasma wave experiment onboard CRRES. The observed electron density is about a factor of 2 lower than the mean of the inferred mass density for an ensemble of frequency combinations based on the uncertainties of the measured spectral peaks but is close to or within the error bars of the inferred mass density. In one of the cases examined, the inferred mass density had a local maximum at the equator, while in the other case the inferred mass density increased monotonically away from the equator.
