Frequencies of standing Alfvén wave harmonics and their implication for plasma mass distribution along geomagnetic field lines: Statistical analysis of CRRES data

<jats:p>The relationship among the frequencies of the harmonics of standing Alfvén waves depends on the variation of plasma mass density along the geomagnetic field line. This in turn means that observed standing wave frequencies may be used to infer the mass density variation, which is difficult to measure with particle instruments on spacecraft. Determination of the density variation is important in understanding mass transport processes in the ionosphere‐magnetosphere system and also in improving magnetospheric diagnostic techniques using ULF waves. We investigate the frequencies of multiharmonic toroidal standing Alfvén waves detected in the electric and magnetic fields measured by the Combined Release and Radiation Effects Satellite (CRRES). The data cover the entire CRRES mission period from July 1990 to October 1991. Using a semi‐automated procedure, we identify over 4000 samples of the fundamental toroidal frequency (<jats:italic>f</jats:italic><jats:sub>1</jats:sub>), which are often accompanied by the second (<jats:italic>f</jats:italic><jats:sub>2</jats:sub>) and third (<jats:italic>f</jats:italic><jats:sub>3</jats:sub>) harmonics. Most (∼3000) fundamental frequency samples are taken at dipole <jats:italic>L</jats:italic> shells from 4 to 8 and at magnetic local time (MLT) from 1200 to 1800, and we perform statistical analyses of the frequencies in this <jats:italic>L</jats:italic>‐MLT domain. The most frequently observed ratios are <jats:italic>f</jats:italic><jats:sub>2</jats:sub>/<jats:italic>f</jats:italic><jats:sub>1</jats:sub> ∼ 2.5 and <jats:italic>f</jats:italic><jats:sub>3</jats:sub>/<jats:italic>f</jats:italic><jats:sub>1</jats:sub> ∼ 4.0 for 4 ≤ <jats:italic>L</jats:italic> < 6 and <jats:italic>f</jats:italic><jats:sub>2</jats:sub>/<jats:italic>f</jats:italic><jats:sub>1</jats:sub> ∼ 2.8 and <jats:italic>f</jats:italic><jats:sub>3</jats:sub>/<jats:italic>f</jats:italic><jats:sub>1</jats:sub> ∼ 4.3 for 6 ≤ <jats:italic>L</jats:italic> < 7. These observations are compared with the theoretical ratios obtained for the density variation of the form ρ = ρ<jats:sub>eq</jats:sub>(<jats:italic>LR</jats:italic><jats:sub><jats:italic>E</jats:italic></jats:sub>/<jats:italic>R</jats:italic>)<jats:sup>α</jats:sup>, where ρ<jats:sub>eq</jats:sub> is the equatorial mass density, <jats:italic>L</jats:italic> is the magnetic shell parameter, <jats:italic>R</jats:italic> is geocentric distance to the field line, and the power law density index α is a free parameter. We find that α ∼ 0.5 fits the average observed frequency ratios at 4 ≤ <jats:italic>L</jats:italic> < 6, consistent with a diffusive equilibrium solution. No single value of α fits the average observed frequency ratios at 6 ≤ <jats:italic>L</jats:italic> < 7. In that case, theoretical solutions indicate that the mass density is locally peaked at the equator; that is, the mass density decreases as one moves off‐equator, then increases again toward the ionosphere. Combined with the results of recent studies of electron density (which have not found such a peak in density at the magnetic equator), this indicates that heavy ions are preferentially concentrated at the magnetic equator.</jats:p>