Richard Eugene Denton ^1* Kazue Takahashi ² David Paul Hartley ³

• ¹ Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire, United States
• ² Applied Physics Laboratory, Johns Hopkins University, Laurel, Maryland, United States
• ³ Department of Physics and Astronomy, College of Liberal Arts and Sciences, The University of Iowa, Iowa City, Iowa, United States

Using observations of mass density inferred from standing Alfv én wave frequencies and electron density inferred from plasma wave frequencies, predominantly for the Combined Release and Radiation Effects Satellite (CRRES) and Van Allen Probes spacecraft, we used symbolic nonlinear regression to find analytical formulas for the equatorial electron density, n e , mass density, ρ m , and average ion mass, M ≡ ρ m /n e . We separate the data into plasmasphere and plasmatrough populations based on the observed values of n e in order to find formulas for plasmasphere, plasmatrough, and both plasmasphere and plasmatrough. Our models depend on position, the solar extreme ultraviolet (EUV) F10.7 flux, geomagnetic activity parameters such as Kp, AE, Dst, and the solar wind dynamic pressure. Formulas for M are presented with or without n e as an input parameter. By examining formulas of varying complexity, we are able to determine the relative importance of the various dependencies. The most important dependencies for n e and ρ m are that they decrease with respect to L shell and geomagnetic activity as specified by parameters such as Kp. The most important dependence of M is that M increases with respect to increasing F10.7. The value of M is close to unity within the plasmasphere, but can be significantly above 1 in the plasmatrough. Although n e and ρ m have maximum value at dusk local time, M has maximum value at dawn local time. The O+ concentration is larger at dawn local time, but the O+ density can be comparable at dawn and dusk because of larger n e at dusk.