Estimating Electron Temperature and Density Using Van Allen Probe Data: Typical Behavior of Energetic Electrons in the Inner Magnetosphere

The Earth's inner magnetosphere contains multiple electron populations influenced by different factors. The cold electrons of the plasmasphere, warm plasma that contributes to the ring current, and the relativistic plasma of the radiation belts often seem to behave independently. Using omni-directional flux and energy measurements from the HOPE and Magnetic Electron Ion Spectrometer instruments aboard the Van Allen Probes, we provide a detailed density and temperature description of the inner magnetosphere, offering a comprehensive statistical analysis of the entire Van Allen Probe era. While number density and temperature data at geosynchronous orbit are available, this study focuses on the warm plasma in the inner magnetosphere . Values of density and temperature are extracted by fitting energy and phase space density to obtain the distribution function. The fitted distributions are related to the zeroth and second moments to estimate the number density and temperature. Analysis has indicated that a two Maxwellian fit is sufficient over a wide range of $L^{\ast }$ and that there are two independent plasma populations. The more energetic population has a median number density of approximately $1.2\times 10^4$ $m^{-3}$ and a temperature of around 130 keV, with a temperature peak observed between L* = 4 and L* = 4.5. This population is relatively uniform in magnetic local time (MLT). In contrast, the less energetic warm electron population has a median number density of about $2.5\times 10^4$ $m^{-3}$ and a temperature of 7.4 keV. Strong statistical trends in density and temperature across both L* and MLT are presented, along with potential sources driving these variations.