Temperature of the plasmasphere from Van Allen Probes HOPE
We introduce two novel techniques for estimating temperatures of very low energy space plasmas using, primarily, in situ data from an electrostatic analyzer mounted on a charged and moving spacecraft. The techniques are used to estimate proton temperatures during intervals where the bulk of the ion plasma is well below the energy bandpass of the analyzer. Both techniques assume that the plasma may be described by a one-dimensional $→\atop{E}$ x $→\atop{B}$ drifting Maxwellian and that the potential field and motion of the spacecraft may be accounted for in the simplest possible manner, i.e., by a linear shift of coordinates. The first technique involves the application of a constrained theoretical fit to a measured distribution function. The second technique involves the comparison of total and partial-energy number densities. Both techniques are applied to Van Allen Probes Helium, Oxygen, Proton, and Electron (HOPE) observations of the proton component of the plasmasphere during two orbits on 15 January 2013. We find that the temperatures calculated from these two order-of-magnitude-type techniques are in good agreement with typical ranges of the plasmaspheric temperature calculated using retarding potential analyzer-based measurements—generally between 0.2 and 2 eV (2000–20,000 K). We also find that the temperature is correlated with L shell and hot plasma density and is negatively correlated with the cold plasma density. Lastly, we posit that the latter of these three relationships may be indicative of collisional or wave-driven heating of the plasmasphere in the ring current overlap region. We note that these techniques may be easily applied to similar data sets or used for a variety of purposes.