The Van Allen Probes mission provides unique measurements of the most energetic radiation belt electrons at ultrarelativistic energies. Simultaneous observations of plasma waves allow for the routine inference of total plasma number density, a parameter that is very difficult to measure directly. On the basis of long-term observations in 2015, we show that the underlying plasma density has a controlling effect over acceleration to ultrarelativistic energies, which occurs only when the plasma number density drops down to very low values (~10 cm-3). Such low density creates preferential conditions for local diffusive acceleration of electrons from hundreds of kilo-electron volts up to >7 MeV. While previous models could not reproduce the local acceleration of electrons to such high energies, here we complement the observations with a numerical model to show that the conditions of extreme cold plasma depletion result in acceleration up to >7 MeV.
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