On the limitations of applying reduced free energy parameter spaces to proton beams in the solar wind

Coulomb collisions impact the solar wind's evolution towards local thermodynamic equilibrium (LTE). As such, the solar wind is a nearly, but not fully collisionless plasma. Instabilities are normal modes that grow with time and constitute an additional class of mechanisms apart from collisions that contribute to the solar wind's evolution towards LTE. The types of growing modes depends on the available free energy sources, the number of which are proportional to the number of ion populations present. While assuming that only a reduced set of free energy sources are significant can make this parameter space and analysis tractable, these assumptions neglect the solar wind's detailed and varying thermal structure. Proton beams are non-LTE structures that markedly impact this thermal structure. This work shows that neglecting the proton beam's contribution limits the reduced parameter space's ability to suitably characterize solar wind instabilities. Nyquist's method is an algorithm that accounts for the effects of all the free energy sources associated with a given set of measurements on the plasma's stability. Applying it to Wind Faraday cup proton beam measurements, we illustrate that proton beams may contribute to unexpected growth of instabilities oblique to the local magnetic field.