  The hot and diffuse nature of the Sun's extended atmosphere allows it to
persist in non-equilibrium states for long enough that wave-particle
instabilities can arise and modify the evolution of the expanding solar wind.
Determining which instabilities arise, and how significant a role they play in
governing the dynamics of the solar wind, has been a decades-long process
involving in situ observations at a variety of radial distances. With new
measurements from Parker Solar Probe (PSP), we can study what wave modes are
driven near the Sun, and calculate what instabilities are predicted for
different models of the underlying particle populations. We model two
hours-long intervals of PSP/SPAN-i measurements of the proton phase-space
density during PSP's fourth perihelion with the Sun using two commonly used
descriptions for the underlying velocity distribution. The linear stability and
growth rates associated with the two models are calculated and compared. We
find that both selected intervals are susceptible to resonant instabilities,
though the growth rates and kind of modes driven unstable vary depending on if
the protons are modeled using one or two components. In some cases, the
predicted growth rates are large enough to compete with other dynamic
processes, such as the nonlinear turbulent transfer of energy, in contrast with
relatively slower instabilities at larger radial distances from the Sun.
