  This study is motivated by recent observations from the Parker Solar Probe
(PSP) mission, which have been identified as the ion-acoustic waves from 15 to
25 solar radii. These observations reveal characteristic sequences of
narrow-band, high-frequency bursts exceeding 100 Hz embedded into a slower
evolution around 1 Hz, persisting for several hours. To explore the potential
role of the ion-acoustic instability (IAI) in these phenomena, we begin by
reviewing classical findings on the IAI within the framework of linear kinetic
theory. Focusing on proton distributions comprising both a core and a beam
component, we analyze the IAI instability range and growth rates within the
parameter regime relevant to PSP observations. Our findings indicate that the
IAI can indeed occur in this regime, albeit requiring electron-to-core and
beam-to-core temperature ratios slightly different from reported values during
electrostatic burst detection. Furthermore, employing 1D kinetic plasma
simulations, we validate the growth rates predicted by linear theory and
observe the saturation behavior of the instability. The resultant nonlinear
structures exhibit trapped proton beam populations and oscillatory signatures
comparable to those observed, both in terms of time scales and amplitude.
