Stability Analysis of the Proton Hammerhead Distribution Observed by Parker Solar Probe: Linear Theory and Fully Kinetic Simulations under Idealised Conditions
The non-adiabatic heating of the slow Solar Wind (SW) remains an open problem, with wave--particle interactions as a primary candidate mechanism. Novel in situ Parker Solar Probe (PSP) observations reveal strongly perpendicular anisotropic velocity distribution functions (VDFs), called "hammerhead", correlated with intense wave activity. These VDFs are systematically measured at the Heliospheric Current Sheet (HCS), making the hammerhead an important kinetic signature of the slow SW. In this work, we employ a fully kinetic particle-in-cell approach, complemented by a linear Vlasov solver to cross-validate the simulation results, to investigate the stability of these VDFs, the timescales over which they evolve, and their interaction with plasma waves. Our main findings indicate that the hammerhead distribution is primarily susceptible to drift-type instabilities, while energy is nonlinearly transferred back to the plasma through a combination of Landau and cyclotron resonances, resulting in net heating in the parallel direction, preferentially energizing the beam proton population. Crucially, these nonlinear interactions do not drastically alter the morphology of the distribution. This suggests the possibility that the hammerhead may be generated locally within the HCS in the inner heliosphere and subsequently advected outward, where it is eventually measured by PSP. This work lays the ground for future investigations into the kinetic physics of the HCS.