Solar wind effects on nonlinear electrostatic structures at the Venusian mantle

Phase-space electron holes, recognised as fundamental nonlinear electrostatic structures in space plasmas, have recently been detected near the mantle boundary of the Venusian magnetosheath by both the Parker Solar Probe (PSP) and the Pioneer Venus Orbiter (PVO). To understand their origin and characteristics, we develop a hydrodynamic model coupled with reductive perturbation theory that incorporates a small population of non-isothermal trapped electrons together with the dynamical effects of solar-wind ions and electrons. This formulation yields a generalised Schamel–Korteweg de Vries equation supporting two distinct classes of nonlinear electrostatic modes: solitary waves and double layers. Using parameter ranges constrained by in situ measurements – including relative densities, drift velocities and temperature ratios – we conduct a detailed parametric investigation of both structures. For the solitary-wave solutions, the model predicts electric field amplitudes of ~ 20 mV m –1 , temporal scales of ~ (2.5-4.5)\, ms and characteristic frequencies of ~ (0.31-5.6) kHz. The double-layer solutions exhibit fields of ~ 18 mV m –1 , durations of ~ 4.5\, ms and frequencies of ~ (0.63-1.6) kHz. These results are in strong agreement with PSP and PVO observations, which report electrostatic fluctuations near 5.4 kHz with amplitudes of ~ 20 mV m –1 . The present analysis therefore provides a consistent physical interpretation of electron-hole structures in the Venusian magnetosheath and highlights their role in mediating kinetic processes at unmagnetised planetary boundaries.