The Impact of Physical Processes on the Radial Evolution of the Distant Pickup Ion Mediated Solar Wind

H⁺ pickup ions (PUIs), formed through charge exchange between solar wind (SW) protons and interstellar neutral hydrogen (ISN H) atoms or by the photoionization of ISN H atoms, play a key role in governing SW dynamics. These PUIs induce MHD waves by generating instabilities, driving turbulence in the outer heliosphere. The ionization cavity size is the distance at which the ISN H density becomes e⁻¹, which is smaller in the upwind direction than in the downwind direction. Consequently, the turbulent shear source affects the SW over a larger distance in the downwind direction than in the upwind direction. Here, we integrate the continuity, momentum, and pressure equations for ISN H with the three fluid (protons, electrons, and H⁺ PUIs) equations and the turbulence transport equations. We numerically solve the coupled four-fluid and turbulence transport equations between 10 and 68 au, and 10 and 115 au, before the heliospheric termination shock in the New Horizons (NH) and Pioneer 10 (P10) directions, respectively. We present the comparison of the theoretical results with the SW proton and PUI data of NH and the SW proton data of P10. We present the theoretical results of the low-frequency MHD turbulence and the cosmic-ray mean free paths along these directions. Finally, we derive the equation for the scattering angle of radio waves by assuming isotropic and Gaussian density turbulence and calculate the scattering angle in the NH and P10 directions.