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Modeling fast solar wind based on the kinetic theory is an important task forscientists. In this paper, we present a two-fluid model for fast solar windwith anisotropic Kappa-Maxwellian electrons and Bi-Maxwellian protons. In thesimulation, the energy exchange between the plasma particles and low-frequencyAlfv\'en waves is considered. A set of eleven coupled equations is derived byapplying the zeroth- to fourth-order moments of the Vlasov equation and themodified electromagnetic Maxwell equations. A characteristic of the Kappadistribution (indicated by $\kappa$ index) is explicit in the equation for theparallel component of the electron heat flux (parallel to the ambient magneticfield line) and differs from the equation derived for the proton heat flux dueto the different nature of the distributions. Within the large $\kappa$ index,the equations for the two-fluid model tend to the equations obtained by theMaxwellian distribution. Using an iterated Crank-Nicolson method, the coupledequations are numerically solved for the fast solar wind conditions. We showthat at (0.3 - 1) AU from the Sun, the electron density, components oftemperature, and components of heat flux follow the power-law behavior. We alsoshowed that near the Earth, the flow speed (electron or proton) increases withdecreasing $\kappa$. We concluded that applying the small $\kappa$ index (thenon-Maxwellian distribution), the extraordinary nature of the solar atmosphere,with its temperature of several million kelvin temperature for electrons, hasbeen captured.

Kappa-Maxwellian electrons and Bi-Maxwellian protons in a two-fluid model for fast solar wind