We have modelled the evolution of the electron velocity distribution function in high-speed solar wind streams, from the collision-dominated corona and into the collisionless interplanetary space. The model solves the kinetic transport equation, with the Fokker-Planck collision operator to describe Coulomb collisions between electrons. We use a test particle approach, where test electrons are injected into a background solar wind. The density, temperature and electric field associated with the background are obtained from a three-fluid solar wind model. The test electrons are in thermal equilibrium with the background at the base of the corona, and we study the evolution of the velocity distribution of the test electrons as a function of altitude. We find that the test particle distribution function is mainly determined by the electric field and the expanding geometry, and to a lesser extent by collisions. The distribution function consists of an almost isotropic, static core which is bound in the electrostatic potential, and a beam-like high-energy tail which escapes. Velocity filtration, due to the energy dependence of the Coulomb cross section, is not alone capable of producing significant beams in the distribution or a temperature moment that increases with altitude. The distribution function is in excellent agreement with the distribution functions observed by the Helios spacecraft in high-speed streams near the orbit of Mercury.

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