The shape of the profile of a high energy, low current beam of finite length has beam investigated. The beam profile shape depends on the initial beam radius, beam perveance, atomic mass number, charge state of ions, and beam length. These parameters can affect the relation between the initial beam radius and the corresponding final one. An optimum initial beam radius corresponding to minimum final beam at the target has been formulated and the relation between them is deduced taking account of the space charge effect. The minimum beam radius at the target was found to be equal to 2.3 of the optimum initial radius. It is concluded that in order to obtain a small beam radius at a target placed at a finite distance from an ion source, a beam of a low perveance, low atomic mass number and high number of electronic charge is required. This is an important detection for micro machining applications using the oscillating electron ion source which produces nearly paraxial thin beam of low perveance. 12 figs.