A model is presented for space charge neutralisation of positive ion beams. The model is used for the particular case of the beams used for magnetic based fusion applications. The beams consist, after a gas neutraliser, of ions and atoms at different energies. Account is taken of the contribution of all beam components to ionization of the background gas. Consideration is also given to not only beam heating of the plasma generated by the beam, due to Coulomb collisions, but also to Coulomb heating by fast electrons produced in ionization by all beam particles and stripping of the neutral components. Two approximations are considered for the motion of the secondary ions out of the beam potential; a drift approximation and a freefall approximation. All the beam plasma parameters can be calculated. The model is applied to a typical extracted beam of deuterium ions of 120 kV, 60 A. It is found that these beams are very highly compensated and that beam plasma heating by the electrons produced is generally greater than that due to the beam ions.