[en] For an intense ion beam, the following power of a solenoid magnet may be increased by many orders of magnitude by adding co-moving electrons. In this type of magnetic lens, the ions are focused by a collective electrostatic field induced in the beam by the action of the solenoid on the electrons. In this thesis, the collective field in such a lens is calculated using linearized perturbation theory and particle-in-cell computer simulation. The dependence of the collective field on the temperature of the neutralizing electrons is investigated using both of these methods and the effects of an applied electric field are included in the calculations. In addition, perturbation calculations of the effects of various errors are presented, including a linear stability analysis of the flow when the beam is in the lens. The results of a proof of principle experiment employing the large contact ionization Cs⁺¹ source at LBL are given. The major finding is that the collective lens focuses the beam, but electron thermal effects distort the space charge field. The simulations give a good quantitative account of the experimental results. The thesis concludes with a discussion of applications