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An experimental study of an intense space charge neutralized ion beam propagating into a solenoidal magnetic field is presented. The data shows that the observed effects are adequately described by a theory for beam propagation. In a previous experiment a similar beam was focused by a short magnetic field where the focal point was outside the field region. This experiment shows that the same theory can be used to describe a beam which comes to a focus within the uniform region of the solenoid. The theory essentially states that ions undergo single particle motion modified by the beam neutralizing electrons which produces focal distances much shorter than ions acting alone. The physics of this type of focusing is similar to the Gabor lens in which electrons that prefill a magnetic mirror produce electrostatic fields which assist in the focusing of a stream of ions. The new theory, assumes a cylindrically symmetric beam which does not significantly perturb the magnetic field, maintenance of local space charge neutrality and perfectly cold neutralizing electrons.