Tunnel ionizing neutral gas with the self-field of a charged particle beam is explored as a possible way of creating plasma sources for a plasma wakefield accelerator [Bruhwiler et al., Phys. Plasmas (to be published)]. The optimal gas density for maximizing the plasma wakefield without preionized plasma is studied using the PIC simulation code OSIRIS [R. Hemker et al., in Proceeding of the Fifth IEEE Particle Accelerator Conference (IEEE, 1999), pp. 3672-3674]. To obtain wakefields comparable to the optimal preionized case, the gas density needs to be seven times higher than the plasma density in a typical preionized case. A physical explanation is given.