Theoretical works by Barnes and Nebel [D. C. Barnes and R. A. Nebel, Phys. Plasmas 5, 2498 (1998); R. A. Nebel and D. C. Barnes, Fusion Technol. 38, 28 (1998)] have suggested that a tiny oscillating ion cloud (referred to as the periodically oscillating plasma sphere or POPS) may undergo a self-similar collapse in a harmonic oscillator potential formed by a uniform electron background. A major uncertainty in this oscillating plasma scheme is the stability of the virtual cathode that forms the harmonic oscillator potential. The electron-electron two-stream stability of the virtual cathode has previously been studied with a fluid model, a slab kinetic model, a spherically symmetric kinetic model, and experimentally [R. A. Nebel and J. M. Finn, Phys. Plasmas 8, 1505 (2001); R. A. Nebel , Phys. Plasmas 12, 040501 (2005)]. Here the mode is studied with a two-dimensional particle-in-cell code. Results indicate stability limits near those of the previously spherically symmetric case. (c) 2006 American Institute of Physics.