Cold atom electron and ion sources produce electron bunches and ion beams by photoionization of laser-cooled atoms. They offer high coherence and the potential for high brightness, with applications including ultra-fast electron-diffractive imaging of dynamic processes at the nanoscale. The effective brightness of electron sources has been limited by nonlinear divergence caused by repulsive interactions between the electrons, known as the Coulomb explosion. It has been shown that electron bunches with ellipsoidal shape and uniform density distribution have linear internal Coulomb fields, such that the Coulomb explosion can be reversed using conventional optics. Our source can create bunches shaped in three dimensions and hence in principle achieve the transverse spatial coherence and brightness needed for picosecond-diffractive imaging with nanometer resolution. Here we present results showing how the shaping capability can be used to measure the spatial coherence properties of the cold electron source. We also investigate space-charge effects with ions and generate electron bunches with durations of a few hundred picoseconds. Future development of the cold atom electron and ion source will increase the bunch charge and charge density, demonstrate reversal of Coulomb explosion, and ultimately, ultra-fast coherent electron-diffractive imaging.