[en] Large transverse wake fields can be generated via the interaction between a relativistic electron or positron bunch and a plasma, and the bunch will therefore be self-pinched. In this paper, we derive a new and general formulation for the plasma wake field in a compact expression. We then suggest that this self-focusing effect can be used as a mechanism to enhance the luminosity for high-energy experiments. A plasma lens based on this effect is suggested with a conceptual design and a numerical example. The problem of background noise is also discussed. (author)