A New Method for High Luminosity

We propose a new method to increase a luminosity in colliding machines, where collective focussings of high current anti-charged streams are employed as final focussing lenses instead of usual high gradient magnets. It is shown that a counter streaming pair of cylindrical positron and hollow electron beams produces necessary focussing forces to lead to a high luminosity, avoiding significant beam-beam effects of thermselves. A tentative scheme to produce the kiloampare positron beams is briefly proposed.