On acceleration of relativistic electrons by any means, the coherent pinch effect brings the relativistic electrons together. The inclusion of a suitable number of positive ions, preferentially heavy ions would stabilize the beam. The heavy trapped nuclei would have to go with the electrons, thus acquire relativistic speeds. The electron beam may be divided into small bunches. This mechanism can accelerate positive nuclei to GeV and TeV energies during solar flares, stellar and galactic high energy events. During the acceleration of 1000 GeV electron bunches, the energy gained by trapped positive nuclei is estimated to reach 10$^{15}$ eV per nucleon. Higher energies can be achieved by head on collision as the energy gained by the target nucleus is proportional to $\gamma^{2},$ however fission reactions and very high energy gamma rays may occur. The principle of this mechanism is applied in electron-ring accelerators.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html