Envelope equations for cylindrically symmetric space charge dominated multi species beam

Abstract

We have derived differential equations for the beam envelope of a cylindrically symmetric space charge dominated multi-species beam. The major contribution here is the inclusion of the emittance growth of each species of the beam resulting from the nonlinear space charge effect of the other species which arises if the beam radius of that particular species is greater than the other species. In addition, we have also discussed the beam selection using slits and considered only the effective values of the current and emittance of each species after the slit for further transport in case the beam size of any species is larger than the slit size or the finite aperture of the beam pipe. Finally, we have studied the transport of proton from 2.45 GHz microwave ion source in the presence of H2+, H3+ species to demonstrate the application of these results. Numerical results are presented for various values of the total beam current and different fractions of p, H2+, and H3+ species.