Space Charge Effects in the Vertical Plane during Injection in a Synchrocyclotron

The evolution of the beam during capture time is followed by means of numerical methods. The space charge field is obtained by constructing, for purposes of calculation, a rectangular network in the beam. All particles of a given parallelepiped are replaced by a single macroparticle of equivalent charge placed at the centre of the parallelepiped. The field produced by all the macroparticles is then calculated at the knots of the network. The field at any other place is found by interpolation. Beam shapes and distribution of particle densities have been calculated in this way for the CERN synchrocyclotron, at various instants in the vertical plane . The mean accelerated current is calculated.