Calculation of accelerating electric fields in the CO2 injector

The accelerating structure in the injecting cyclotron for O.A.E. can be divided, if one takes the inflector exit as departure point, into the following two regions: 1. the relatively complex central zone comprising three accelerating gaps which is flanked by vertical pillars destined to increase the transit time factor and, at the same time, to reduce the influence of electric field vertical components; 2. the so-called 'large radius' subsequent zone where the gaps are no longer radially delimited. To study the behavior of the individual trajectories in these fields, the equations of motion must be integrated step by step (for instance by Runge-Kutta method) what implies the knowledge of field (or at least of potential) in every point. This is the method for the calculation of potential contour maps which is presented here; the potentials are static, and a sinusoidal time variation is subsequently applied to perform dynamical calculations. The paper has the following sections: 1. Introduction; 2. Potential and large radius field components; 2.1. Calculation of median plane potential; 2.2. Calculation of the off-median-plane potential and field; 3. Potential in the central region; 4. Further Developments