Energy and time spreads of the ion beam caused by the spiral inflector

The spiral inflector (Root, M.S. Thesis, Ph.D. Thesis, University of British Columbia), as a part of the axial injection system of a cyclotron, is designed to inflect the ion beam with the introduction of a negligible energy spread. However, how close its real performance is to the analytical prediction depends on how close the operating conditions are to the assumed analytical stand-alone configuration. If the space in the central region of the cyclotron is limited, the electric field of the inflector and that of the electrodes of the radiofrequency (RF) system overlap, and the relevant zero-potential surface is quite complex. The dependence of the beam energy and time spreads after the inflector exit on the distance from the inflector exit was studied. The beam simulation results show that the beam energy spread decays with the distance from the inflector exit as expected, but that at 8 mm from the inflector exit it can still have the significant value of 0.67 keV (3% of the input energy). The beam time spread is of no interest if a continuous beam is to be produced. However, in the case of a bunched beam, even the smallest obtained value for the output time spread of 3.5 ns (10% of the period of the RF system) may have an important influence on the total efficiency of the machine. Our results demonstrate that both of these spreads need to be taken into account in the further beam simulations between the RF electrodes.