Longitudinal particle dynamics in the Tritron

Tritron is the name of a separated-orbit cyclotron. The accelerated ions are strongly focused in a beam-transfer system consisting of superconducting, individually adjustable channel-magnets with alternating gradients along a spiral orbit. The particles are focused longitudinally as in a synchrotron by strong accelerating voltages produced by superconducting, fixed frequency cavities. Rather high harmonic numbers can be used resulting in a dense pattern of energy levels. The bunches execute fixed coherent synchrotron oscillations. Therefore the final energy can be varied considerably, thus partially filling the gaps between neighbouring levels. In addition the noncentral particles oscillate incoherently with respect to the central particle. The analytical results on the longitudinal particle dynamics are in good agreement with results obtained from a computer code simulating the Tritron by means of the matrix formalism.