Theory of the Cyclotron

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Abstract
The processes of formation of the initial ions in the cyclotron are reviewed, after which the various processes by which the ions are lost from resonance are considered. A theory of the loss of ions by collision or by electron capture is given and is compared with measurements made on the variation of the high energy beam current with gas pressure: satisfactory agreement is found. The inhomogeneity of the magnetic field of the 60‐inch Berkeley cyclotron has been measured, and an analysis of the electric and magnetic focusing in that cyclotron is made. Rose's work on the loss of ions resulting from their getting out of phase with the radiofrequency voltage is applied to the calculation of V0, the voltage necessary to apply to the dees just to get a beam. As an example, the value of V0 is computed for the 60‐inch cyclotron, and is found to be in good agreement with the directly measured value. The wandering of the ion paths is reviewed and is applied to the calculation of the inhomogeneity of the energy of emergent beam. Measurements made on the homogeneity of the energy of the protons from the 37‐inch cyclotron are compared to the calculations. Finally, the question of shimming the magnetic field of a cyclotron is considered. It is suggested that the magnetic field be made to decrease from the center with a constant dH/dr. For this shape of magnetic field, analytic expressions are derived for the magnitudes of dH/dr and V0, and methods for attaining such a field are suggested.

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