H.L. Hagedoorn

The theory of accelerated particles in cyclotrons

Abstract A theory has been developed, which describes the acceleration process and its influence on the beam quality in cyclotrons. In the derivation use is made of the Hamiltonion formalism. The theory is generally applicable in the study of the influence of the energy and the phase on the radial phase plane and vice versa. It turns out that in cyclotrons with a one-Dee acceleration structure an instable radial phase plane may occur for negative central position phases. In cyclotrons with a two-Dee acceleration structure these effects are even much more important and may lead to serious distortions of the beam and large centering problems. This holds especially at the first turns in the cyclotron, and in the case of large harmonic numbers for the acceleration frequency. Numerical calculations illustrate this for several existing cylotrons. Experimental evidence exists.

Measurements and second-order calculations of the Eindhoven beam transport system

Abstract The horizontal and vertical emittances of the extracted beam from the Eindhoven A.V.F. cyclotron have been measured for different particle energies and yields For the 45° bending magnets non-linear effects have been extracted from orbit integrations and comparison is made with the theoretical estimations of the second-order coefficients. These increase the ΔE/E value calculated by the linear approximation by 0.02%. This implies that with entrance and exit slit widths of 0.5% mm an analysed beam of 2 μA out of 100 μA with an energy spread of 0.05% fwhm is obtainable.

The use of a phase space representation for the design of a beam transport system with doubly achromatic and dispersive modes of operation

Abstract The beam transport system for the Eindhoven AVF-cyclotron is described. Phase space representation is applied to yield dispersive properties and beam envelopes. The analysis is restricted mainly to a 90° deflecting subsystem composed of two 45° magnets and three magnetic quadrupole lenses. This system allows either a doubly achromatic or a highly dispersive mode of operation. The analysed beam will have an energy spread of 0.5% fwhm with entrance and exit slits of 1 mm width. Currents of 10 μA analysed beam are expected. The total width of the beam does not exceed 20 mm, except horizontally at the position of the two 45° magnets in the dispersive mode. The inner diameter of the beam pipes is 45 mm.

Improvements of the central region of the Eindhoven AVF cyclotron

Abstract Electric field components in the acceleration gap of the central region of the Eindhoven AVF cyclotron have been determined, for several different geometries of the cyclotron centre, employing the magnetic analogue technique. Effects of changes of the puller shape have been investigated. Measurements and numerical calculations show that a substantial improvement of the axial focusing properties of particles at the first few turns is obtained, when at the position of the orbit the electric field component along the dee gap is constant or has a positive derivative with respect to radius. Tests with a new puller in the cyclotron have shown an increase of the beam current of at least a factor three with respect to the old situation.

A radial-longitudinal coupling effect for cyclotrons with a one-Dee system

Abstract A radial-longitudinal coupling effect for cyclotrons with a one-Dee system is described by means of analytical formulas. When high harmonic acceleration is used, the beam in the radial-phase space will be stretched for negative or positive hf phases, especially at the beginning of the acceleration. Three ways to reduce the coupling effect are considered.

The effect of a bevelled Dee on the beam centering process in an AVF cyclotron

Abstract The influence of a bevelled Dee on the particle motion in an AVF cyclotron is discussed. This is done theoretically by considering the influence of a suddenly increasing first harmonic field perturbation, equivalent to this effect, on the motion of the orbit centre. The influence of such a bevelled Dee is also seen in experiments.

Special applications of a general orbit theory for accelerated particles in cyclotrons

Abstract In an earlier paper a general orbit theory for accelerated particles has been described. The influence of the accelerating structure on the betatron motion was clearly shown. In this paper we will indicate how azimuthally varying fields can be incorporated, yielding for example the gap-crossing resonance. The theory is further applied to synchrocyclotrons showing the applicability to the description of synchrotron oscillations. Finally the theory is applied to the situation in an omegatron.

Numerical calculations in the extraction process of the Eindhoven AVF cyclotron

The general equations of motions are integrated, taking into account the coupling of the horizontal and vertical motions. Extraction parameters as first-harmonic field perturbations, the imperfection resonance v r = 1, and the difference (coupling) resonance v r = 2 v z are discussed. Special attention is given to representation of the v r = 2 v z resonance. The amplitude and azimuthal position of a first-harmonic field perturbation, in order to obtain a good extraction efficiency, are numerically determined.

On the effect of very small irregularities at the pole faces of a cyclotron magnet on the quality of the ion beam

Abstract The variations of the magnetic induction in the median plane of a cyclotron magnet induced by small grooves (e.g. 25 μm modulation) at the iron surface are calculated. The stochastic variation of the field index due to these field disturbances has a deteriorating effect on the beam quality when the distance between successive orbits is larger than some typical radia interval within which a field variation changes in sign. An approximative calculation of this effect is presented and it is shown that, under certain circumstances, the beam quality seriously deteriorates.

Interpretation of signals acquired from capacitive phase probes in an isochronous cyclotron

Abstract Non-interceptive capacitive pick-up probes have been mounted in the vacuum chamber of the Eindhoven University of Technology A.V.F. cyclotron. With them the internal beam intensity and the HF phase angle with respect to the accelerating voltage phase angle are measured continuously. This paper describes the dependence of the intensity and phase angle of the second harmonic component of the probe signals on deviations from isochronism.