Orbits in an AVF cyclotron

Hagedoorn, H.L.; Verster, N.F.

doi:10.1016/s0029-554x(62)80032-9

Cited by 50 publications

(20 citation statements)

References 2 publications

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“…Both methods have been implemented and give good results. As an example we use the following formula for finding the first harmonic cosine component from the closed orbit shift [2]:…”

Section: Shimming Strategymentioning

confidence: 99%

Magnetic field calculation and shimming of the self-extraction cyclotron

Kleeven¹,

Beeckman²,

Lucas³

et al. 2001

AIP Conference Proceedings

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The self-extraction cyclotron is a 14 MeV H+ machine from which the beam extracts without a deflector. This is achieved with a special shaping of the magnetic field. Detailed 3D magnetostatic models have been constructed of this cyclotron, in order to accurately calculate the extraction process. Shimming of removable pole tips has been used to isochronize the machine and to remove harmonic errors. A software simulation of the shimming has been made, in order to accelerate the convergence of this process. First extracted beam has been obtained. There is good agreement between the calculations and measurements. Results of TOSCA calculations, mapping and shimming are presented.

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“…Both methods have been implemented and give good results. As an example we use the following formula for finding the first harmonic cosine component from the closed orbit shift [2]:…”

Section: Shimming Strategymentioning

confidence: 99%

Magnetic field calculation and shimming of the self-extraction cyclotron

Kleeven¹,

Beeckman²,

Lucas³

et al. 2001

AIP Conference Proceedings

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“…The Hamiltonian which describes the linear motion of a particle with a relative momentum deviation 6 is: (2) (2) in the bending magnets (see (9)). The expression (25) for the natural chromaticity is correct up to the second degree in the Fourier components of the field.…”

Section: Discussionmentioning

confidence: 99%

Some Aspects on Linear and Non-Linear Orbit Motion in Storage Rings

Backer

Corsten

Hagedoorn

1979

IEEE Trans. Nucl. Sci.

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Our purpose is the development of a general analytical theory which describes the orbit motion of particles in a storage ring, including the effect of the acceleration, analogous as done for cyclotrons1'2. We only present here the start, neglecting the effect of the RF system.We will use a Hamilton formalism with action and angle variables and show that this leads, after several correct transformations2,3, to expressions for the offenergy function , tunes and chromaticities. This theory can be extended to the influence of non-linear elements as sextupoles and octupoles and long straight sections on the orbit motion.Our treatment only needs direct field quantities in the form of Fourier components of the guide field elements. No a priori information about the lattice functions ( n,a etc.) is required, whereas normally one uses415 the behaviour of these functions as provided by lattice designing matrix codes.The results of the analytical theory as given here will be compared with numerical results applied on the lattice of the proposed Dutch dedicated synchrotron radiation storage ring PAMPUS6.Introduction. The orbit motion of a charged particle in a magnetic field with respect to an equilibrium orbit, can be described in curvilinear co-ordinates by a general Hamil-

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“…At this point, it is important to recall the contribution of the Thomas focusing to the vertical tune, which is usually quoted in the literature in several equivalent ways [1,[18][19][20][21][22]:…”

Section: B Thomas Focusingmentioning

confidence: 99%

Tune compensation in nearly scaling fixed field alternating gradient accelerators

Tahar

Méot

2020

Phys. Rev. Accel. Beams

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In this paper, we investigate the stability of the particle trajectories in fixed field alternating gradient accelerators (FFAs) in the presence of field errors. The emphasis is on the scaling radial sector FFA type: A collaboration work is ongoing in view of better understanding the properties of the 150 MeV scaling FFA at Kyoto University Institute for Integrated Radiation and Nuclear Science in Japan and progress toward high-intensity operation. Analysis of certain types of field imperfections revealed some interesting features that required the development of an analytical model based on the scalloping angle of the orbits. This helped explain some of the experimental results as well as generalize the concept of a scaling FFA to a nonscaling one for which the tune variations obey a well-defined law. Based on this, a compensation scheme of tune variations in imperfect scaling FFAs is presented. This is the cornerstone of a novel concept of a fixed tune FFA in which the scaling is not achieved at every azimuthal position of the ring but rather in an average sense.

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Orbits in an AVF cyclotron

Cited by 50 publications

References 2 publications

Magnetic field calculation and shimming of the self-extraction cyclotron

Magnetic field calculation and shimming of the self-extraction cyclotron

Some Aspects on Linear and Non-Linear Orbit Motion in Storage Rings

Tune compensation in nearly scaling fixed field alternating gradient accelerators

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