Stability of a Uniform-Density Breathing Beam with Circular Cross Section

Gluckstern, R.L.; Cheng, Wen‐Hao; Ye, Huanchun

doi:10.1103/physrevlett.75.2835

Cited by 54 publications

(51 citation statements)

References 4 publications

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“…(14) can be written as a superposition of the general solution of the homogeneous equation [i.e., Eq. (14) with A z 0] and a particular solution of the full equation (14).…”

Section: The Vlasov-poisson Equationsmentioning

confidence: 99%

Resonance analysis for a space charge dominated beam in a circular lattice

Venturini

Gluckstern

2000

Phys. Rev. ST Accel. Beams

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We use the linearized Vlasov-Poisson equations to study the response of a Kapchinskij-Vladimirskij beam to magnetic multipole errors in a circular lattice. This work extends the calculation of Gluckstern [Proceedings of the Linac Conference, 1970 (Fermilab, Batavia, IL, 1970, p. 811] to the case of nonideal periodic lattices. The smooth approximation is assumed. We determine the resonance conditions as well as the amplitude of the excited collective modes as a function of the error size outside the stopbands. We find that the frequencies associated with lattice resonances are a subset of the beam natural eigenfrequencies. The result is used to study the motion of test particles crossing the boundary of the beam core. Close to resonance the model predicts the emergence of a halo if sufficiently large gradient errors are present. Application is made to the University of Maryland Electron Ring.

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“…(14) can be written as a superposition of the general solution of the homogeneous equation [i.e., Eq. (14) with A z 0] and a particular solution of the full equation (14).…”

Section: The Vlasov-poisson Equationsmentioning

confidence: 99%

Resonance analysis for a space charge dominated beam in a circular lattice

Venturini

Gluckstern

2000

Phys. Rev. ST Accel. Beams

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“…2 with the stable region enclosed by the solid curve, a reproduction of Ref. 4. The stability regions of the (3,0) and (4,0) modes, enclosed by dashes and dot-dashes, respectively, are also shown.…”

Section: Collective-motion Approachmentioning

confidence: 99%

“…4. The stability regions of the (3,0) and (4,0) modes, enclosed by dashes and dot-dashes, respectively, are also shown. These latter two modes become unstable at zero mismatch when the tune depressions are less than 0.3859 and 0.3985, respectively.…”

Section: Collective-motion Approachmentioning

confidence: 99%

“…In the notation of Gluckstern, Cheng, Kurennoy, and Ye, I 0 is the average beam current and v 0 the longitudinal velocity of the beam particles. The perturbed distribution generates an electric potential G, which is given by the Poisson's equation 1 (u, v,u,v ; θ) , (3.3) so that the Hill's equations in the two transverse planes becomë 4) where stands for the transverse emittance of the beam and m 0 the rest mass of the beam particle. For small perturbation, the perturbation distribution is proportional to the derivative of the unperturbed distribution.…”

Section: Collective-motion Approachmentioning

confidence: 99%

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Particle-beam approach to collective instabilities—application to space-charge dominated beams

Ng¹,

Lee²

1999

AIP Conference Proceedings

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“…The physical origin of these particles is beyond the scope of the particle-core model. However, they could be present in the tail of the initial distribution or they could be generated by instabilities of the core [8,22]. The effects of test particles on the core and the mutual Coulomb interactions among test particles are neglected.…”

Section: Three-dimensional Particle-core Modelmentioning

confidence: 99%

Beam halo studies using a three-dimensional particle-core model

Qiang

Ryne

2000

Phys. Rev. ST Accel. Beams

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In this paper we present a study of beam halo based on a three-dimensional particle-core model of an ellipsoidal bunched beam in a constant focusing channel including the effects of nonlinear rf focusing. For an initially mismatched beam, three linear envelope modes -a high frequency mode, a low frequency mode, and a quadrupole mode-are identified for an azimuthally symmetric bunched beam. The high frequency mode has three components all in phase; the low frequency mode has the transverse components in phase and the longitudinal component 180 ± out of phase; the quadrupole mode has no longitudinal component, and the two transverse components in the mode are 180 ± out of phase. We also study the case of an ellipsoidal bunched beam without azimuthal symmetry and find that the high frequency mode and the low frequency mode are still present but the quadrupole mode is replaced by a new mode with transverse components 180 ± out of phase and a nonzero longitudinal component. Previous studies, which generally addressed the situation where the longitudinal-to-transverse focusing strength is roughly 0.6 or less, conclude that the oscillation of the high frequency mode is predominantly transverse, and that of the low frequency mode is predominantly longitudinal. In this paper we present a systematic study of the features of the modes as a function of the longitudinal-to-transverse focusing strength ratio. We find that, when the ratio is greater than unity, the high frequency mode may contain a significant longitudinal component. Thus, excitation of the high frequency mode in this situation can be responsible for the formation of longitudinal beam halo. Furthermore, while previous studies have observed halo amplitudes roughly 2-3 times the matched beam edge, for the present parameters we observe much larger amplitudes (5 times or more). This is due to the fact that the longitudinalto-transverse focusing ratio used here is greater than that of previous studies. The finding of large transverse halo amplitude can have significant impact on the design of high-intensity ion accelerators where the longitudinal-to-transverse focusing ratio is slightly greater than unity in some parts of the linac.

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Stability of a Uniform-Density Breathing Beam with Circular Cross Section

Cited by 54 publications

References 4 publications

Resonance analysis for a space charge dominated beam in a circular lattice

Resonance analysis for a space charge dominated beam in a circular lattice

Particle-beam approach to collective instabilities—application to space-charge dominated beams

Beam halo studies using a three-dimensional particle-core model

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