Confinement criterion for a highly bunched beam

Hess, Mark; Chen, Chiping

doi:10.1063/1.1319639

Cited by 20 publications

(38 citation statements)

References 7 publications

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“…This self-field parameter limit is similar to a limit that the authors computed for a uniform-focusing magnetic field, z extB e B = [13]. The only difference is that the rms magnetic field on the left-hand side of Eq.…”

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confidence: 53%

“…Beam loss has also been attributed to be a limiting factor in the proton storage ring (PSR) [9] at Los Alamos and in the relativistic heavy ion collider (RHIC) [10] at Brookhaven. While the physics of confining continuous charged beams has been studied extensively in plasma physics [2] and vacuum electronics [4], the confinement properties of bunched beams, like those used in the SLAC PPM klystrons and other high-intensity rf accelerators, have only had modest investigation [11][12][13].…”

mentioning

confidence: 99%

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Beam confinement in periodic permanent magnet focusing klystrons

Hess

Chen

2002

Physics Letters A

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confidence: 53%

mentioning

confidence: 99%

Beam confinement in periodic permanent magnet focusing klystrons

Hess

Chen

2002

Physics Letters A

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“…An example of periodically focused off-axis Vlasov equilibrium was discussed in detail to show the possibility of finding beam solutions for which the envelope equation is stable, whereas the centroid motion is unstable, revealing the importance of centroid motion to the overall beam confinement properties. The purpose of the present theory is to help understanding results of existing and proposed experiments in particle acceleration and high power microwave sources, where off-axis dynamics is of relevance [14].…”

Section: 244801 (2004) P H Y S I C a L R E V I E W L E T T E R S mentioning

confidence: 99%

“…Actually, this simplifying assumption is generally used in the analysis of intense beams [8] because the axis is an equilibrium for the beam centroid, and the equilibrium is stable if smooth-beam approximations are employed where the periodic fluctuations of the focusing field are averaged out [14]. In some cases, however, we may expect the onset of a parametric resonance involving the centroid motion and the focusing field oscillations.…”

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Equilibrium and Stability of Off-Axis Periodically Focused Particle Beams

2004

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A general equation for the centroid motion of free, continuous, intense beams propagating off axis in solenoidal periodic focusing fields is derived. The centroid equation is found to be independent of the specific beam distribution and may exhibit unstable solutions. A new Vlasov equilibrium for off-axis beam propagation is also obtained. The properties of the equilibrium and the relevance of centroid motion to beam confinement are discussed. DOI: 10.1103/PhysRevLett.93.244801 PACS numbers: 41.85.Ja, 05.45.-a A fundamental understanding of the kinetic equilibrium and stability properties of certain systems is sought. These systems include periodically focused high-current, low emittance beams. The understanding we seek is crucial for a variety of applications. Among them are advanced particle accelerators and coherent radiation sources. For a long time, the Kapchinskij-Vladimirskij (KV) distribution [1] was the only Vlasov [2] equilibrium distribution known for the propagation of periodically focused intense particle beams. Equilibrium and stability analysis based on the KV beam have been critical to the development and understanding of the physics of intense beams [3][4][5][6][7][8][9][10][11]. More recently, it has been shown that the KV distribution can be generalized to allow for rigid beam rotation with respect to the Larmor frame in periodic solenoidal focusing fields [12]. Studies indicate that rotation may have an important role in particle beam stability [13].In the derivation of these Vlasov equilibria it is always assumed that the beam is perfectly aligned with the symmetry axis of the focusing field [1,6,12]. Actually, this simplifying assumption is generally used in the analysis of intense beams [8] because the axis is an equilibrium for the beam centroid, and the equilibrium is stable if smooth-beam approximations are employed where the periodic fluctuations of the focusing field are averaged out [14]. In some cases, however, we may expect the onset of a parametric resonance involving the centroid motion and the focusing field oscillations. This would destabilize the centroid motion and heavily affect the overall beam dynamics. In such conditions the averaging procedure is no longer valid and a detailed description of the centroid dynamics becomes mandatory.In this Letter, we derive from a kinetic VlasovMaxwell description a general equation for the centroid motion of free, continuous, intense beams propagating off axis in solenoidal periodic focusing fields. It is shown that the centroid obeys a Mathieu-type equation. The equation is independent of the specific beam distribution and becomes unstable whenever the oscillatory frequency of the centroid, which is related to the rms focusing field strength per lattice, is commensurable with the focusing field periodicity itself. In the particular case of a uniform beam density around the beam centroid, we show that there exists a self-consistent Vlasov equilibrium distribution for the beam dynamics. The beam envelope that determines the outer radi...

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“…In a series of modern high-intensity vacuum electronic devices it is expected that off-axis beam dynamics develops as a result of small deviations between the beam injection direction and the magnetic axis. 4 This is potentially hazardous since offaxis dynamics can ultimately lead to collision between the charged beam and the conducting walls surrounding the focusing system. 4,5 Off-axis dynamics also represent a type of beam mismatch and it is of interest to learn whether or not off-axis beams can decay into equilibrium with accompanying emittance growth.…”

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confidence: 99%

Combined centroid-envelope dynamics of intense, magnetically focused charged beams surrounded by conducting walls

2006

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In this paper we analyze the combined envelope-centroid dynamics of magnetically focused high-intensity charged beams surrounded by conducting walls. Similar to the case where conducting walls are absent, it is shown that the envelope and centroid dynamics decouple from each other. Mismatched envelopes still decay into equilibrium with simultaneous emittance growth, but the centroid keeps oscillating with no appreciable energy loss. Some estimates are performed to analytically obtain characteristics of halo formation seen in the full simulations.

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Confinement criterion for a highly bunched beam

Cited by 20 publications

References 7 publications

Beam confinement in periodic permanent magnet focusing klystrons

Beam confinement in periodic permanent magnet focusing klystrons

Equilibrium and Stability of Off-Axis Periodically Focused Particle Beams

Combined centroid-envelope dynamics of intense, magnetically focused charged beams surrounded by conducting walls

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