Generalized impedances and wakes in asymmetric structures

Heifets, S.; Wagner, Andreas; Zotter, B.

doi:10.2172/663316

Cited by 20 publications

(24 citation statements)

References 2 publications

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“…On the other hand, in structures with noncircular cross sections, also quadrupolar wakes are excited [2] which are independent of the offset of the driving particle, but proportional to the displacement of the test particle. As an illustration, Fig.…”

Section: Transverse Impedances and Wake Fieldsmentioning

confidence: 99%

“…For noncircular chambers, and as long as the geometry has an up-down and a left-right symmetry, then the general form of the wake impulse can be written neglecting a small contribution of the higher-order wakes near the beam line as [2] …”

Section: (2002)mentioning

confidence: 99%

“…The vacuum chambers in the magnets of the HER have octagonal cross section, halfway between rectangular and elliptic, but in any case not circularly symmetric. A general analysis of transverse wake fields in such a chamber had recently been completed [2]. There it was found that the transverse wake fields can be represented as superpositions of dipole and quadrupole fields.…”

Section: Introductionmentioning

confidence: 99%

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Tune shifts of bunch trains due to resistive vacuum chambers without circular symmetry

Chao¹,

Heifets²,

Zotter³

2002

Phys. Rev. ST Accel. Beams

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We present an explanation for the opposite signs of the horizontal and vertical tune shifts of bunch trains which have been observed recently in several high-energy storage rings. This result can be understood in terms of the long-range quadrupolar wakes of noncircular vacuum chambers with finite resistivity. In vacuum chambers with circular cross section, the dominant transverse wake driven by a leading particle and seen by a trailing test particle is dipolar and is proportional only to the transverse offset of the driving particle. The contributions of preceding bunches or previous turns tend to cancel, as they add with oscillatory factors. On the other hand, quadrupolar wakes are independent of the offset of the driving particle, and thus the contributions of preceding bunches and turns are strictly additive. Since quadrupole fields are focusing in one plane and defocusing in the plane orthogonal to it, their effects on tune shifts in these planes have opposite signs. Their cumulative effect also explains the large values of the tune shifts measured in PEP-II, which exceeded estimates from other impedance sources by factors of 3 to 4. Our analysis also offers a connection to the familiar Laslett tune shift.

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Section: Transverse Impedances and Wake Fieldsmentioning

confidence: 99%

Section: (2002)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Tune shifts of bunch trains due to resistive vacuum chambers without circular symmetry

Chao¹,

Heifets²,

Zotter³

2002

Phys. Rev. ST Accel. Beams

View full text Add to dashboard Cite

show abstract

“…Consider an ultrarelativistic beam flowing along the z direction between two parallel plates horizontally aligned. If the distance between the leading and trailing particle is jzj, the momentum of the trailing particle traversing a structure of length L will be modified by [3,14] cÁp z ¼ ÀqQW k ðzÞ (1)…”

Section: A Wake Functionsmentioning

confidence: 99%

“…The terms proportional to the displacement of the leading particle, i.e., to X or Y, are called dipole wakes while the ones proportional to the displacement of the trailing particle, i.e., to x or y, are called quadrupole wakes [15]. Note that in a circular pipe and ultrarelativistic limit the quadrupole wakefields vanish due to symmetry, while extra terms can be present in pipes with lower symmetries [14].…”

Section: A Wake Functionsmentioning

confidence: 99%

Coupling impedance and wake functions for laminated structures with an application to the Fermilab Booster

Macridin

Spentzouris

Amundson

et al. 2011

Phys. Rev. ST Accel. Beams

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We calculate the impedance and wake functions for laminated structures with parallel-plane and circular geometries in the ultrarelativistic limit. We critically examine the approximations used in the literature for the coupling impedance in laminated chambers and find that most of them are not justified because the wall surface impedance is large. A comparison between flat and circular geometry impedances is presented. We apply our calculation in a state-of-the-art beam dynamics simulation of the Fermilab Booster which includes nonlinear optics, laminated wakefields, and space charge impedance. The latter can have a significant effect away from the ultrarelativistic limit. Even though the simulations and the comparison with the experiment are done at the Booster injection energy, where the relativistic factor ¼ 1:42, we find good agreement between our calculation of the coherent tune shift and recent experimental measurements.

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Tune shift due to the quadrupolar resistive-wall impedance of an elliptical beam pipe

Wang

et al. 2022

Nuclear Instruments and Methods in Physics Research Section A:

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Generalized impedances and wakes in asymmetric structures

Cited by 20 publications

References 2 publications

Tune shifts of bunch trains due to resistive vacuum chambers without circular symmetry

Tune shifts of bunch trains due to resistive vacuum chambers without circular symmetry

Coupling impedance and wake functions for laminated structures with an application to the Fermilab Booster

Tune shift due to the quadrupolar resistive-wall impedance of an elliptical beam pipe

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