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The impedance acts back on the beam and can cause a variety of effects, often considered deleterious for accelerator functioning. In general, impedance effects are classified under the category of "collective effects" due to the fact that the whole beam must be considered together, and not just a
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863:
single particle. The whole beam may, however, cause particular changes in the dynamics of individual particles such as tune shifts and coupling. Whole beam changes include emittance growth and instabilities that can lead to beam loss.
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495:{\displaystyle Z_{||}(\omega )=R_{s}{\frac {1-iQ({\frac {\omega _{r}}{\omega }}-{\frac {\omega }{\omega _{r}}})}{1+Q^{2}\left({\frac {\omega _{r}}{\omega }}-{\frac {\omega }{\omega _{r}}}\right)^{2}}}}
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In the absence of detailed geometric modeling, one can use various models to represent different aspects of the accelerator beam pipe structure.
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is a quantity that characterizes the self interaction of a charged particle beam, mediated by the beam environment, such as the
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895:
A. Chao, Physics of
Collective Beam Instabilities in High Energy Accelerators, Wiley Publishers, 1993. Available
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188:{\displaystyle Z_{0}^{||}(\omega )=\int _{-\infty }^{\infty }{\frac {dz}{c}}e^{-i\omega z/c}W_{0}^{'}(z)}
966:
288:. Substantial impedance is generated in transitions, where the shape of the beam pipe changes. The
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The impedance is defined at all positions along the beam trajectory. The beam travels through a
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From this expression and the fact that the wake function is real, one can derive the property:
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787:{\displaystyle W(s)={\frac {q}{2\pi b}}{\sqrt {\frac {c}{\sigma }}}{\frac {1}{s^{3/2}}}}
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696:{\displaystyle Z(\omega )={\frac {1-i}{cb}}{\sqrt {\frac {\omega }{2\pi \sigma }}}}
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The impedance is defined as the
Fourier transform of the Wakefunction.
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http://www-spires.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-11052.pdf
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The corresponding longitudinal wakefield is approximately given by
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The transverse wake-function from the resistive wall is given by
38:, RF cavities, and other elements encountered along the
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270:{\displaystyle Z^{*||}(\omega )=Z^{||}(-\omega )}
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848:{\displaystyle W(s)\approx {\frac {1}{s^{1/2}}}}
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921:"The Short‐Range Resistive Wall Wakefields"
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872:https://impedance.web.cern.ch/impedance/
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586:Given a circular beam piper of radius
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311:For the longitudinal case, one has
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50:Definition in terms of wakefunction
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18:Impedance (Accelerator Physics)
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292:are another important source.
280:Important sources of impedance
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953:. You can help Knowledge by
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858:Effect of Impedance on beam
571:{\displaystyle \omega _{r}}
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1021:
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551:, the quality factor, and
1005:Accelerator physics stubs
578:the resonant frequency.
619:{\displaystyle \sigma }
949:-related article is a
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303:One such model is the
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524:{\displaystyle R_{s}}
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1000:Accelerator physics
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307:Broadband resonator
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32:Accelerator Physics
877:2018-07-04 at the
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599:{\displaystyle b}
544:{\displaystyle Q}
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16:(Redirected from
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582:Resistive Wall
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36:vacuum chamber
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955:expanding it
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44:storage ring
27:
26:
290:RF cavities
40:accelerator
994:Categories
884:References
818:≈
754:σ
739:π
687:σ
684:π
677:ω
657:−
642:ω
614:σ
560:ω
468:ω
464:ω
459:−
454:ω
445:ω
404:ω
400:ω
395:−
390:ω
381:ω
366:−
341:ω
262:ω
259:−
230:ω
212:∗
142:ω
136:−
111:∞
106:∞
103:−
99:∫
89:ω
28:Impedance
875:Archived
867:See also
171:′
945:This
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951:stub
897:here
42:or
30:in
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812:s
809:(
806:W
778:2
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770:3
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762:1
751:c
742:b
736:2
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721:s
718:(
715:W
681:2
668:b
665:c
660:i
654:1
648:=
645:)
639:(
636:Z
594:b
564:r
539:Q
517:s
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485:2
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472:r
449:r
438:(
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427:Q
423:+
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375:(
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347:=
344:)
338:(
332:|
327:|
322:Z
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256:(
250:|
245:|
240:Z
236:=
233:)
227:(
221:|
216:|
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180:z
177:(
163:0
159:W
153:c
149:/
145:z
139:i
132:e
126:c
122:z
119:d
95:=
92:)
86:(
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20:)
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