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The '''momentum compaction''' or '''momentum compaction factor''' is a measure for the [[momentum]] dependence of the recirculation path length for an object that is bound in cyclic motion (closed orbit). It is used in the calculation of particle paths in circular [[particle accelerator]]s (like [[synchrotron]]s), and for astronomical objects that are bound by [[gravitation]].


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For a [[perturbation theory|perturbed]] [[orbit]], the momentium compaction factor is defined as the derivative of normalized path length difference to normalized momentum<ref>{{cite book
| last1 = Conte | first1 = Mario
| last2 = McKay | first2 = William W.
| title = An Introduction to the Physics of Particle Accelerators
  | publisher = [[World Scientific]]
| edition = 2nd
| date=Apr 2008
| isbn= 978-981-277-961-8
| url= http://www.worldscibooks.com/physics/6683.html
}}</ref>
 
<math>\alpha_p = \frac{\mathrm{d}L / L} {\mathrm{d}p / p} = \frac{p}{L} \frac{\mathrm{d}L}{\mathrm{d}p} =\frac{1}{L} \oint \frac{D_{x}(s)}{\rho(s)}\mathrm{d}s</math>.
<ref>{{cite book|last1=Minty|first1=Michiko G.
|last2=Zimmermann|first2=Frank
|title=Measurement and Control of Charged Particle Beams|year=2003|publisher=Springer-Verlag|location=Berlin, Heidelberg, New York|isbn=3-540-44187-5|page=159}}</ref>
Furthermore the momentum compaction is closely connected to the so called slip-factor<ref>{{cite book
| last1 = Steinhagen | first1 = R. J.
| title = CERN Accelerator School Beam Diagnostics / Tune and chromaticity diagnostics
| publisher = [[CERN]]
| date=August 2009
 | page=343
  |editor = Daniel Brandt
}}</ref> <math>\eta</math>
with the horizontal dispersion <math>D_x</math> and the [[gyroradius]] <math>\rho</math>
 
<math>\alpha_p = \frac{1}{\gamma^{2}}-\eta</math>
 
wherein <math>\gamma</math> is the [[Lorentz factor]].
 
==References==
{{reflist}}
 
{{Accelerator-stub}}
[[Category:Accelerator physics]]
[[Category:Orbits]]

Revision as of 21:15, 4 January 2014

The momentum compaction or momentum compaction factor is a measure for the momentum dependence of the recirculation path length for an object that is bound in cyclic motion (closed orbit). It is used in the calculation of particle paths in circular particle accelerators (like synchrotrons), and for astronomical objects that are bound by gravitation.

For a perturbed orbit, the momentium compaction factor is defined as the derivative of normalized path length difference to normalized momentum[1]

αp=dL/Ldp/p=pLdLdp=1L∮Dx(s)ρ(s)ds. [2] Furthermore the momentum compaction is closely connected to the so called slip-factor[3] η with the horizontal dispersion Dx and the gyroradius ρ

αp=1γ2−η

wherein γ is the Lorentz factor.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

Template:Accelerator-stub

  1. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

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  2. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  3. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
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