|
|
| Line 1: |
Line 1: |
| 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]].
| | My name is Shantae and I am studying International Relations and Japanese Studies at Sainte-Foy-Les-Lyon / France.<br><br>Feel free to surf to my blog post [http://brokerltd.com/adv_cpa_network.html cpa affiliate network] |
| | |
| 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]]
| |
My name is Shantae and I am studying International Relations and Japanese Studies at Sainte-Foy-Les-Lyon / France.
Feel free to surf to my blog post cpa affiliate network