By J. Jowett
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Additional info for Particle Accelerators - CERN Summer Student Program [lectures]
QHorizontal β-function and dispersion now have different behaviour qDispersion suppressor (special quadrupoles and missing bending magnets) used to reduce Dx to zero in interaction and RF region. qLow-β insertion used to reduce β-functions to very small values at interaction point. qVertical β-function is still “out of phase” with horizontal except at the interaction point. qA more-or-less FODO section for the RF cavities. qOptics design work has to concentrate most on satisfying all the constraints in the straight sections.
Jowett Particle Accelerators, Lecture 3, Page 14 Equations of Motion qCoordinates Time difference between arrival of a particle and the arrival of the “synchronous” particle τ. M. Jowett Particle Accelerators, Lecture 3, Page 15 Small Oscillations qLinearise the equations of motion (not really justified! see Sands or other books) dε eV&0 τ − U 0′ ε = dt E0 T0 ⇒ d 2τ dτ α 2 + + Ω 2s τ = 0 ε 2 dt dt U′ where α ε = 0 , 2T0 α c eV&0 Ω = E0 T0 2 s are the damping rate and synchrotron frequency. Describes a weakly-damped harmonic oscillator τ(t ) = Ae − α ε t cos(Ω s t − ϕ −0 ) Conjugate variable ε oscillates out of phase.
M. Jowett Particle Accelerators, Lecture 4, Page 3 LEP1 (partial) Parameter List Circumference Average bending radius No. of experimental collision points No. of bunches per beam No. of normal bending magnets No. of quadrupoles No. of sextupoles No. of wiggler magnets No. of electrostatic separators No. of 5-cell Cu RF cavity units No. M. 07 m m 10,4 GeV m MeV ms nm 10,3 cm GeV MeV ms nm 10,3 m MV Particle Accelerators, Lecture 4, Page 4 Schematic view of LEP qGreatly exaggerated vertical scale in underground part !
Particle Accelerators - CERN Summer Student Program [lectures] by J. Jowett