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4 – Beam Dynamics of Ion and Electron Linacs 34
Longitudinal g dynamics y → Ions are accelerated around a (linac=negative) synchronous phase. → Particles around the synchronous one perform oscillations in the longitudinal phase space. → FFrequency of f small ll oscillations: ill ti ω 2 l = ω 2 0 ( −ϕ ) qE0T sin 2 2π mc βγ → Tends to zero for relativistic particles γ>>1. → Note phase damping of oscillations: Δϕ = const 3/ 4 ( β γ ) 3 λ 3/ 4 ΔW = const × ( β γ ) At relativistic velocities phase oscillations stop, the beam is compressed in phase around the initial phase. phase The crest of the wave can be used for acceleration. 35
Page 1 and 2: Introduction to RF Linear Accelerat
Page 3 and 4: (v/c)^2 ( 1 Proton and Electron Vel
Page 5 and 6: Example: Superconducting Proton Lin
Page 7 and 8: RF input λ p TM01 field configurat
Page 9 and 10: Slowing down waves: the disc- loade
Page 11 and 12: eam Traveling wave linac structures
Page 13 and 14: mode 0 mode π/2 mode 2π/3 mode π
Page 15 and 16: Comparing traveling and standing wa
Page 17 and 18: Disc-loaded structures operating in
Page 19 and 20: Examples p of DTL Top; CERN Linac2
Page 21 and 22: eam Multigap linac structures: the
Page 23 and 24: Proton linac architecture - cell le
Page 25 and 26: Multi-gap Superconducting linac str
Page 27 and 28: Quarter Wave Resonators Simple 2-ga
Page 29 and 30: Focusing solenoids Examples: p an e
Page 31 and 32: Electron linac architecture EXAMPLE
Page 33: Heavy y Ion Linac Architecture EXAM
Page 37 and 38: Transverse dynamics - Space charge
Page 39 and 40: Transverse equilibrium in ion and e
Page 41 and 42: x_rms beaam size [m] High-intensity
Page 43 and 44: 55. DDouble bl periodic i di accele
Page 45 and 46: Mechanical errors differences in f
Page 47 and 48: The Side Coupled p Linac To operate
Page 49 and 50: The Cell-Coupled Drift Tube Linac W
Page 51 and 52: The Radio Frequency Quadrupole (RFQ
Page 53 and 54: RFQ Qpproperties p - 2 3. The dista
Page 55 and 56: How to create a quadrupole RF mode
Page 57 and 58: Electron sources: give energy to th
Page 59 and 60: Accelerating structure: the choice
Page 61 and 62: Mains Transforms mains power into D
Page 63: Bibliography g p y 1. Reference Boo

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