mode - CERN Accelerator School
mode - CERN Accelerator School mode - CERN Accelerator School
2 – Periodic Accelerating Structures 6
RF input λ p TM01 field configuration Wave propagation in a cylindrical pipe E-field B-field In a cylindrical waveguide different modes can propagate (=Electromagnetic field distributions, ttransmitting itti power and/or d/ iinformation). f ti ) Th The fi field ld iis the superposition of waves reflected by the metallic walls of the pipe → velocity and wavelength of the modes will be different from free space p (c, λ) To accelerate particles, we need a mode with longitudinal E-field component on axis: a TM mode (Transverse Magnetic, B z=0). The simplest is TM01. We enter RF power at a frequency exciting the TM01 mode: E-field periodic on axis, wavelength λ p depends on frequency and on cylinder radius. Wave velocity ( (called ll d “ph “phase s velocity”) l it ”) is vph= λ λp/T /T = λ λpf f = ω/k /kz with ith kz=2π/λp The relation between frequency ω and propagation constant k is the DISPERSION RELATION (red curve on plot), a fundamental property of waveguides. 7
- Page 1 and 2: Introduction to RF Linear Accelerat
- Page 3 and 4: (v/c)^2 ( 1 Proton and Electron Vel
- Page 5: Example: Superconducting Proton Lin
- 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 and 34: Heavy y Ion Linac Architecture EXAM
- Page 35 and 36: Longitudinal g dynamics y → Ions
- 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
RF input<br />
λ p<br />
TM01 field configuration<br />
Wave propagation in a<br />
cylindrical pipe<br />
E-field<br />
B-field<br />
In a cylindrical waveguide different <strong>mode</strong>s can<br />
propagate (=Electromagnetic field distributions,<br />
ttransmitting itti power and/or d/ iinformation). f ti ) Th The fi field ld iis<br />
the superposition of waves reflected by the metallic<br />
walls of the pipe → velocity and wavelength of the<br />
<strong>mode</strong>s will be different from free space p (c, λ)<br />
To accelerate particles, we need a <strong>mode</strong> with<br />
longitudinal E-field component on axis: a TM <strong>mode</strong><br />
(Transverse Magnetic, B z=0). The simplest is TM01.<br />
We enter RF power at a frequency exciting the TM01<br />
<strong>mode</strong>: E-field periodic on axis, wavelength λ p depends<br />
on frequency and on cylinder radius. Wave velocity<br />
( (called ll d “ph “phase s velocity”) l it ”) is vph= λ λp/T /T = λ λpf f = ω/k /kz with ith<br />
kz=2π/λp The relation between frequency ω and propagation<br />
constant k is the DISPERSION RELATION (red<br />
curve on plot), a fundamental property of waveguides.<br />
7
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