mode - CERN Accelerator School
mode - CERN Accelerator School mode - CERN Accelerator School
ω electric field pattern - mode A 60 50 40 30 20 10 0 open waveguide dispersion curve Dispersion relation for the disc-loaded waveguide mode B electric field pattern - mode B mode A 0 40 k=2π/λ Wavelengths with λp/2~ l will be most affected by the discs discs. On the contrary contrary, for λ λp=0 =0 and λ λp=∞ =∞ the wave does not see the discs → the dispersion curve remains that of the empty pipe. At λ λp/2= /2= l , the wave will be confined between the discs, and present 2 “polarizations” (mode A and B in the figure), 2 modes with same wavelength but different frequencies → the dispersion curve splits into 2 branches, separated by a stop band. In the disc-loaded waveguide, the lower branch of the dispersion curve is now “distorted” in such a way that h we can find f d a range of f ffrequencies with h vph = c → we can use it to accelerate a particle beam! WWe have h built a linac lin c for f v~c c → a TRAVELING WAVE (TW) ELECTRON LINAC 10
eam Traveling wave linac structures → Disc-loaded waveguide designed for v ph=c at a given frequency, equipped with an input and an output coupler. → RF power is introduced via the input coupler. Part of RF power is dissipated in the structure, part is taken by the beam (beam loading) and the rest is absorbed in a matched load at the end of the structure. Usually, structure length is such that ~30% of power goes to the load. load → The “traveling wave” structure is the standard linac for electrons from β~1. → Can not be used for ions at v
- 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: Slowing down waves: the disc- loade
- 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
- Page 57 and 58: Electron sources: give energy to th
- Page 59 and 60: Accelerating structure: the choice
ω<br />
electric field pattern - <strong>mode</strong> A<br />
60<br />
50<br />
40<br />
30<br />
20<br />
10<br />
0<br />
open waveguide<br />
dispersion curve<br />
Dispersion relation for the<br />
disc-loaded waveguide<br />
<strong>mode</strong> B<br />
electric field pattern - <strong>mode</strong> B<br />
<strong>mode</strong> A<br />
0 40 k=2π/λ<br />
Wavelengths with λp/2~ l will be most affected by<br />
the discs discs. On the contrary contrary, for λ λp=0 =0 and λ λp=∞ =∞ the<br />
wave does not see the discs → the dispersion<br />
curve remains that of the empty pipe.<br />
At λ λp/2= /2= l , the wave will be confined between the<br />
discs, and present 2 “polarizations” (<strong>mode</strong> A and B<br />
in the figure), 2 <strong>mode</strong>s with same wavelength but<br />
different frequencies → the dispersion curve<br />
splits into 2 branches, separated by a stop band.<br />
In the disc-loaded waveguide, the lower branch of<br />
the dispersion curve is now “distorted” in such a<br />
way that h we can find f d a range of f ffrequencies with h<br />
vph = c → we can use it to accelerate a particle<br />
beam!<br />
WWe have h built a linac lin c for f v~c c → a TRAVELING<br />
WAVE (TW) ELECTRON LINAC<br />
10
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