Collective Effects and Beam
Measurements in Particle Accelerators
beam diagnostics and fundamental limitations to
the performance of high-intensity accelerators
http://ab-abp-rlc.web.cern.ch/ab-abp-rlc/
See also slides on Measurements, ideas, curiosities
F. Ruggiero
CERN
Univ. “La Sapienza”, Rome, 20–24 March 2006
Wakefield for a pill-box cavity
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Animation showing a bunch of charged particles
moving on the cavity axis and the corresponding
electric field lines computed by the program ABCI
Courtesy Andreas Wagner
http://awagner.home.cern.ch/awagner/
F. Ruggiero
CERN
Collective Effects and Beam Measurements
TRISIM3D simulation of a LEP bunch
E = 22 GeV, Qs = 0.092, I = 0.3 mA
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3-dimensional computer simulation of single bunch
collective effects in particle accelerators
top and side view of the particle distribution turn by
turn, over 60 turns
Courtesy Andreas Wagner
http://awagner.home.cern.ch/awagner/
F. Ruggiero
CERN
Collective Effects and Beam Measurements
CERN Linac4
layout and parameters
95keV
H-
3MeV
RFQ
Radio
Frequency
Quadrupole
352 MHz
6m
1 Klystron
1 MW
3MeV
CHOPPER
Chopper
352 MHz
3.6 m
Drift Tube
Linac
352 MHz
13.4 m
3 tanks
5 klystrons
4 MW
Courtesy A. Lombardi
CERN
90MeV
160MeV
CCDTL
SCL
Cell-Coupled
Drift Tube
Linac
352 MHz
25.3 m
24 tanks
8 klystrons
6.5 MW
Side Coupled
Linac
Duty cycle:
0.1% phase 1 (Linac4)
3-4% phase 2 (SPL)
(RF design: 15%)
Total Linac4:
80 m,
18 klystrons
F. Ruggiero
DTL
40MeV
704 MHz
28 m
20 tanks
4 klystrons
12 MW
4 different structures,
(RFQ, DTL, CCDTL, SCL)
2 frequencies
current: 40 mA (avg. in
pulse), 65 mA (bunch)
Collective Effects and Beam Measurements
Transverse tune depression
Instabilities in a Linac
=Longitudinal to transverse phase advanc
F. Ruggiero
CERN
Courtesy A. Lombardi
Collective Effects and Beam Measurements
Intra-Beam Scattering
(simplified formulae by K. Bane, EPAC 2002)
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 zIBS
Hx
8 3e 3 / 2s zs δ3
1
 2
b av

2
rp cN b (log )
sδ
e


IBS
x
IBS
z
e
s δ2 H x
For the LHC, the average
dispersion invariant is
<Hx>~0.03 m, bav~100 m, and
the Coulomb logarithm (log)~24
Note that the transverse IBS
growth rate is about
proportional to the particle
density in the 6D phase space
Nb/(e2szsd)
F. Ruggiero
CERN
IBS growth times for long
super-bunches in the LHC
as a function of the rms
momentum spread sd
Collective Effects and Beam Measurements