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2009fermi
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4
Study of different components found in particle accelerator
Subsections
10
. Drift
10
.
1
Theory without space charge
10
.
1
.
1
Simple case
10
.
1
.
2
Introducing transverse momentum correlation in the distribution
10
.
1
.
3
Beam waist interpretation
10
.
2
Influence of the space charge in a drift
11
. Dipoles
11
.
1
Theory
11
.
1
.
1
Equation of motion
11
.
1
.
2
Successions of dipole - reducing the energy spread
11
.
1
.
3
Fringe fields
11
.
1
.
4
Effective length
11
.
2
Dipole fields from measurement
11
.
2
.
1
Coordinates conventions
11
.
2
.
2
Organization of measurement data
11
.
2
.
3
Field map from measurement
11
.
3
Comparisons between dipole measurements and Astra modelization
11
.
3
.
1
Modelization of dipoles in Astra
11
.
3
.
2
Comparison of the different fields
11
.
3
.
3
Fit with Henge's field fall-off model
12
. Compressors
12
.
1
Introduction to compressors theory
12
.
2
Adapting simulation parameters to fit reference path
12
.
3
Maximum compression
12
.
3
.
1
Introducing correlation directly in the bunch
12
.
4
Phase space plots
12
.
4
.
1
Transversal phase space, with and without space charge
12
.
4
.
2
Longitudinal phase space, with and without space charge
12
.
4
.
3
Projected densities for the phase space with space charge forces at the end of the compressor
12
.
4
.
4
Introducing correlation with a cavity
13
. Emittance exchanger
13
.
1
Adapting simulation parameters to fit reference path
13
.
2
Emittance measurements method
14
. Study of a cavity
14
.
1
Fields inside a cavity
14
.
1
.
1
Longitudinal component
14
.
1
.
2
Correlation introduced by a cavity between
and the energy
14
.
1
.
2
.
1
The fields time phase
14
.
1
.
2
.
2
The fields scaling
14
.
1
.
3
Determination of the cavity matrix
14
.
1
.
3
.
1
Notation used for the cavity
14
.
2
An example of transportation matrix: five cell cavity
14
.
2
.
1
Equation of motion in a pillbox
14
.
2
.
2
The One cell pill box model
14
.
2
.
3
Cavity Transit matrix
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Emmanuel Branlard
http://emmanuel.branlard.free.fr/