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List of Figures

1. Convention used for the longitudinal phase space
2. Legend of phase space plots
3. Convention used to define dipole pole tip coordinates
2.1. Curvilinear system of coordinates used in particle beam dynamics
2.2. Illustration of the relative coordinates
3.1. Illustration of the matrix formalism in optics - case of a drift
3.2. Different convention for the longitudinal phase space
3.3. Graphical representation of the Twiss-parameters
4.1. Problem of unadapted mesh
4.2. Global process of space charge calculation
4.3. Frame definition - laboratory - rest frame - bunch frame
6.1. Cylindrical distribution: Longitudinal field along z - comparison between simulation and theory
6.2. Form factor data and plot
6.3. Ellipsoidal distribution: Longitudinal field along z - comparison between simulation and theory
6.4. Comparison of theoretical (dashed) and numerical longitudinal field
7.1. Rms value of the longitudinal field for a spheroidal distribution
7.2. Maximum value of the longitudinal field for a spheroidal distribution
7.3. Relative difference between theory and simulation for different ellipsoids for the three components of the field
7.4. Rms value of the longitudinal field for a cylindrical distribution
7.5. Maximum value of the longitudinal field for a cylindrical distribution
8.1. Canonical directions on which the fields are plotted
8.2. Coin shape cylinder before and after rotation: canonical directions
8.3. Rotation algorithm - Longitudinal Field
8.4. Rotation algorithm - Longitudinal Field
9.1. Phase space ellipse for a cylinder of emittance $\epsilon _{nx}=5$ mmrad.mm. for different set of parameters and units
9.2. Phase space ellipse for an ellipsoidal distribution with gaussian momentum
10.1. Evolution of the transversal space charge for a drift without space charge
10.2. Evolution of the longitudinal space charge for a drift without space charge
10.3. Evolution of the transversal space charge for a drift without space charge for a focusing beam
10.4. Evolution of the beam envelop for a focusing beam - beam waist definition
10.5. Evolution of the transversal space charge for a drift with space charge forces
10.6. Evolution of the longitudinal space charge for a drift with space charge forces
11.1. Illustration of the dependence on the momentum for the bending radius of a dipole
11.2. Definitions of the dipole origins
11.3. Dipoles dimensions at A0
11.4. Field map from the experimental measurement for the dipoles of A0
11.5. Magnetic field map as modelized by Astra for the dipoles of A0
11.6. Comparison between the measurement fields and astra modelized fields
11.7. Fitting the measured fields with a fringe field model
12.1. Evolution of a bunch though a compressor
12.2. Scheme of a compressor made of 4 dipoles and corresponding sign of the magnetic fields
12.3. Reference path through the four dipoles of the compressor
12.4. Deflection angle along the trajectory in the compressor
12.5. Longitudinal phase space before and after the compressor, without space charge forces
12.6. Longitudinal phase space before and after the compressor, with space charge forces
12.7. Size of the bunch after compression for different correlated energy spread
12.8. Emittance after compression for different correlated energy spread
12.9. Transversal phase space for the compressor without space charge forces
12.10. Transversal phase space for the compressor with space charge forces
12.11. Longitudinal phase space for the compressor without space charge forces
12.12. Transversal phase space for the compressor with space charge forces
12.13. Phase space at the end of the compressor with densities on each axis
13.1. Scheme of an emittance exchanger made of 4 dipoles and corresponding sign of magnetic fields
13.2. Reference path through the four dipoles in the dogleg configuration
13.3. Deflection angle along the trajectory through the dogleg
14.1. Fermilab cavity schema and picture
14.2. $E_{z0}$ (red) in MV/m and the sine oscillating function (blue) adjusted in phase without scale
15.1. Dipoles hard edge coordinates for A0 emittance exchange lattice
16.1. NML facility
16.2. Dipoles hard edge coordinates for NML compressor lattice
A.1. Screen generated by the function ppSummaryPlot
A.2. Screen generated by the function ppSigmaPlot
D.1. Scheme of beam line elements at A0
E.1. Ellipsoid at rest with two rotations: the two rotation steps
E.2. Ellipsoid at rest with two rotations: canonical directions
E.3. Rotation algorithm - Longitudinal Field
E.4. Sphere at low energy: canonical directions
E.5. Rotation algorithm - Longitudinal Field along longitudinal direction
E.6. Rotation algorithm - Longitudinal Field along transverse direction
E.7. Rotation algorithm - Transverse Field in y direction
G.1. Cylindrical distribution - along for different $\sigma _z$
G.2. Cylindrical distribution - along z for different $\sigma _z$
G.3. Ellipsoidal distribution - along z for different $\sigma _z$
G.4. Ellipsoidal distribution - along z for different $\sigma _z$

Subsections

Introduction

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Emmanuel Branlard
http://emmanuel.branlard.free.fr/