Preface |
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xi | |
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1 | (12) |
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1.1 Differences or Differentials? |
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1 | (2) |
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1.2 Phase Space Co-ordinates |
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3 | (2) |
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1.3 Iterations, Ancient and Modern |
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5 | (1) |
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1.4 Accelerator History: The Two Golden Ages |
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6 | (7) |
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10 | (3) |
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13 | (11) |
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13 | (3) |
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2.2 Transverse Motion through Magnets |
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16 | (3) |
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2.3 Matrix Equations of Motion |
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19 | (5) |
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22 | (2) |
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3 Strong Focusing Transverse Optics |
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24 | (13) |
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3.1 Linear Stability and Twiss Functions |
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25 | (2) |
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3.2 Turn-by-Turn Motion in Phase Space |
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27 | (2) |
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3.3 Propagation across a Fraction of a Turn |
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29 | (1) |
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3.4 Continuous Propagation |
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30 | (2) |
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32 | (5) |
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35 | (2) |
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4 Longitudinal and Off-Momentum Motion |
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37 | (13) |
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4.1 Constant Momentum Offset: Transverse Motion |
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37 | (2) |
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4.2 The Dispersion Function |
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39 | (2) |
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4.3 Oscillating Momentum: Longitudinal Motion |
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41 | (4) |
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45 | (5) |
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48 | (2) |
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5 Action and Emittance --- One Particle or Many? |
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50 | (13) |
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5.1 Transverse Action-Angle Co-ordinates |
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50 | (2) |
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5.2 Unnormalised Emittances and Beam Sizes |
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52 | (2) |
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5.3 Tune Spread and Filamentation |
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54 | (2) |
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5.4 Linac (Phase Space Area) Emittances |
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56 | (2) |
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5.5 Normalised Emittance and Adiabatic Damping |
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58 | (2) |
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5.6 Longitudinal Phase Space Parameters |
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60 | (3) |
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61 | (2) |
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63 | (10) |
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6.1 Normal and Skew Multipole Magnets |
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63 | (2) |
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6.2 Iron-Dominated Magnets |
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65 | (1) |
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6.3 Conductor-Dominated Magnets |
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66 | (1) |
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6.4 Field Quality and Errors |
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67 | (6) |
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69 | (4) |
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73 | (10) |
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73 | (1) |
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74 | (2) |
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7.3 Cylindrical Resonant Cavities --- Pill-Boxes |
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76 | (3) |
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7.4 Cavity Performance Limits |
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79 | (4) |
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81 | (2) |
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8 Linear Errors and Their Correction |
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83 | (11) |
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8.1 Trajectory and Closed Orbit Errors |
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83 | (5) |
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88 | (1) |
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8.3 Tune Shifts and L-Waves |
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89 | (5) |
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92 | (2) |
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9 Sextupoles, Chromaticity and the Henon Map |
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94 | (13) |
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9.1 Chromaticity in a FODO Lattice |
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94 | (2) |
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9.2 Chromaticity Correction |
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96 | (2) |
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9.3 The Henon Map --- A Unit Strength Sextupole in 1-D |
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98 | (2) |
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9.4 A Taxonomy of 1-D Motion |
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100 | (3) |
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103 | (4) |
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104 | (3) |
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10 Octupoles, Detuning and Slow Extraction |
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107 | (9) |
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10.1 Single Octupole Lattice |
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107 | (2) |
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10.2 Discrete Motion in Action-Angle Space, (J, φ) |
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109 | (1) |
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10.3 Two-Turn Motion with Q ~ 1/2 |
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110 | (1) |
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10.4 Slow Extraction near the Half-Integer |
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111 | (5) |
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113 | (3) |
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11 Synchrotron Radiation --- Classical Damping |
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116 | (15) |
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11.1 Spectrum and Distribution Pattern |
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116 | (3) |
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11.2 Energy Loss Per Turn and Longitudinal Damping |
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119 | (5) |
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11.3 Continuous Acceleration |
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124 | (2) |
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11.4 Transverse Damping and Partition Numbers |
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126 | (5) |
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128 | (3) |
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12 Synchrotron Radiation --- Quantum Excitation |
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131 | (10) |
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132 | (2) |
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12.2 Horizontal Emittance |
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134 | (4) |
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138 | (3) |
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139 | (2) |
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13 Linacs --- Protons and Ions |
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141 | (18) |
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142 | (3) |
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13.2 Multi-Cell Synchronism |
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145 | (2) |
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147 | (6) |
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13.4 Radio Frequency Quadrupoles |
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153 | (4) |
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13.5 Beam Losses and Haloes |
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157 | (2) |
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158 | (1) |
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159 | (11) |
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14.1 Longitudinal and Transverse Focusing |
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159 | (2) |
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161 | (1) |
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162 | (2) |
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14.4 Recirculating and Energy Recovery Linacs |
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164 | (2) |
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166 | (4) |
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169 | (1) |
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15 The Beam-Beam Interaction and 1-D Resonances |
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170 | (11) |
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15.1 Round Beam-Beam Interaction |
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170 | (4) |
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15.2 First-Order Theory of 1-D Resonances |
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174 | (2) |
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15.3 Resonance Island Tunes and Widths |
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176 | (5) |
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180 | (1) |
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181 | (10) |
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182 | (2) |
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184 | (3) |
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16.3 Dynamical Zones in Tune Modulation Space |
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187 | (4) |
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190 | (1) |
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Appendix A Selected Formulae for Accelerator Design |
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191 | (7) |
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A.1 Matrices for Linear Motion through Accelerator Elements |
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191 | (5) |
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A.2 Propagation of Twiss Functions |
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196 | (2) |
References |
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198 | (3) |
Index |
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201 | |