Preface ......................................................... v
1 Physics with Trapped Charged Particles ....................... 1
M. Knoop, N. Madsen and R.C. Thompson
1.1 Introduction ............................................ 1
1.2 History of Ion Traps .................................... 2
1.3 Principles of Ion Traps ................................. 3
1.4 Creation, Cooling and Detection of Ions ................. 8
1.5 Applications of Ion Traps .............................. 16
1.6 Conclusions and Outlook ................................ 22
2 Detection Techniques for Trapped Ions ....................... 25
M. Knoop
2.1 Electronic Techniques .................................. 26
2.2 Fluorescence Techniques ................................ 35
3 Cooling Techniques for Trapped Ions ......................... 43
D.M. Segal and Ch. Wunderlich
3.1 Introduction ........................................... 43
3.2 Non-laser Cooling Techniques ........................... 45
3.3 Laser Cooling .......................................... 48
3.4 Laser Cooling Using Electromagnetically Induced
Transparency ........................................... 70
3.5 Cavity Cooling ......................................... 76
3.6 Cooling Scheme Combining Laser Light and RF ............ 77
4 Accumulation, Storage and Manipulation of Large Numbers of
Positrons in Traps I - The Basics ........................... 83
С.M. Surko
4.1 Overview ............................................... 84
4.2 Positron Trapping ...................................... 86
4.3 Positron Cooling ....................................... 96
4.4 Confinement and Characterization of Positron Plasmas
in Penning-Malmberg Traps ............................. 101
4.5 Radial Compression Using Rotating Electric Fields -
the "Rotating-wall" (RW) Technique .................... 111
4.6 Concluding Remarks .................................... 120
5 Accumulation, Storage and Manipulation of Large Numbers
of Positrons in Traps II - Selected Topics ................. 129
С.M. Surko, J.R. Danielson and T.R. Weber
5.1 Overview .............................................. 130
5.2 Extraction of Beams with Small Transverse Spatial
Extent ................................................ 131
5.3 Multicell Trap for Storage of Large Numbers of
Positrons ............................................. 143
5.4 Electron-Positron Plasmas ............................. 156
5.5 Concluding Remarks .................................... 166
6 Waves in Non-neutral Plasma ................................ 173
F. Anderegg
6.1 Diocotron Waves ....................................... 173
6.2 Plasma Waves .......................................... 181
6.3 Cyclotron Waves ....................................... 190
7 Internal Transport in Non-neutral Plasma ................... 195
F. Anderegg
7.1 Types of Collisions ................................... 195
7.2 Test Particle Transport ............................... 196
7.3 Heat Transport ........................................ 208
7.4 Transport of Angular Momentum ......................... 212
7.5 Table of Transport Coefficients ....................... 216
8 Antihydrogen Formation and Trapping ........................ 219
N. Madsen
8.1 Introduction .......................................... 219
8.2, Introduction to Antihydrogen Formation and Trapping ... 220
8.3 Antiproton Catching and Pre-cooling ................... 223
8.4 Trapped Particles and Magnetic Multipoles ............. 224
8.5 The Rotating-wall Technique ........................... 225
8.6 Antiproton Preparation ................................ 227
8.7 Positron Preparation .................................. 229
8.8 Evaporative Cooling of Charged Particles .............. 230
8.9 Merging Antiprotons and Positrons ..................... 231
8.10 Trapped Antihydrogen and its Detection ................ 232
8.11 Conclusions and Outlook ............................... 235
9 Quantum Information Processing with Trapped Ions ........... 239
C.F. Roos
9.1 Introduction .......................................... 239
9.2 Storing Quantum Information in Trapped Ions ........... 241
9.3 Preparation, Manipulation and Detection of an
Optical Qubit ......................................... 242
9.4 Entangling Quantum Gates .............................. 245
9.5 Quantum State Tomography .............................. 251
9.6 Elementary Quantum Protocols and Quantum Simulation ... 255
10 Optical Atomic Clocks in Ion Traps ......................... 261
H.S. Margolis
10.1 Introduction .......................................... 261
10.2 Principles of Operation ............................... 262
10.3 Systems Studied and State-of-the-art Performance ...... 266
10.4 Systematic Frequency Shifts ........................... 268
10.5 Conclusions and Perspectives .......................... 271
11 Novel Penning Traps ........................................ 275
J. Verdú
11.1 Introduction .......................................... 275
11.2 Penning Traps ......................................... 276
11.3 The CPW Penning Trap .................................. 277
11.4 The Real CPW Penning Trap ............................. 282
11.5 Compensation of Electric Anharmonicities .............. 284
11.6 Conclusions ........................................... 285
12 Trapped Electrons as Electrical (Quantum) Circuits ......... 289
J. Verdú
12.1 Introduction .......................................... 289
12.2 The Induced Charge Density ............................ 291
12.3 Detection of the Electron's Motion .................... 292
12.4 Equivalent Electrical Circuit of the Trapped
Particle .............................................. 295
12.5 Coupling the Cyclotron Motion to a Superconducting
Cavity ................................................ 298
12.6 Conclusions ........................................... 301
13 Basics of Charged Particle Beam Dynamics and Application
to Electrostatic Storage Rings ............................. 305
A.I. Papash and C.P. Welsch
13.1 Introduction .......................................... 306
13.2 Relativistic Energy and Momentum ...................... 310
13.3 Basic Features of Magnetic and Electrostatic Bends .... 311
13.4 Betatron Oscillations ................................. 316
13.5 Quadrupole Magnets .................................... 320
13.6 Strong Focusing ....................................... 322
13.7 Summary ............................................... 325
14 Electrostatic Storage Rings - An Ideal Tool for
Experiments at Ultralow Energies ........................... 327
A.I. Papash, A.V. Smirnov and C.P. Welsch
14.1 Introduction .......................................... 328
14.2 Common Features of Electrostatic Storage Rings ........ 329
14.3 Electrostatic Deflectors of Different Shapes .......... 333
14.4 Electric Field Distribution in Electrostatic
Deflectors ............................................ 336
14.5 Equations of Motion in an Electrostatic Deflector ..... 340
14.6 Nonlinear Effects in ESRs ............................. 343
14.7 Ion Kinetics and Long-term Beam Dynamics in
Electrostatic Storage Rings ........................... 344
14.8 Benchmarking of Experiments ........................... 353
14.9 Conclusions and Outlook ............................... 355
Index ......................................................... 359
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