| Preface | 6 |
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| Contents | 8 |
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| Part I Electromagnetic Trap Properties | 12 |
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| 1 Summary of Trap Properties | 13 |
| 1.1 Trapping Principles in Paul Traps | 13 |
| 1.1.1 General Principles | 15 |
| 1.1.2 Potential Depth | 17 |
| 1.1.3 Motional Spectrum | 18 |
| 1.1.4 Optimum Trapping Conditions | 18 |
| 1.1.5 Storage Time | 19 |
| 1.1.6 Ion Density Distribution | 20 |
| 1.1.7 Storage Capability | 20 |
| 1.1.8 Paul Trap Imperfections | 21 |
| 1.2 Trapping Principles in Penning Traps | 23 |
| 1.2.1 Theory of the Ideal Penning Trap | 23 |
| 1.2.2 Motional Spectrum in Penning Traps | 25 |
| 1.2.3 Penning Trap Imperfections | 26 |
| 1.2.4 Storage Time | 28 |
| 1.2.5 Storage Capability | 30 |
| 1.2.6 Spatial Distribution | 30 |
| 1.3 Trap Techniques | 31 |
| 1.3.1 Trap Loading | 31 |
| In-trap Ion Creation | 31 |
| Ion Injection from Outside | 31 |
| 1.3.2 Trapped Particle Detection | 33 |
| Destructive Detection | 33 |
| Nondestructive Detection | 34 |
| 1.4 Ion Cooling Techniques | 38 |
| 1.4.1 Buffer Gas Cooling | 38 |
| 1.4.2 Resistive Cooling | 39 |
| 1.4.3 Laser Cooling | 40 |
| 1.4.4 Radiative Cooling | 43 |
| Part II Mass Spectrometry | 45 |
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| 2 Mass Spectrometry Using Paul Traps | 46 |
| 2.1 The Quadrupole Ion Trap as a Mass Spectrometer | 49 |
| 2.2 The ``Mass Instability Method'' of Detection | 50 |
| 2.3 Sources of Mass Error in Ion Ejection Methods | 53 |
| 2.4 Nonlinear Resonances in Imperfect Quadrupole Trap | 53 |
| 2.5 Quadrupole Time-of-Flight Spectrometer | 55 |
| 2.6 Tandem Quadrupole Mass Spectrometers | 57 |
| 2.7 Tandem Quadrupole Fourier Transform Spectrometer | 59 |
| 2.8 Silicon-Based Quadrupole Mass Spectrometers | 61 |
| 3 Mass Spectroscopy in Penning Trap | 64 |
| 3.1 Systematic Frequency Shifts | 64 |
| 3.1.1 Electric Field Imperfections | 64 |
| 3.1.2 Magnetic Field Imperfections | 66 |
| 3.1.3 Misalignements and Trap Ellipticity | 66 |
| 3.1.4 Image Charges | 67 |
| 3.1.5 Magnetic Field Fluctuations | 67 |
| 3.2 Observation of Motional Resonances | 69 |
| 3.2.1 Nondestructive Observation | 69 |
| 3.2.2 Destructive Observation | 72 |
| 3.3 Line Shape of Motional Resonances | 75 |
| 3.3.1 Nondestructive Detection | 75 |
| 3.3.2 Destructive Detection | 77 |
| Dipole Excitation | 77 |
| Quadrupole Excitation | 78 |
| Ramsey Excitation | 79 |
| 3.4 Experimental Procedures | 81 |
| 3.4.1 Reference Ions | 82 |
| 3.5 Selected Results | 85 |
| 3.5.1 Stable and Long Lived Isotopes | 86 |
| 3H 3He Mass Difference | 86 |
| Proton/Electron Mass Ratio | 87 |
| Proton/Antiproton Mass Ratio | 87 |
| Cs Mass and the Fine Structure Constant | 87 |
| SI Mass and the Kilogram | 88 |
| 3.5.2 Short-Lived Isotopes | 88 |
| Part III Spectroscopy with Trapped Charged Particles | 91 |
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| 4 Microwave Spectroscopy | 92 |
| 4.1 Zeeman Spectroscopy | 92 |
| 4.1.1 g-Factor of the Free Electron | 93 |
| 4.1.2 g-Factor of the Bound Electron | 102 |
| 4.1.3 Atomic g-Factor | 108 |
| 4.1.4 Nuclear gI-Factor | 110 |
| 4.2 Hyperfine Structures in the Ground States | 112 |
| 4.2.1 Summary of HFS Theory | 112 |
| 4.2.2 Early Experiments | 114 |
| 4.2.3 Laser Microwave Double Resonance Spectroscopy | 120 |
| 4.3 Microwave Atomic Clocks | 125 |
| 4.3.1 Definition of the Unit of Time | 125 |
| 4.3.2 Trapped Ion Microwave Standards | 128 |
| The JPL 199Hg+ Standard | 130 |
| The NIST 199Hg+ Standard | 132 |
| Other Possible Ion Microwave Standards | 135 |
| 5 Optical Spectroscopy | 136 |
| 5.1 Optical Frequency Standards | 136 |
| 5.1.1 Theoretical Limit to Laser Spectral Purity | 136 |
| 5.1.2 Laser Stabilization | 138 |
| 5.1.3 Single Ion Optical Frequency Standards | 140 |
| Servo-Related Limit on Stability: The Dick Effect | 140 |
| Quantum Projection Noise | 142 |
| The 199Hg+ Optical Standard | 143 |
| Optical Frequency Standards Based on Alkaline Earth Ions | 145 |
| Optical Frequency Standard Based on 171Yb+ Ion | 148 |
| Optical Frequency Standard based on 115In+ Ion | 151 |
| Optical Frequency Standard Based on 27Al+ Ion | 152 |
| 5.1.4 Correction of Systematic Errors | 154 |
| The Electric Quadrupole Shift | 155 |
| The Quadratic Zeeman Shift | 156 |
| Relativistic Doppler Shift | 157 |
| Quadratic Stark Shifts | 158 |
| Gravitational Red Shift | 158 |
| Other Systematic Biases | 158 |
| 5.1.5 Optical Frequency Measurement | 159 |
| 5.2 Progress in Standards | 164 |
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