Theoretical foundations of synchrotron and storage ring RF systems. ([2015])

• Record Type: Book
• Further Information: Note: Harald Klingbeil, Ulrich Laier, Dieter Lens.
• Authors: Klingbeil, Harald; Laier, Ulrich; Lens, Dieter
• Contents: Preface; Contents; Formula Symbols; 1 Introduction; References; 2 Theoretical Fundamentals; 2.1 Fourier Analysis and Application to Beam Signals; 2.1.1 Fourier Series; 2.1.2 Spectrum of a Dirac Comb; 2.1.3 Different Representations of the Fourier Series; 2.1.4 Discrete Fourier Transform; 2.1.4.1 Motivation of the Transformation Formula; 2.1.4.2 Symmetry Relations; 2.1.4.3 Interpretation of the Spectral Components; 2.1.4.4 Inverse DFT; 2.1.4.5 Conclusion; 2.1.5 Fourier Transform; 2.1.5.1 Fourier Transform of a Single Cosine Pulse; 2.1.5.2 Convolution; 2.1.5.3 Relation to the Fourier Series. 2.1.6 Consequences for the Spectrum of the Beam Signal2.2 Laplace Transform; 2.3 Transfer Functions; 2.4 Mathematical Statistics; 2.4.1 Gaussian Distribution; 2.4.2 Probabilities; 2.4.3 Expected Value; 2.4.4 Unbiasedness; 2.4.5 Uniform Distribution; 2.5 Bunching Factor; 2.6 Electromagnetic Fields; 2.7 Special Relativity; 2.8 Nonlinear Dynamics; 2.8.1 Equivalence of Differential Equations and Systems of Differential Equations; 2.8.2 Autonomous Systems; 2.8.2.1 Time Shift; 2.8.2.2 Phase Space; 2.8.3 Existence and Uniqueness of the Solution of Initial Value Problems. 2.8.3.1 Existence of a Local Solution2.8.3.2 Uniqueness of a Local Solution; 2.8.3.3 Maximal Interval of Existence; 2.8.3.4 Global Solution; 2.8.3.5 Linear Systems of Ordinary Differential Equations; 2.8.4 Orbits; 2.8.5 Fixed Points and Stability; 2.8.6 Flows of Linear Autonomous Systems; 2.8.7 Topological Orbit Equivalence; 2.8.8 Classification of Fixed Points of an Autonomous Linear System of Second Order; 2.8.9 Nonlinear Systems; 2.8.10 Characteristic Equation; 2.9 Continuity Equation; 2.10 Area Preservation in Phase Space; 2.10.1 Velocity Vector Fields; 2.10.2 Maps. 2.10.3 Liouville's Theorem2.11 Hamiltonian Systems; 2.11.1 Example for Motivation; 2.11.2 Arbitrary Number of Variables; 2.11.3 Flow in Phase Space; 2.11.4 Fixed Points of a Hamiltonian System in the Plane; 2.11.5 Hamiltonian as Lyapunov Function; 2.11.6 Canonical Transformations; 2.11.7 Action-Angle Variables; 2.11.7.1 Introductory Example; 2.11.7.2 Basic Principle; 2.11.8 LC Circuit with Nonlinear Inductance; 2.11.9 Mathematical Pendulum; 2.11.9.1 Energy Balance; 2.11.9.2 Hamilton's Equations; 2.11.9.3 Oscillation Period; 2.11.10 Vlasov Equation; 2.11.11 Outlook; References. 3 RF Acceleration3.1 Centripetal Force; 3.2 Simplified Model Synchrotron; 3.3 Tracking Equations; 3.4 Phase Slip Factor and Transition Energy; 3.5 Accelerating Voltage; 3.6 Synchrotron Oscillation; 3.7 Principal Axes; 3.8 Hamiltonian; 3.9 Separatrix; 3.10 Symmetry with Respect to Transition Energy and Sign of Charge; 3.11 Orbits; 3.12 Bucket Area; 3.13 Approximation of Bucket Area; 3.14 Ratio of Bucket Height to Bucket Length; 3.15 Choice of the Harmonic Number; 3.16 Revolution Time in the Stationary Bucket; 3.17 Bunch Area; 3.18 Ratio of Bunch Height to Bunch Length.
• Publisher Details: New York : Springer
• Publication Date: 2015
• Copyright Date: 2015
• Extent: 1 online resource (461 pages), illustrations
• Subjects: 519 530 530.8 539.73 620.5 621.3; Physics; Particle accelerators; Synchrotrons; Storage rings; Particle accelerators; Storage rings; Synchrotrons; Technology & Engineering -- Microwaves; Science -- Weights & Measures; Science -- Nanostructures; Mathematics -- Applied; Microwave technology; Mensuration & systems of measurement; Nanotechnology; Mathematical modelling; Particle acceleration; Microwaves; Science -- Nuclear Physics; Particle & high-energy physics; Electronic books
• Languages: English
• ISBNs: 9783319071886; 3319071882
• Related ISBNs: 9783319071879
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.