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Summary: Modern Map Methods in Particle Beam Physics
Review: This book is a fine study of the dynamics of beam particles exhibited in particle accelerators. It deals with the description of the motion of particles in accelerators to very high precision over short times and the analysis of the topology of the evolution of state space over long times. The book has seven chapters. Chapter 1 deals with the dynamics of particles and fields. There are 5 subsections : Beams and Beam Physics ; Differential Equations, Determinism and Maps ; Lagrangian Systems ; Hamiltonian Systems ; Fields and Potentials. An interesting idea here is the use of the Hamiltonian to represent energy particle
in which the particle can be ' squeezed ' and when let go, it returns to its original shape. This property is called symplecity and is akin to the motion of an incompressible liquid within a structure of guidance surfaces : The surfaces can never be crossed, and the closer they lie together, the faster the liquid flows. Chapter 2 deals with the differential algebraic techniques which are used to study weakly nonlinear motion of particles in accelerators linked to the common concept of the transfer map of the dynamics of those particles. There are 5 subsections here :
Differential Algebraic Techniques ; Function Spaces and Their Algebras ; Taylor Differential Algebras ; Advanced Methods ;
Appendix on Third ODE Integrator. Chapter 3 deals with Fields. All the fields here are governed by Maxwell's equations. There are 2 subsections here : Analytic Field Representation ; Practical Utilization of Field Information. Chapter 4 deals with the properties of maps. Maps are used to describe the flows for the ordinary differential equations occurring in beam physics. There are 4 subsections :
Maps : Properties ; Manipulations ; Symmetries ; Representations. Chapter 5 deals with the calculation of maps. There are 5 subsections : Maps : Calculation ; The Particle Optical Equations of Motion ; Equations of Motion for Spin ; Maps Determined by Algebraic Relations ; Maps Determined by Differential Equations. Chapter 6 deals with imaging systems. As described in the book, imaging systems are devices used for the purpose of measuring position, momentum , energy or mass of charged particles, in which microscopes and spectrometers are included. There are 4 subsections : Introduction ; Aberration and Their Correction ;
Reconstructive Correction of Aberrations ; Aberration Correction via Repetitive Symmetry . Chapter 7 deals with repetitive systems. As described in the book, all repetitive systems require that the particles remain
confined in the ring, which means that the motion is stable in that their coordinates do not exceed a certain bound d. The study of the dynamics of repetitive systems has long been a key concern of beam physics. There are 5 subsections : Repetitive Systems ; Linear Theory ; Parameter-Dependent Linear Theory ;
Normal Forms ; Symplectic Tracking. The book is a liking for those who love mathematics. Going through the book, one can find and is amazed how mathematics can provide the modern technology for the construction of very effective and very accurate accelerator machines to meet the objectives of various scientific fields.
Rating:
Summary: Modern Map Methods in Particle Beam Physics
Review: This book is a fine study of the dynamics of beam particles in particle accelerators. It deals with the description of the motion of particles in accelerators to very high precision over short times and the analysis of the topology of the evolution of state space over long times. The book has seven chapters. Chapter 1 deals with the dynamics of particles and fields. There are 5 subsections : Beams and Beam Physics ; Differential Equations, Determinism and Maps ; Lagrangian Systems ; Hamiltonian Systems ; Fields and Potentials. An interesting idea here is the use of the Hamiltonian to represent energy particle in which the particle can be 'squeezed' and when let go, it returns to its original shape. This property is called symplecity and is akin to the motion of an incompressible liquid within a structure of guidance surfaces : The surfaces can never be crossed, and the closer they lie together, the faster the liquid flows. Chapter 2 deals with the differential algebraic techniques which are used to study weakly nonlinear motion of particles in accelerators linked to the common concept of the transfer map of the dynamics of those particles. There are 5 subsections here :
Differential Algebraic Techniques ; Function Spaces and Their Algebras ; Taylor Differential Algebras ; Advanced Methods ;
Appendix on Third ODE Integrator. Chapter 3 deals with Fields. All the fields here are governed by Maxwell's equation. There are 2 subsections here : Analytic Field Representation ; Practical Utilization of Field Information. Chapter 4 deals with the properties of maps. Maps are used to describe the flows for the ordinary differential equations occurring in beam physics. There are 4 subsections :
Maps : Properties ; Manipulations ; Symmetries ; Representations. Chapter 5 deals with the calculation of maps. There are 5 subsections : Maps : Calculation ; The Particle Optical Equations of Motion ; Equations of Motion for Spin ; Maps Determined by Algebraic Relations ; Maps Determined by Differential Equations. Chapter 6 deals with imaging systems. As described in the book, imaging systems are devices used for the purpose of measuring position, momentum, energy or mass of charged particles, in which microscopes and spectrometers are included. There are 4 subsections : Introduction ; Aberration and Their Correction ;
Reconstructive Correction of Aberrations ; Aberration Correction via Repetitive Symmetry. Chapter 7 deals with repetitive systems. As described in the book, all repetitive systems require that the particles remain confined in the ring, which means that the motion is stable in that their coordinates do not exceed a certain bound d. The study of the dynamics of repetitive systems has long been a key concern of beam physics. There are 5 subsections : Repetitive
Systems ; Linear Theory ; Parameter-Dependent Linear Theory ;
Normal Forms ; Symplectic Tracking. The book is a liking for those who love mathematics. Going through the book, one can find and is amazed how mathematics can provide the modern technology for the construction of very effective and very accurate accelerator machines to meet the objectives of various scientific fields.
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