Contemporary Accelerator Physics

The following sections are included:

• Preface

• Contents

The following sections are included:

• Introduction

• Hamiltonian Formalism

• Canonical Transformations

• Electric and Magnetic Fields

• Synchro-Betatron Formalism in Beam Dynamics

The following sections are included:

• Introduction

• The Transfer Matrix

• Hill's Equation and Floquet's Theorem

• Twiss Parameters and Courant-Snyder Invariant

• Action-Angle Variables and Beam Emittance

• Adiabatic Damping of Betatron Oscillations

The following sections are included:

• Introduction

• General Description and Basic Properties of a Nonlinear Resonance

• The Method of Effective Potential

• Stability Analysis of Third and Fourth Order Resonances

• The Method of Successive Linearization

• Adiabatic Crossing of a Nonlinear Resonance

• Periodic Crossing of a Nonlinear Resonance

The following sections are included:

• Introduction

• Classical Perturbation Theory

• Effect of Linear and Nonlinear Perturbations in One Dimension

• Secular Perturbation Theory

• The Method of Formal Series

• Renormalization Transformation for Two Resonances

The following sections are included:

• Introduction

• Renormalization Group Method

• The Method of Multiple Scales

• Renormalization Group Analysis of Hill's Equation

• Renormalization Group Reduction of Nonlinear Resonances

• Reduction of Nonlinear Resonances Using the Method of Multiple Scales

• Renormalization Group Reduction of Hamilton's Equations of Motion

The following sections are included:

• Introduction

• Nonlinear Transfer Maps of Betatron Motion

• Linear Transfer Maps

• The Henon Map

• Resonance Structure of the Henon Map

• Renormalization Group Reduction of a Generic Transfer Map

• The Standard Chirikov-Taylor Map

The following sections are included:

• Introduction

• The Liouville Theorem and the Liouville Equation

• Ensemble of Identical Macroscopic Systems

• The Method of Microscopic Phase Space Density

• The Equation for the Microscopic Phase Space Density with a Small Source

• The Generalized Kinetic Equation

• The Balescu-Lenard Kinetic Equation

• The Landau Kinetic Equation

• The Approximate Collision Integral and the Generalized Kinetic Equation

The following sections are included:

• Introduction

• Projection Operator Method

• Renormalization Group Reduction of the Liouville Equation

• Modulational Diffusion

• The Liouville Operator and the Probenius-Perron Operator

The following sections are included:

• Introduction

• The Vlasov Equation for Collisionless Beams

• The Hamiltonian Formalism for Solving the Vlasov Equation

• Propagation of an Intense Beam Through a Periodic Focusing Lattice

• Propagation of an Intense Beam with a Uniform Phase-Space Density

• Dynamical Equations for the Beam Envelope and for the Mean Emittance

• Solution of the Equations for the Boundary Curves

• Description of Beam Dynamics in Terms of Lagrangian Variables

• Landau Damping

The following sections are included:

• Introduction

• Renormalization Group Reduction of the Hydrodynamic Equations

• The Parametric Wave-Particle Resonance

• The Nonlinear Schrodinger Equation for a Single Mode

• Nonlinear Damped Waves in Intense Beams

• Fluctuation Spectrum and Turbulence

The following sections are included:

• Bibliography

• Index