Preface; Contents; 1 Introduction; 1.1 Historical Remarks; 1.2 Important Other Sources of Reading; 1.3 What Are Space Charge Dominated Beams?; 1.4 Incoherent and Coherent Effects; 1.5 Terminology of Resonance, Coherence and Instability; 1.6 Analytical and Simulation Approaches; 1.7 Overview; References; 2 Phase Space Dynamics in Theory and Simulation; 2.1 Basics of Kinetic Theory; 2.1.1 Single Particle Motion in a Smooth Field; 2.1.2 Fokker-Planck Equation; 2.1.3 Liouville and Vlasov-Poisson Equations; 2.1.4 Fluid Models; 2.2 Emittance and Anisotropy; 2.2.1 Trace Space Emittances

2.2.2 Rms Emittances and Rms Equivalent Beams2.2.3 Anisotropy Factor; 2.3 Multiparticle Simulation Effects; 2.3.1 Rms Entropy and Simulation Noise; 2.3.2 Application to TRACEWIN Code; References; 3 Vlasov and Envelope Analysis; 3.1 Vlasov Techniques; 3.1.1 Linearized 1D Vlasov-Poisson Equations; 3.1.2 Linearized 2D Vlasov-Poisson Equations; 3.1.3 Application to Periodic Focusing; 3.1.4 Further Comments; 3.2 Envelope Equations; 3.2.1 Rms Envelope Equations; 3.2.2 Smooth Approximation; 3.2.3 Chernin's Equations; 3.2.4 Core-Test-Particle Model; References; 4 Matched Beams

4.1 Distribution Functions and Their Properties4.2 Linear and Nonlinear Space Charge Forces; 4.3 Selfconsistent Non-KV Equilibria; 4.3.1 Anisotropic Beams; 4.3.2 Shielding by Space Charge; 4.3.3 Periodic Focusing; 4.4 Incoherent Space Charge Effects on Resonances; 4.4.1 Incoherent Space Charge Tune Shifts; 4.4.2 Structural Incoherent Space Charge Resonances; 4.4.3 Simulation Examples; References; 5 Modes of Space Charge Interaction; 5.1 Characteristics of Space Charge Interaction; 5.1.1 Mechanisms of Growth; 5.1.2 Sources of Driving Energy; 5.2 Incoherent vs. Coherent Oscillations

5.2.1 Characteristics of Coherent Oscillations5.2.2 Simulation Example; 5.3 Vlasov Theory of Coherent Eigenmodes in Anisotropic 2D Beams; 5.3.1 Modes of Different Order; 5.3.2 Basic Equations; 5.3.3 Different Order Mode Frequencies; 5.3.3.1 Second Order Even Modes; 5.3.3.2 Second Order Odd Modes; 5.3.3.3 Third Order Modes; 5.3.3.4 Fourth Order Modes; 5.3.4 Overview on Coherent Mode Frequencies; 5.4 Negative Energy Modes and Free Energy; 5.4.1 Basic Concept; 5.4.2 Multi-stream Instability of Phase Space Filaments; 5.4.3 Negative Energy Modes in a Potential; 5.5 Landau Damping

5.5.1 General Observations5.5.2 Tune ``Footprints'' with Space Charge; 5.6 Fluid Models; References; 6 Beam Mismatch and Halo; 6.1 Fundamental Mechanisms; 6.1.1 Characterization of Core and Halo; 6.1.2 Rms Mismatch Conversion; 6.1.3 Core-Test-Particle Model; 6.2 Examples of Self-consistent 2D Simulation; 6.2.1 Mismatch Conversion; 6.2.2 Interpretation; 6.3 Density Mismatch and Nonlinear Field Energy; References; 7 Coherent Parametric Instabilities; 7.1 Parametric Instability Conditions; 7.1.1 Single Particle Parametric Resonances; 7.1.2 Coherent Parametric Instabilities