Short description:

This book explores the outstanding and rather novel diagnostics of the fast ions and fast ion-driven instabilities coupled to modern theory of near-critical nonlinear wave-particle systems with the particle source and wave damping.

Long description:

This book explores the physics of fast ions and fast ion- driven instabilities. It also describes modern theory of near- critical nonlinear wave? particle systems with the particle source and wave damping. Such a theory was developed by H.L. Berk and B.N. Breizman in the mid- 1990s, and it delivered outstanding results successfully explaining the experimentally observed collective phenomena driven by energetic ions.

A systematic and step-by-step analysis of resonant interactions between the waves in plasmas and various types of energetic ion populations is presented and analyzed, taking the readers on an exciting journey into the world of nonlinear physics and cutting-edge experiments performed on the world?s major magnetic fusion machines.

The phenomena described in this book will be of interest for researchers studying fusion, solar plasma, space plasma, and for a broader realm of scientists working in nonlinear phenomena.

Key Features:

• Features experimental data and the Berk-Breizman theory on nonlinear evolution of energetic particle-driven waves


• Describes in simple terms, the recent advances in the diagnostics of energetic particles and Alfvén waves


• Presents a systematic overview of extrapolating results presented in other types of plasmas (e.g., solar and space) and nonlinear systems.

The new book by S.Sharapov and B.Breizman covers an area that is of crucial importance for magnetic fusion physics. In fact, fast ions are an essential element of the burning plasma regime, in which the self-heating of the plasma via fusion-generated (fast) alpha particles dominates over external heating. Such regime is largely unexplored and is necessarily the one in which magnetic fusion power plants will operate.

Drs Sharapov and Breizman are top scientists in the field of fast ion and burning plasma physics. They are both theoreticians, but have also worked side by side with experimentalists and have always been innovative both in terms of theory tools and of interconnections between these tools and between theory and experiment. The book reflects such proximity, as it illustrates the basic theory elements behind the fast ion phenomena in fusion plasma, but also corroborates the formal aspects with experimental findings and clear discussions of the implications.

- Ambrogio Fasoli, EPFL and Swiss Plasma Center, Lausanne, Switzerland, February 2025

Table of Contents:

Chapter 1: Classical Behavior of Fusion-born Alpha-particles. Chapter 2: Wave-particle Resonant Interaction: Theory Versus Experiment. Chapter 3: Energetic Particle-Driven Modes of Spontaneous Frequency Sweeping. Chapter 4: The Fishbones. Chapter 5: Equilibrium and Alfvén Eigenmodes in Tokamak Plasma. Chapter 6: Drive, Damping, and Excitation Threshold for Alfvén Eigenmodes. Chapter 7: Alfvén Cascade Modes in Reversed Magnetic Shear Equilibria. Chapter 8: Multiple Modes and Global Transport of Energetic Particles. Appendix A: Cubic Equation Derivation. Appendix B: Reduced Model for the Weakly Nonlinear Fishbones. Appendix C: Flux Coordinates for Tokamak Equilibrium. Appendix D: Radiative Damping for TAE. Appendix E: Trapped Electron Collisional Damping for TAE. Appendix F: Wave Energy of TAE in Numerical Assessment of the TAE.