Nonlinear dynamics and chaos inside the FRC

The eld-reversed con guration (FRC) is a toroidal-shaped magnetic- eld geometry used for con ning plasmas for the purpose of controlled production of fusion energy. Because of angular symmetry, the 3-D system can be expressed as two coupled highly nonlinear oscillators. Due to high nonlinearity of the equations of motion, the behavior of the system is very complex, showing regimes of both chaotic and integrable motion. This book investigates the dynamics of this complex, yet analytically tractable, system. The basic structure of phase-space is investigated analytically and with Poincare surface-of-section plots. The regime of adiabatic chaos that occurs in elongated FRCs is studied, deriving conditions for integrable motion. The effect of a small odd-parity rotating magnetic eld (RMF) on ion heating is also addressed. The energy gains are found to be large, con rming the effectiveness of RMF in heating the ions. This book is suitable for students and researchers interested in fusion. It is also intended as an exploration of a complicated but interesting and analytically tractable dynamical system, applying techniques from nonlinear dynamics.

Autorentext

Alexandra S. Landsman, PhD: Graduated in 2005 from Princeton University with a doctorate in Plasma Physics. Professor of Physics at James Madison University. Research interests lie in nonlinear dynamics and applications.

Klappentext

The eld-reversed con guration (FRC) is a toroidal-shaped magnetic- eld geometry used for con ning plasmas for the purpose of controlled production of fusion energy. Because of angular symmetry, the 3-D system can be expressed as two coupled highly nonlinear oscillators. Due to high nonlinearity of the equations of motion, the behavior of the system is very complex, showing regimes of both chaotic and integrable motion. This book investigates the dynamics of this complex, yet analytically tractable, system. The basic structure of phase-space is investigated analytically and with Poincare surface-of-section plots. The regime of adiabatic chaos that occurs in elongated FRCs is studied, deriving conditions for integrable motion. The effect of a small odd-parity rotating magnetic eld (RMF) on ion heating is also addressed. The energy gains are found to be large, con rming the effectiveness of RMF in heating the ions. This book is suitable for students and researchers interested in fusion. It is also intended as an exploration of a complicated but interesting and analytically tractable dynamical system, applying techniques from nonlinear dynamics.