Physics of burning plasmas in toroidal magnetic confinement devices

Abstract

Some of the crucial physics aspects of burning plasmas magnetically confined in toroidal systems are presented from the viewpoint of nonlinear dynamics. Most of the discussions specifically refer to tokamaks, but they can be readily extended to other toroidal confinement devices. Particular emphasis is devoted to fluctuation induced transport processes of mega electron volts energetic ions and charged fusion products as well as to energy and particle transports of the thermal plasma. Long time scale behaviours due to the interplay of fast ion induced collective effects and plasma turbulence are addressed in the framework of burning plasmas as complex self-organized systems. The crucial roles of mutual positive feedbacks between theory, numerical simulation and experiment are shown to be the necessary premise for reliable extrapolations from present day laboratory to burning plasmas. Examples of the broader applications of fundamental problems to other fields of plasma physics and beyond are also given.

Shear Alfvén wave continuous spectrum within magnetic islands

“…In fusion plasmas, fast ions in the MeV energy range have velocities comparable with the typical Alfvén speed. In addition, SAW group velocity is directed along the magnetic field line and, therefore, fast ions can stay in resonance and effectively exchange energy with the wave [1,2]. SAW in a nonuniform equilibrium experience collisionless dissipation (continuum damping [3,4,5]), due to singular structures that are formed where the SAW continuum is resonantly excited.…”

“…In tokamaks, the magnetic field intensity varies along the field line. This creates gaps in the SAW continuous spectrum [6] due to translational symmetry breaking, analogous to electrons traveling in a periodic lattice [1,2]. Two types of collective shear Alfvén instabilities exist in tokamak plasmas: energetic-particle continuum modes (EPM) [7], with frequency determined by fast particle characteristic motions, and discrete Alfvén eigenmodes (AE), with a frequency inside SAW continuum gaps [8].…”

“…Two types of collective shear Alfvén instabilities exist in tokamak plasmas: energetic-particle continuum modes (EPM) [7], with frequency determined by fast particle characteristic motions, and discrete Alfvén eigenmodes (AE), with a frequency inside SAW continuum gaps [8]. The former can become unstable provided the drive exceeds a threshold determined by the continuum damping absorption; the latter, have a generally lower instability threshold, being practically unaffected by continuum damping [1,2,3,4,5]. For this reason, the importance of understanding the continuum radial structure is clear, if one faces the problem of reaching the ignition condition with magnetically confined fusion plasmas, due to the potential impact of AE stability on the plasma confinement.…”

Nonlinear Dynamics and Complex Behaviors in Magnetized Plasmas of Fusion Interest

“…Simflar considerations can be made for other toroidal magnetized plasma equilibria, such as steUarators, or -more generally -for any general periodic modulation of the B field strength. As a consequence of this lattice symmetry breaking, frequency gaps are formed in the s.A. continuous spectrum, similar to forbidden energy bands for electrons moving in a onedimensional crystal lattice [6,8,9]. The best known example is the toroidicity induced frequency gap [17], however each equilibrium geometry modulation generates its own particular structures in the s.A. continuous spectrum [6,8,9].…”

“…General references on the first issue are provided by the ITER physics basis [4] and its recent update [5], while recent and sufficiently comprehensive reviews can be found in [6,7,8]. On the second issue, experimental investigation is in the very early development stage, so only fairly recent theoretical reviews are available [6,8,9].…”