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.

A toroidal, nonlinear, electrostatic fluid-kinetic hybrid electron model is formulated for global gyrokinetic particle simulations of driftwave turbulence in fusion plasmas. Numerical properties are improved by an expansion of the electron response using a smallness parameter of the ratio of driftwave frequency to electron transit frequency. Linear simulations accurately recover the real frequency and growth rate of toroidal ion temperature gradient (ITG) instability. Trapped electrons increase the ITG growth rate by mostly not responding to the ITG modes. Nonlinear simulations of ITG turbulence find that the electron thermal and particle transport are much smaller than the ion thermal transport and that small scale zonal flows are generated through nonlinear interactions of the trapped electrons with the turbulence.

Comprehensive analysis of the largest first-principles simulations to date shows that stochastic wave-particle decorrelation is the dominant mechanism responsible for electron heat transport driven by electron temperature gradient turbulence with extended radial streamers. The transport is proportional to the local fluctuation intensity, and phase-space island overlap leads to a diffusive process with a time scale comparable to the wave-particle decorrelation time, determined by the fluctuation spectral width. This kinetic time scale is much shorter than the fluid time scale of eddy mixing.

Nonlinear saturation of toroidal Alfvén eigenmodes (TAE) via mode-mode couplings is investigated both analytically and numerically. It is demonstrated that, as the TAE mode amplitude increases, the corresponding nonlinear ponderomotive force produces a fine-structure density modulation, which then causes enhanced energy dissipation in the short scales and leads eventually to the nonlinear saturation of TAE.

Alfvén waves are electromagnetic perturbations inherent to magnetized plasmas that can be driven unstable by a free energy associated with gradients in the energetic particles' distribution function. The energetic particles with velocities comparable to the Alfvén velocity may excite Alfvén instabilities via resonant wave-particle energy and momentum exchange. Burning plasmas with large population of fusion born super-Alfvénic alpha particles in magnetically confined fusion devices are prone to excite weakly-damped Alfvén eigenmodes (AEs) that, if allowed to grow unabated, can cause a degradation of fusion performance and loss of energetic ions through a secular radial transport. In order to control the fast-ion distribution and associated Alfvénic activity, the fusion community is currently searching for external actuators that can control AEs and energetic ions in the harsh environment of a fusion reactor. Most promising control techniques are based on (i) variable fast-ion sources to modify gradients in the energetic particles' distribution, (ii) localized electron cyclotron resonance heating to affect the fast-ion Plasma Physics and Controlled Fusion