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

Global gyrokinetic particle simulations and nonlinear gyrokinetic theory indicate that electron temperature gradient (ETG) instability saturates via nonlinear toroidal coupling. In such nonlinear interactions, the wave energy at the unstable high toroidal-mode number domain cascades towards the more stable lower toroidal-mode number domain via scatterings off the driven lowmode number quasi-modes. During the saturation process, there is little zonal flow generation and the radial fluctuation envelopes maintain extended structures. The nonlinear coupling process depends critically on the toroidal geometry and, as such, represents a new paradigm for the spectral cascade of drift wave turbulence in toroidal systems.

An improved gyrokinetic electron and fully kinetic ion (GeFi) particle simulation scheme is presented for the investigation of linear collisionless tearing mode instability in a two-dimensional Harris current sheet under a finite guide field B G and a realistic ion-to-electron mass ratio m i /m e . Due to the removal of the rapid electron cyclotron motion while retaining the finite electron Larmor radii, wave-particle interaction, and off-diagonal components of the electron pressure tensor, the GeFi model can be used to investigate the physics of magnetic reconnection with a realistic m i /m e in a large-scale current sheet, which in general possesses wave modes ranging from Alfvén waves to lower hybrid/whistler waves, with wave frequency ω < e , where e is the electron gyrofrequency. As a necessary step of utilizing the code for magnetic reconnection, the linearized GeFi scheme is benchmarked by comparing the simulation results using a δf method against direct numerical solutions of the tearing-instability eigenmode equations, as well as those obtained analytically via asymptotic matching.

Localized electrostatic wave modes due to relativistic ion cyclotron instabilities are observed in a hybrid particle-in-cell simulation under a magnetic field with sinusoidal nonuniformity. In order to investigate the physical mechanism of the simulation results, an analytical theory, adopting a parabolic approximation around a magnetic field minimum, has been developed based on an absolute instability condition along with systematic expansion procedures. The spatial structure, growth rate and frequency of the localized wave modes predicted by the theory are found to agree well with those of simulation. In this work, we demonstrate that the instabilities can survive even when the magnetic variation is much larger than the Lorentz factor minus one. Furthermore, both the simulation and the theory show that the wave mode can exist where its frequency is smaller than the local harmonic cyclotron frequency, violating the well-known requirement for driving relativistic cyclotron instabilities.