Dynamics of shear Alfvén waves and energetic particles are crucial to the performance of burning fusion plasmas. This article reviews linear as well as nonlinear physics of shear Alfvén waves and their self-consistent interaction with energetic particles in tokamak fusion devices. More specifically, the review on the linear physics deals with wave spectral properties and collective excitations by energetic particles via wave-particle resonances. The nonlinear physics deals with nonlinear wave-wave interactions as well as nonlinear wave-energetic particle interactions. Both linear as well as nonlinear physics demonstrate the qualitatively important roles played by realistic equilibrium nonuniformities, magnetic field geometries, and the specific radial mode structures in determining the instability evolution, saturation, and, ultimately, energetic-particle transport. These topics are presented within a single unified theoretical framework, where experimental observations and numerical simulation results are referred to elucidate concepts and physics processes.

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A theory of long‐period (Pc 3 to Pc 5) magnetic pulsations is presented based on the idea of a steady state oscillation of a resonant local field line that is excited by a monochromatic surface wave at the magnetosphere. A coupled wave equation between the shear Alfvén wave representing the field line oscillation and the surface wave is derived and solved for the dipole coordinates. The theory gives the frequency, the sense of polarizations, orientation angle of the major axis, and the ellipticity as a function of magnetospheric parameters. It also clarifies some of the contradicting ideas and observations in relation to the sense of polarization and excitation mechanism. At lower latitude it is shown that the orientation angle rather than the sense of rotation is a more critical parameter in finding the direction of wave propagation in the azimuthal coordinate and hence in finding the evidence of wave excitation at the magnetospheric surface by the solar wind.