Alfvén waves discovered by Hannes Alfvén (1942 Nature150 405) are fundamental electromagnetic oscillations in magnetized plasmas existing in the nature and laboratories. Alfvén waves play important roles in the heating, stability and transport of plasmas. The anisotropic nearly incompressible shear Alfvén wave is particularly interesting since, in realistic non-uniform plasmas, its wave spectra consist of both the regular discrete and the singular continuous components. In this Alfvén lecture, I will discuss these spectral properties and examine their significant linear and nonlinear physics implications. These discussions will be based on perspectives from my own research in both space and laboratory fusion plasmas, and will demonstrate the positive feedback and cross-fertilization between these two important sub-disciplines of plasma physics research. Some open issues of nonlinear Alfvén wave physics in burning fusion as well as magnetospheric space plasmas will also be explored.
Ion acceleration in plasmas with Alfvén waves