Alfvén waves discovered by Hannes Alfvén (1942 Nature 150 405) 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.

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The results of numerical simulation of mass transfer in semidetached non‐magnetic binaries are presented. We investigate the morphology of gaseous flows on the basis of three‐dimensional gas‐dynamical calculations of interacting binaries of different types (cataclysmic variables and low‐mass X‐ray binaries). We find that taking into account a circumbinary envelope leads to significant changes in the stream–disc morphology. In particular, the obtained steady‐state self‐consistent solutions show an absence of impact between the gas stream from the inner Lagrangian point L1 and the forming accretion disc. The stream deviates under the action of the gas of the circumbinary envelope, and does not cause the shock perturbation of the disc boundary (traditional hotspot). At the same time, the gas of the circumbinary envelope interacts with the stream and causes the formation of an extended shock wave, located on the stream edge. We discuss the implication of this model without hotspot (but with a shock wave located outside the disc) for interpretation of the observations. The comparison of synthetic light curves with observations proves the validity of the discussed gas‐dynamical model without hotspot. We have also considered the influence of the circumbinary envelope on the mass transfer rate in semidetached binaries. The obtained features of flow structure in the vicinity of L1 show that the gas of the circumbinary envelope plays an important role in the flow dynamics, and that it leads to significant (in order of magnitude) increase of the mass transfer rate. The most important contribution to this increase is from the stripping of the mass‐losing star atmosphere by interstellar gas flows. The parameters of the formed accretion disc are also given in the paper. We discuss the details of the obtained gaseous flow structure for different boundary conditions on the surface of mass‐losing star, and show that the main features of this structure in semidetached binaries are the same for different cases. The comparison of gaseous flow structure obtained in two‐ and three‐dimensional approaches is presented. We discuss the common features of the flow structures and the possible reasons for revealed differences.

A time‐dependent numerical simulation of relativistic wind interaction with interstellar medium was performed. The winds are ejected from the magnetosphere of rotation‐powered pulsars. The particle flux in the winds is isotropic while the energy flux is strongly anisotropic. Pure hydrodynamical winds and magnetized winds with magnetization in the range 3 × 10−3–10−1 were modelled. The numerical solutions reproduce the most spectacular features observed in the central part of the plerions: toroidal structure and jet‐like features. A comparison of the solutions with the observations confirms that magnetization of the wind from a pulsar in the Crab nebula is of the order of 3 × 10−3. The plasma flow in the nebula is variable. The variability has different time‐scales. Non‐periodic 2–3 yr scale variations are superimposed on the quasi‐periodical variations with period ∼40 yr. An increase of the wind's magnetization results in a decrease of the size of the synchrotron nebula. The size of the Vela nebula can be reproduced provided that the wind from Vela is more highly magnetized then the wind from Crab. Nevertheless, the magnetization of the wind from the Vela pulsar is most likely below 0.1.