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The paper is dedicated to the anniversary of the discovery of Alfv\'en waves.The concept of Alfv\'en waves has played an outstanding role in the formationand development of cosmical electrodynamics. A distinctive feature of Alfv\'enwaves is that at each point in space the group velocity vector and the externalmagnetic field vector are collinear to each other. As a result, Alfv\'en wavescan carry momentum, energy, and information over long distances. We brieflydescribe two Alfv\'en resonators, one of which is formed in the ionosphere, andthe second presumably exists in the Earth's radiation belt. The existence of anionospheric resonator is justified theoretically and confirmed by numerousobservations. The second resonator is located between reflection points locatedhigh above the Earth symmetrically with respect to the plane of the geomagneticequator. Keywords: Alfv\'en velocity, dispersion law, group velocity, geometricoptics, heavy ions.

Alfv\'en waves: To the 80th anniversary of discovery