  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 formation
and development of cosmical electrodynamics. A distinctive feature of Alfv\'en
waves is that at each point in space the group velocity vector and the external
magnetic field vector are collinear to each other. As a result, Alfv\'en waves
can carry momentum, energy, and information over long distances. We briefly
describe two Alfv\'en resonators, one of which is formed in the ionosphere, and
the second presumably exists in the Earth's radiation belt. The existence of an
ionospheric resonator is justified theoretically and confirmed by numerous
observations. The second resonator is located between reflection points located
high above the Earth symmetrically with respect to the plane of the geomagnetic
equator. Keywords: Alfv\'en velocity, dispersion law, group velocity, geometric
optics, heavy ions.
