  Vector displacements expressed in spherical coordinates are proposed. They
correspond to electromagnetic fields in vacuum that globally rotate about an
axis and display many circular patterns on the surface of a sphere. The fields
basically satisfy the set of Maxwell's equations, but enjoy further properties
that allow them to be suitably interpreted as solutions of a plasma model that
combines electrodynamics with the Euler's equation for fluids. Connection with
magnetohydrodynamics can also be established. The fields are extended with
continuity outside the sphere in a very peculiar manner. In order to avoid
peripheral velocities of arbitrary magnitude, as it may happen for a rigid
rotating body, they are organized to form successive encapsulated shells, with
substructures recalling successive ball-bearing assemblies. A recipe for the
construction of these solutions is provided by playing with the eigenfunctions
of the vector Laplace operator. Some applications relative to astronomy are
finally discussed.
