  The orbital polarization of twisted electrons carrying an intrinsic orbital
angular momentum is not influenced by field perturbations in arbitrary magnetic
fields. This property means an existence of the Siberian snake-like behavior
for an orbital polarization of a beam of twisted electrons in cyclotrons with
the main magnetic field and magnetic focusing. As a result, the acceleration of
twisted electron beams in cyclotrons necessary for their applications in
high-energy-physics experiments considerably simplifies.
