Cosmic rays should obviously generate cascades of product particles while propagating in space as a result of interactions with fields, radiation and matter. Such phenomena, referred to cosmic-ray ensembles (CRE), are expected to differ in shapes, sizes and constituents, and thus became a key point of the Cosmic-Ray Extremely Distributed Observatory (CREDO) Collaboration scientific program. The research dedicated to comprehensive studies of CRE requires an alternative approach to the detection of cosmic rays, taking into account their spatial and/or temporal correlations on the global scale. However, a potential observation of at least parts of CRE at Earth could make a valuable contribution to the up-to-date cosmic ray astrophysics, even though it poses a technical challenge. One of the most common scenarios of CRE formation is the synchrotron radiation of charged particles propagating in omnipresent magnetic fields. We present the updated results of CRE simulations for this case, discussing the physics conditions favourable for the observation of such particle cascades, as well as practical perspectives of this research direction.