In studies of interaction of matter with laser fields of extreme intensity there are two limiting cases of a multi-beam setup maximizing either the electric field or the magnetic field. In this work attention is paid to the optimal configuration of laser beams in the form of an m-dipole wave, which maximizes the magnetic field. We consider in such highly inhomogeneous fields the advantages and specific features of laser-matter interaction, which stem from individual particle trajectories that are strongly affected by gamma photon emission. It is shown that in this field mode qualitatively different scenarios of particle dynamics take place in comparison with the mode that maximizes the electric field. A detailed map of possible regimes of particle motion (ponderomotive trapping, normal radiative trapping, radial and axial anomalous radiative trapping), as well as angular and energy distributions of particles and gamma photons, is obtained in a wide range of laser powers up to 300 PW and reveals signatures of radiation losses experimentally detectable even with subpetawatt lasers.