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Magnetized plasma studies are necessary for many applied studies including laser-driven inertial fusion, modeling astrophysical relevant phenomena, as well as innovative industrial and medical applications. An interesting method of generating highly magnetized plasma can be based on interaction of a laser with spiral-shaped cavity (snail-like) targets. The target shaped in this way can represent a central area of a spherical pellet that is not irradiated radially, but through an entrance hole allowing the laser beam to almost impact its inner surface tangentially [15]. In the reported experiment, snail targets of various diameters were irradiated by linearly or circularly polarized radiation of the PALS iodine laser delivering ~500 J, 350-ps and 1.315-μm pulses on targets. A 3-frame complex interferometry demonstrated that plasma is generated on the entire inside and outside surface of the snail-target, starting from the very beginning of the laser-target interaction. The time resolved records of the magnetic field and the electron density distribution inside and outside the snail-target characterize the changes in the structure of the magnetized plasma. Inside the target, the magnetic field survives long after the termination of the laser-matter interaction, namely longer than 10 ns. Compared to a circularly polarized laser pulse, the irradiation of targets with a p-polarized beam increases both the emission of hot electrons and the intensity of the magnetic field. The emission of hot electrons is not isotropic, and their energy distribution cannot be characterized by a single temperature.