Here we present three-dimensional MHD models for the Parker instability in a thick magnetized disk, including the presence of a spiral arm. The $B$-field is assumed parallel to the arm, and the model results are applied to the optical segment of the Carina-Sagittarius arm. The characteristic features of the undular and interchange modes are clearly apparent in the simulations. The undular mode creates large gas concentrations distributed along the arm. This results in a clear arm/inter-arm difference: the instability triggers the formation of large interstellar clouds inside the arms, but generates only small structures with slight density enhancements in the inter-arm regions. The resulting clouds are distributed in an antisymmetric way with respect to the midplane, creating an azimuthal corrugation along the arm. For conditions similar to those of the optical segment of the Carina-Sagittarius arm, it has a wavelength of about 2.4 kpc. This structuring can explain the origin of both HI superclouds and the azimuthal corrugations in spiral arms. The wavelength matches the corrugation length derived with the young stellar groups located in the optical segment of the Carina-Sagittarius arm. Keywords: Galaxy: kinematics and dynamics -- Galaxy: structure -- Instabilities -- ISM: clouds -- ISM: magnetic fields -- ISM: structure -- MHD
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