Concave circular arc density interfaces (CDIs) are relevant to a deformed diaphragm separating different pressure gases in a shock tunnel or an expansion tube, where it is known that the Richtmyer-Meshkov instability (RMI) limits facility performance. Considering CDIs characterized by different curvatures (kappa), numerical investigations of the RMI in both hydrodynamics (hydro) and magnetohydrodynamics (MHD) are performed. In the hydro cases, the largest curvature case appears to be the most unstable one, with the largest amounts of vorticities deposited on the CDIs. In the MHD cases, the interplay between the RMI and the magnetic field is investigated. On the one hand, the RMI can be compressed by magnetic fields. The stronger the magnetic field is, the smoother the density interface will be. The magnetic pressure alleviates pressure deviations along two sides of the CDIs, reducing baroclinic effects. Meanwhile, the magnetic tension force induces Alfven waves, which transport vorticities away from density interfaces. On the other hand, magnetic fields can be amplified by the RMI, indicating that more amplification occurs when the initial magnetic field is weak, and magnetic lines are severely distorted in such cases. Besides, the evolutions of the kinetic energy and the magnetic energy are discussed. The results indicate that there is no energy transfer between them, and the magnetic energy mainly concentrates on the MHD wave fronts. The change of the enstrophy against time demonstrates that the vorticity energy decreases when the strength of initial magnetic fields increases.