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A magnetic flux threading through magnetic atomic rings can induce topological superconductivity. It provides a novel approach to achieving low-dimensional topological superconductivity for the tradition ways require spin-orbit coupling or helical magnetic order. In this paper, we introduce a topological superconductor model by depositing a ferromagnetic atomic ring on the surface of a two-dimensional s-wave superconductor. When the moments of the magnetic atoms are perpendicular to the external magnetic field, a magnetic flux can induce topological superconductivity. Considering practical experiments, for the magnetic atomic chain breaks the inversion symmetry of the surface of the two-dimensional substrate, the Rashba spin-orbit coupling (SOC) thereby is introduced, leading to the appearance of helical magnetic order in the atomic chain. According to previous researches, this helical magnetic order ensures that the magnetic moments of the ring are perpendicular to the external magnetic field, and the patch angle of neighbor moments of the helical order is proportional to the strength of the SOC. However, the helical order or Rashba SOC may introduce topological superconductivity by them own. It is meaningful to investigate the influence of the effects of the Rashba SOC and helical magnetic order on the flux induced topological superconducting states. We find that the Rashba SOC has a disruptive effect on the existing topological state, while helical magnetic order merely shifts its transition position in the parameter space. Therefore, when selecting materials for experiment, it's advisable to choose those with a small strength of Rashba SOC.
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