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In this paper, a detailed analysis for superradiant stability of the systemcomposed by a $D$-dimensional Reissner-Nordstr\"{o}m-anti-de Sitter (RN-AdS)black hole and a reflecting mirror under charged scalar perturbations arepresented in the linear regime. It is found that the stability of the system isheavily affected by the mirror radius as well as the mass of the scalarperturbation, AdS radius and the dimension of space-time. In a higherdimensional space-time, the degree of instability of the superradiant modeswill be severely weakened. Nevertheless, the degree of instability can bemagnified significantly by choosing a suitable value of the mirror radius.Remarkably, when the mirror radius is smaller than a threshold value the systembecomes stable. We also find that massive charged scalar fields cannot triggerthe instabilities in the background of $D$-dimensional asymptotically flat RNblack hole. For a given scalar charge, a small RN-AdS black hole can besuperradiantly unstable, while a large one may be always stable under chargedscalar field with or without a reflecting mirror. We also show that theseresults can be easily expounded and understood with the help of factorizedpotential analysis.

Superradiant instability of $D$-dimensional Reissner-Nordstr\"{o}m-anti-de Sitter black hole mirror system