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In this study, a detailed investigation of the problem of sheath is presented using the fluid model in a magnetized three‐component dusty plasma system comprising positive ions, dust grains with variable charge and q‐non‐extensive electrons (i.e., the electrons evolve far away from their Maxwellian thermodynamic equilibrium [q = 1]). The effects of q‐non‐extensivity parameter on the plasma sheath parameters are studied numerically. A significant change is observed in the quantities characterizing the sheath with the presence of the super‐extensive electrons (q < 1) and sub‐extensive electrons (q > 1). In addition, based on the orbital motion limited theory, by taking various forces acting on the dust particle into consideration, the dynamics of the dust located within the sheath, that is, the dust grain charging inside the sheath, is examined under different values of q. It is found that the q‐non‐extensivity has affected significantly the dynamics and the charging process of the dust grains in the sheath.

We have investigated the structure of a magnetized sheath of dusty plasma in the presence of secondary electrons emitted by the micro-size dust particles in the context of the Tsallis statistics. The fluid model is used to analyze numerically the effects of the nonextensivity parameter q on the emission of secondary electrons and therefore, on the sheath structure as well as the dust dynamics. The results show that the secondary emission yield increases with the decrease of the parameter of nonextensivity q and consequently, the dust charge becomes less negative with its range of values playing a primordial role in the secondary electron emission rate. The quantities characterizing the sheath are significantly affected by the secondary electron emission (SEE) from the dust. It is seen that as the SEE rises at a given value of q(q&lt;0.91), the sheath potential decreases as well as its absolute value at the wall. In addition, the dynamics of the dust particles is also affected by the emission of secondary electrons.