  Advanced tokamak scenarios often feature equilibriums with zero and reversed
magnetic shear. To isolate and investigate their impacts on the resistive wall
mode (RWM) instability analytically, we construct a series of cylindrical
limiter equilibriums with reversed magnetic shear in the core and zero magnetic
shear towards plasma edge, as a prototype of the configurations in advanced
tokamak scenarios. Uniform plasma pressure is assumed, so that we can focus our
analysis on the current-driven RWMs. Based on the reduced ideal MHD equations,
analytical solutions for the $n=1$ resistive wall mode are obtained, which
indicate that increasing the reversal of magnetic shear in the core region
enhances the RWM instability, whereas the widened region of zero shear near
edge leads to lower growth rate of RWM, except when the $q$ value with zero
magnetic shear approaches rational values. On the other hand, enhanced positive
shear at plasma edge is found to be stabilizing on RWM. NIMROD calculation
results confirm these analytical findings.
