  The global electrostatic mode in pair-ion plasmas is discussed for cylindric
geometry and for a radially inhomogeneous equilibrium density. In the case of a
Gaussian radial density profile, exact analytical eigen solutions are found in
terms of the Kummer confluent hypergeometric functions. The mode is identified
as a convective cell propagating in the poloidal and axial direction, having at
the same time a standing wave structure in the radial direction.
