A fully kinetic, non-local stability analysis of the Bennett equilibrium for a cylindrical plasma column is presented. The perturbations of the equilibrium distribution function constructed from the constants of motion may be divided into the adiabatic and non-adiabatic parts. The dominant trajectories of the particles are betatron orbits, and from an integration over these orbits the radial eigenmode equation is obtained. Expressing the electrostatic potential in terms of the vacuum eigenfunctions, i.e. the Bessel functions, yields a matrix dispersion relation. The wave-particle resonance in the analysis is spatially localized, owing to the betatron nature of the particle orbits. The eigenvalues of the problem are computed numerically.