By combining the linear theory and numerical simulations, we study the response of a radially bounded axisymmetric plasma to relativistic charged particle beams in a wide range of plasma densities. We present analytical expressions for the magnetic field generated in the dense plasma, prove vanishing of the wakefield potential beyond the trajectory of the outermost plasma electron, and follow the wakefield potential change as the plasma density decreases. At high plasma densities, wavefronts of

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... electron density and radial electric field are distorted because of beam charge and current neutralization, while wavefronts of wakefield potential and longitudinal electric field are not. At plasma densities lower than or of the order of beam density, multiple electron flows develop in and outside the plasma, resulting in nonzero wakefield potential around the plasma column.