[en] An expression is derived for the configurational energy E/sub c/ required to establish a guiding-center plasma with an arbitrary charge distribution rho/sub q/, which is energetically bound to a neutron star with aligned magnetic and rotational axes. Radiation processes cause the atmosphere to go to the state of minimum total energy which is consistent with both the guiding-center constraints and the stellar source of the plasma. It is argued that energy considerations require that rho/sub q/ can have only one sign along the near-equatorial and the near-polar magnetic surfaces (with opposite signs). In lieu of exact radiating dynamic solutions, the consequences of assuming this constraint hold for all magnetic surfaces are considered in the present study. It is further argued that E/sub c/ is the dominant contribution to the total energy of the stellar atmosphere E/sub T/, under the above conditions. The minimum E/sub T/ may therefore be adequately estimated by determining the solution of deltaE/sub c/=0, produced by the constraint-conserving variations deltarho/sub q/ of the charge density. A simple (''shell'') trial function for rho/sub q/, which satisfies the constraint and has several arbitrary parameters, is optimized by minimizing the corresponding E/sub c/. This ''constrained shell'' model indicates that the atmosphere will be contained within several stellar radii, will maintain a low density region directly outside the star, and will change the sign of rho/sub q/ closer to the poles that the usual force-free configuration