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A general approach is established to examine confinement properties of both non-neutral and neutral axially symmetric plasmas. In this approach, problems are reduced to finding total minimum energy states under the conservation of total angular momentum and total number of particles. First, the well-known result of a non-neutral plasma in a cylindrical system is reproduced for checking the approach. Second, the approach is applied to analysis of confinement properties of tokamak plasmas with a transport barrier and it is shown that the tokamak with an internal transport barrier is in the minimum energy state.