Stability of Vlasov equilibria. Part 2. One non-ignorable co-ordinate

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Abstract
The solution of the linearized Vlasov equation is given for an arbitrary equilibrium Hamiltonian in which there is only one non-ignorable co-ordinate. The solution written in terms of integrals with respect to time which only extend over the bounce period of an equilibrium orbit in its equivalent one-dimensional potential. A closed-form solution and a solution based on a Fourier expansion are given. Explicit formulae are presented for Cartesian and cylindrical co-ordinates.