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On the Vlasov-Poisson system of equations for an inhomogeneous cylindrical plasma

The formal solution of the linearized Vlasov-Poisson system of equations is carried out for an inhomogeneous strongly magnetized plasma column. The system considered is closely related to several experiments in magnetically confined cylindrical plasmas. A generalization of the Fourier-Laplace method of solution is presented using expansion in the appropriate set of orthonormal functions to handle the boundary value problem in finite systems. The Fourier-Bessel components of the dielectric constant epsilon /sub //m/ll '(k, omega ) for the cylindrical inhomogeneous plasma and a matrix dispersion relation are derived to study the propagation of waves in the bounded system. In the case of neutral plasmas in equilibrium, the problem of finding the roots of the dispersion relation is equivalent to solving an eigenvalue equation. The method is applied to study a typical case in a Q-machine.