On modeling of nonrelativistic cylindrical oscillations in plasma

In order to study the nonrelativistic cylindrical oscillations in plasma, an initial boundary value problem for a system of nonlinear partial differential equations is formulated. Approximate solutions to this problem are constructed on the basis of a finite-difference method and the numerical analytic perturbation techniques. It is found that the destruction of plasma oscillations is qualitatively similar to the plasma wakefield destruction. The asymptotic lower and upper estimates obtained for the time instant of oscillation destruction are in good agreement with the well-known results.