Nonlinear Dynamics of Cylindrical Waves in Isentropic Plasma

Based on the hydrodynamic description, the dynamics of nonlinear cylindrical waves in an isentropic plasma are investigated. The problem is considered in an electrostatic formulation for a two-dimensional plasma medium where ions form a stationary background. Proceeding from the particular, exact solution of hydrodynamic equations, we obtain the system of differential equations which describes the electron’s dynamics, taking into account the finite temperature of electrons. Moreover, we find the conditions when this system is reduced to the generalized Ermakov–Pinney equation which was used for analyzing electron dynamics. In the present calculations, a parabolic-in-radius temperature profile was used, associated with an electron density varying only with time. In the framework of the model that worked out, the influence of initial conditions and thermal effects on the regular and singular dynamics of excited waves are discussed. It is shown that the development of singular behavior due to intrinsic nonlinearity is avoided by taking into account thermal effects and the initial rotation of the electron flow.