The dynamics of nonlinear cylindrical Langmuir waves in an isothermal plasma, where ions form a stationary background, has been studied within the framework of hydrodynamic description. The problem has been considered in the electrostatic formulation for two-dimensional geometry. A system of differential equations describing the dynamics of electrons with finite temperature has been obtained using a partial, exact solution for the equations of hydrodynamics. In calculations, a concave temperature profile parabolic over radius associated with an electron density changing only in time has been used. In this model, the influence of initial conditions and thermal effects on the regular dynamics of excited waves and the development of hydrodynamic singularities in the electron beam have been discussed. Estimates that specify the permissible range of plasma parameters, at which either regular wave behavior is realized or the electron wave breaks down, have been obtained. It has been shown that the development of singular behavior due to the intrinsic nonlinearity can be avoided by taking into account the thermal effects and the initial rotation of the electron beam. These results may be useful for establishing the mechanisms of nonequilibrium energy/momentum transfer in plasma media with finite electron and ion temperatures. Estimations specifying the admissible range of plasma parameters have been derived.
Karimov et al. (2025) studied this question.