On the stabilization of nonlinear cylindrical oscillations in a plasma with a current

The mathematical model of the effect of axial current in plasma on cylindrical nonrelativistic nonlinear oscillations is constructed. The result of the coordinated interaction of electromagnetic fields and particles is a nonlinear traveling wave. For its initialization, the method for constructing missing initial conditions based on solving a linear problem in the form of Fourier-Bessel integrals is proposed. Numerical simulation of a traveling wave is carried out using the scheme of the finite difference method of the second order of accuracy. It is shown that the wave velocity increases with an increase in the magnitude of the current, which contributes to the removal of energy from the initial region of localization of oscillations. For this reason, the breaking effect is realized much later in time, that is, stabilization of oscillations is observed.