Symmetric and Anti-Symmetric Damping Modes of Trivelpiece–Gould Waves in Weakly and Completely Ionized Plasma Waveguides

The collision effects on the low-frequency ion-acoustic Trivelpiece–Gould wave are investigated in weakly and completely ionized plasma waveguides by using the normal mode analysis. In weakly ionized plasma waveguides, it is found that the dependence of the harmonic mode on the absolute value of the scaled damping rate shows the opposite tendency for large and small radii of the cylindrical waveguide. It is also is found that the scaled damping rates for both weakly and completely ionized plasma waveguides decrease with an increase of the electron temperature. It is interesting to note that the scaled damping rate for weakly ionized plasma waveguides shows anti-symmetric behavior when the Trivelpiece–Gould wave propagates in the negative-z direction. However, it is found that the scaled damping rate for completely ionized plasma waveguides shows the symmetric behavior when the Trivelpiece–Gould wave propagates in the negative-z direction.

Spectral Features of Systems With Chaotic Dynamics

Using the Lorentz model and Hamiltonian systems without dissipation as an example, spectral methods for analyzing the dynamics of systems with chaotic behavior are considered. The insufficiency of the traditional approach to the study of perturbation dynamics based on an analysis of the roots of the classical spectral equation is discussed. It is proposed to study nonlinear systems using the method of constructing spectral equations with different eigenvalues, which allows one to take into account the randomness and multiplicity of states. The spectral features of instability and chaos for systems without dissipation are shown by the example of short-wave perturbations of a flow of a weakly ionized plasma gas.