On One Widely-Spread Inaccuracy and Its Elimination in the Theories of Nonlinear Electrostatic Waves in Plasma Based on the Sagdeev’s Pseudopotential Approach

A Sagdeev pseudopotential analysis is developed for the propagation of nonlinear periodic ion-acoustic waves in a plasma comprising cold fluid ions and Boltzmann electrons. To achieve a mathematically and physically consistent description, three essential requirements have to be obeyed: There is charge flux and mass conservation per cycle for both the species, the solutions reduce for very small amplitudes to linear waves, and the nonlinear periodic structures are generated by a perturbation of the undisturbed equilibrium. This is needed because many treatments in the literature of similar problems give inconsistent results, failing on one or more of the stated conditions, whether a reductive perturbation or a pseudopotential analysis is used. Once the Sagdeev pseudopotential is established, a detailed numerical analysis and a variety of graphical representations indicate that the periodic nonlinear structures are mostly subacoustic, in contrast to the better known supersonic solitons for the same or related plasma compositions. For a fixed propagation speed, it is shown that the wavelength of the solutions increases with amplitude.

Sagdeev pseudopotential analysis of nonlinear periodic ion-acoustic plasma waves

Verheest,

Olivier

2023

Nonlinear periodic ion-acoustic waves in nonthermal plasmas

Verheest,

Olivier

2024

A Sagdeev pseudopotential analysis is developed for the propagation of nonlinear periodic ion-acoustic waves in a plasma comprising cold fluid ions and various models of nonthermal electron descriptions. In plasma nonlinear wave studies, whether addressing solitary or periodic modes, the more common nonthermal distributions are the Cairns, kappa, and Tsallis models. A mathematically and physically consistent description incorporates three evident properties: there is conservation per cycle of ion and electron densities in addition to ion flux, the solutions reduce for very small amplitudes to linear waves, and the nonlinear periodic structures are generated by a perturbation of the undisturbed equilibrium. After establishing the corresponding general analytical methodology, a numerical analysis is given, with illustrative graphs, for the nonthermal Cairns, superthermal kappa, and nonextensive Tsallis distributions.

Periodic nonlinear dust-acoustic waves in multispecies dusty plasmas

Verheest,

Olivier

2024

A pseudopotential analysis is presented for the propagation of nonlinear periodic dust-acoustic waves in a dusty plasma comprising cold negative dust, Boltzmann electrons, and Boltzmann or Cairns nonthermal positive ions, extending thus earlier treatments for ion-acoustic waves in electron–proton plasmas. The dusty plasma model where both electrons and ions are Boltzmann does not admit solitons, but works for nonlinear periodic waves. For consistency in the periodic case, two properties are required: conservation per cycle of species densities and that for very small amplitudes the waves resemble linear waves. The first property has to be imposed through a global perturbation of the undisturbed equilibrium, whereas the second property follows naturally from the formalism. After obtaining the general analytical methodology, a numerical analysis is discussed and illustrated with graphs for the electrostatic potential profile, the Sagdeev pseudopotential, the wave electric field, and the three different species densities, first for the Boltzmann and thereafter for the Cairns ions.