A new reductive perturbation formalism for ion acoustic cnoidal waves

Olivier, Carel P.; Verheest, Frank

doi:10.1017/s0022377822000964

Cited by 4 publications

(3 citation statements)

References 20 publications

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“…If one looks at the various treatments of nonlinear periodic structures in acoustic wave studies, one reaches the surprising conclusion that nobody seemed to have worried about the excess or loss of densities, until very recently the problem was realized and treated in three different papers. [1][2][3] These three papers contain references to the many papers where the analysis is not consistent from a physics point of view. As detailed comments were given earlier, the deficient papers will not be cited again here.…”

Section: Introductionmentioning

confidence: 99%

“…In the three recent papers, [1][2][3] the same cold ion model was used. The relative popularity of the cold ion model, not only in our earlier Phys.…”

Section: Introductionmentioning

confidence: 99%

“…As to the hot electron distributions that provide the pressure, the other prerequisite to sustain the waves, the three recent papers mentioned opted to use a Maxwellian model but treated the problem by various methods: reductive perturbation theory (RPT) 1 and two Sagdeev pseudopotential analyses (SPA). One of the latter 2 uses the Lambert W function 4 to obtain an analytical solution, while the other 3 follows a more conventional Sagdeev analysis 5 that allows the inclusion of other conservation laws than just the species' mass or charge densities and the possibility of extending the hot electron description.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear periodic ion-acoustic waves in nonthermal plasmas

Verheest,

Olivier

2024

Physics of Plasmas

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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.

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Section: Introductionmentioning

confidence: 99%

“…In the three recent papers, [1][2][3] the same cold ion model was used. The relative popularity of the cold ion model, not only in our earlier Phys.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear periodic ion-acoustic waves in nonthermal plasmas

Verheest,

Olivier

2024

Physics of Plasmas

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Comment on “Arbitrary amplitude ion-acoustic supersolitons in negative ion plasmas with two-temperature superthermal electrons” [Phys. Plasmas 29, 092101 (2022)]

2023

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In a recent paper, “Arbitrary amplitude ion-acoustic supersolitons in negative ion plasmas with two-temperature superthermal electrons” [Phys. Plasmas 29, 092101 (2022)], Kumar and Mishra deal with the study of ion-acoustic solitary and supersolitary waves in a four-component plasma consisting of positive ions and negative ions along with two temperature superthermal electrons. Unfortunately, the reported results are incorrect.

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Sagdeev pseudopotential analysis of nonlinear periodic ion-acoustic plasma waves

Verheest,

Olivier

2023

Physics of Plasmas

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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.

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A new reductive perturbation formalism for ion acoustic cnoidal waves

Cited by 4 publications

References 20 publications

Nonlinear periodic ion-acoustic waves in nonthermal plasmas

Nonlinear periodic ion-acoustic waves in nonthermal plasmas

Comment on “Arbitrary amplitude ion-acoustic supersolitons in negative ion plasmas with two-temperature superthermal electrons” [Phys. Plasmas 29, 092101 (2022)]

Sagdeev pseudopotential analysis of nonlinear periodic ion-acoustic plasma waves

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