Oblique propagation of solitary electrostatic waves in magnetized plasmas with cold ions and nonthermal electrons

Oblique propagation of large amplitude electrostatic waves and solitary structures is investigated in magnetized plasmas, comprising cold fluid ions and Cairns nonthermally distributed electrons, by using a Sagdeev pseudopotential formalism. To perform the analysis, quasineutrality is assumed, so that in normalized variables the electrostatic potential and the occurrence of solitary structures are governed by three parameters: the Mach number M, the typical Cairns parameter beta, and the angle theta between the directions of propagation and the static magnetic field. Below a critical beta, only positive compressive solitons are possible, and their amplitudes increase with increasing beta, M, and theta. Above the critical b, there is coexistence between negative rarefactive and positive compressive solitons, and the range of negative solitons, at increasing M, ends upon encountering a double layer or a singularity. The double layer amplitudes (in absolute value) increase with beta but are independent of theta. Roots of the Sagdeev pseudopotential beyond the double layer are not accessible from the undisturbed conditions, because of an intervening singularity where the pseudopotential becomes infinite. Recent claims of finding supersolitons beyond a double layer appear to be based on a misinterpretation of the nature of the singularity

Head-on collisions of electrostatic solitons in nonthermal plasmas

In contrast to overtaking interactions, head-on collisions between two electrostatic solitons can only be dealt with by an approximate method, which limits the range of validity but offers valuable insights. Treatments in the plasma physics literature all use assumptions in the stretching of space and time and in the expansion of the dependent variables that are seldom if ever discussed. All models force a separability to lowest order, corresponding to two linear waves with opposite but equally large velocities. A systematic exposition of the underlying hypotheses is illustrated by considering a plasma composed of cold ions and nonthermal electrons. This is general enough to yield critical compositions that lead to modified rather than standard Korteweg-de Vries equations, an aspect not discussed so far. The nonlinear evolution equations for both solitons and their phase shifts due to the collision are established. A Korteweg-de Vries description is the generic conclusion, except when the plasma composition is critical, rendering the nonlinearity in the evolution equations cubic, with concomitant repercussions on the phase shifts. In the latter case, the solitons can have either polarity, so that combinations of negative and positive solitons can occur, contrary to the generic case, where both solitons necessarily have the same polarity

Electrostatic flat-top solitons near double layers and triple root structures in multispecies plasmas : how realistic are they?

Electrostatic flat-top solitons are a new acoustic-type nonlinear mode and found to be a generic feature accompanying the occurrence of double layers and/or triple root structures, in multispecies plasmas admitting the latter. Their existence domains can be parameterized by the difference between their velocities and the double layer or triple root velocities, but these velocity differences turn out to be extremely small, of the order 10 5 or less. The onset of their flat top character in the electrostatic potential is clearly seen in the corresponding electric field or charge density profiles. However, even at the limit of the numerical accuracy for vanishing velocity differences, their profiles are still soliton-like, very unlike those of double layers or triple root structures. So although the Sagdeev potential varies continuously as the structure velocity approaches that of the double layer or triple root structure, the character of the nonlinear modes changes in a discontinuous manner. For sufficiently wide flat-top solitons, the electric field signature looks very much like two unipolar signals with opposite polarities, where unipolar electric fields typically characterize double layers or triple root structures. We are not aware of flat-top solitons having been reported to date, and their extremely limited existence range raises the question of whether they may be observable at all, unless helped by a fortunate stroke of serendipity. This topic requires suitable numerical simulations to ascertain their stability and interaction properties

Stringent limitations on reductive perturbation studies of nonplanar acoustic solitons in plasmas

More than fifty years ago, the Korteweg-de Vries equation was shown to describe not only solitary surface waves on shallow water, but also nonlinear ion-acoustic waves. Because of the algorithmic ease of using reductive perturbation theory, intensive research followed on a wide range of wave types. Soon, the formalism was extended to nonplanar modes by introducing a stretching designed to accommodate spherically and cylindrically symmetric ion-acoustic waves. Over the last two decades many authors followed this approach, but almost all have ignored the severe restrictions in parameter space imposed by the Ansatz. In addition, for other steps in the formalism, the justification is often not spelled out, leading to effects that are physically undesirable or ambiguous. Hence, there is a need to critically assess this approach to nonplanar modes and to use it with the utmost care, respecting the restrictions on its validity. Only inward propagation may be meaningfully studied and respect for weak nonlinearities of at most 1/10 implies that one cannot get closer to the axis or centre of symmetry than about 30 Debye lengths. Thus, one is in a regime where the modes are quasi-planar and not particularly interesting. Most papers disregard these constraints and hence reach questionable conclusions

Dust-ion-acoustic supersolitons in dusty plasmas with nonthermal electrons

Supersolitons are a recent addition to the literature on large-amplitude solitary waves in multispecies plasmas. They are distinguished from the usual solitons by their associated electric field profiles which are inherently distinct from traditional bipolar structures. In this paper, dust-ion-acoustic modes in a dusty plasma with stationary negative dust, cold fluid protons, and nonthermal electrons are investigated through a Sagdeev pseudopotential approach to see where supersolitons fit between ranges of ordinary solitons and double layers, as supersolitons always have finite amplitudes. They therefore cannot be described by reductive perturbation treatments, which rely on a weak amplitude assumption. A systematic methodology and discussion is given to distinguish the existence domains in solitary wave speed and amplitude for the different solitons, supersolitons and double layers, in terms of compositional parameters for the plasma model under consideration. DOI: 10.1103/PhysRevE.87.04310