Frank Verheest

Waves and instabilities in dusty space plasmas

Astrophysical dust occurs in many circumstances, like interstellar and circumstellar media, and between and around planets and comets. Typical Solar System applications include planetary rings, asteroid zones, cometary comae and tails, and regions of Earths lower magnetosphere. Dust grains immersed in ambient plasmas are electrically charged by various processes and interact with electromagnetic fields. Intriguing phenomena observed in the 1980s by Voyager cameras and attributed to charged dust are radial spokes in the B-ring and braids in the F-ring of Saturn. Collective effects become important when the dust intergrain distance is smaller than the plasma Debye length, and start from observations that micron-sized dust grains can have very high negative charges and in proportion even higher masses. Characteristic dust frequencies are considerably smaller than corresponding electron or ion quantities, giving rise to new low-frequency eigenmodes, which could explain some of the low-frequency noise in space and astrophysical plasmas. Repelling electrostatic forces between charged dust grains prevent planetary rings from collapsing to very thin sheets, and oscillations in transverse ring thickness give rise to resonant phenomena, held responsible for gaps in the rings of Jupiter and Saturn. Further features are connected with fluctuating dust charges, which imply highly nontrivial source and/or sink terms in the description, and those in turn lead to new electrostatic and electromagnetic instabilities. Many different papers are reviewed which discuss waves and instabilities in dusty space plasmas, both with fixed and variable dust charges, at the linear level and, at the nonlinear level, involving double layers, solitons, vortices and other waves. These studies are at present far ahead of what observations can corroborate, a situation not likely to change soon due to the paucity of coming solar system missions concerned with planetary or cometary phenomena.

Nonlinear dust-acoustic waves in multispecies dusty plasmas

Abstract A study is made of nonlinear dust-acoustic waves in a dusty plasma, which consists of any number of cold negatively charged dust grain species, in addition to the presence of the more usual isothermal hot and cold electrons and isothermal positive ions. The Sagdeev potential is obtained in general, together with limits on rarefactive solutions for the dust-acoustic solitons. Weak dust-acoustic solitons can be described by a modified Korteweg-de Vries equation. An application is given to a dusty plasma with one kind of negative grains, in the presence of protons, all electrons having been accreted unto the dust grains. Such dusty plasmas can support rarefactive supersonic solitons, in contrast to the usual ion-acoustic solitons which are compressive. Compressive weak dust-acoustic solitons are less likely to occur. When some streaming is included, one finds a slight decrease in the amplitude of the solitons.

Large amplitude dust-acoustic solitary waves and double layers in nonthermal plasmas

A systematic investigation has been made of large amplitude dust-acoustic solitary waves in plasmas consisting of negatively charged cold dust in the presence of either nonthermally distributed ions or electrons, with a particular emphasis on the delimitation of the compositional parameter space where such structures can be generated. The occurrence of negative electrostatic potential solitary waves is for higher Mach numbers limited by infinite dust compression. On the positive potential side solitary waves are possible until double layers are encountered, provided two distinct aspects of the dusty plasma compositions are fulfilled: Sufficient nonthermality in the ions and sufficient negative charge on the dust, the electron presence not really being required. There is then a region in parameter space where both negative and positive solitary structures can coexist. When electrons are the nonthermal plasma constituent, only negative potential waves are possible.

Ion- and electron-acoustic solitons in two-electron temperature space plasmas

Properties of ion- and electron-acoustic solitons are investigated in an unmagnetized multicomponent plasma system consisting of cold and hot electrons and hot ions using the Sagdeev pseudopotential technique. The analysis is based on fluid equations and the Poisson equation. Solitary wave solutions are found when the Mach numbers exceed some critical values. The critical Mach numbers for the ion-acoustic solitons are found to be smaller than those for electron-acoustic solitons for a given set of plasma parameters. The critical Mach numbers of ion-acoustic solitons increase with the increase of hot electron temperature and the decrease of cold electron density. On the other hand, the critical Mach numbers of electron-acoustic solitons increase with the increase of the cold electron density as well as the hot electron temperature. The ion-acoustic solitons have positive potentials for the parameters considered. However, the electron-acoustic solitons have positive or negative potentials depending whether ...

Nonlinear perpendicular propagation of ordinary mode electromagnetic wave packets in pair plasmas and electron-positron-ion plasmas

The nonlinear amplitude modulation of electromagnetic waves propagating in pair plasmas, e.g., electron-positron or fullerene pair-ion plasmas, as well as three-component pair plasmas, e.g., electron-positron-ion plasmas or doped (dusty) fullerene pair-ion plasmas, assuming wave propagation in a direction perpendicular to the ambient magnetic field, obeying the ordinary (O-) mode dispersion characteristics. Adopting a multiple scales (reductive perturbation) technique, a nonlinear Schrodinger-type equation is shown to govern the modulated amplitude of the magnetic field (perturbation). The conditions for modulation instability are investigated, in terms of relevant parameters. It is shown that localized envelope modes (envelope solitons) occur, of the bright- (dark-) type envelope solitons, i.e., envelope pulses (holes, respectively), for frequencies below (above) an explicit threshold. Long wavelength waves with frequency near the effective pair plasma frequency are therefore unstable, and may evolve int...

Potential hill electron-acoustic solitons and double layers in plasmas with two electron species

In the description of (high-frequency) electron-acoustic solitons in a plasma consisting of positive ions, cool electrons, and hot electrons, the dynamics of the ions plays no essential role and can be eliminated from the treatment, the ions merely providing a constant positive background. It is widely believed that in such a plasma only potential dip solitary waves can be generated. In a potential dip the cooler electrons are compressed and the hotter electrons rarefied, both being driven towards their sonic points, the cooler ones from above, the hotter ones from below. This transonic feature gives rise to the solitary wave. However, it is shown that the restriction to potential dip solitons is due to the neglect of the inertia of the hot electrons, implicitly or explicitly assumed by most authors. If hot electron inertia is retained, there exists a parameter range where potential hill solitary waves are formed, with both electron species being driven away from their sonic points. This has important consequences for the reinterpretation of several astrophysical phenomena involving two-electron plasmas.

Generation mechanism for electron acoustic solitary waves

Nonlinear electron acoustic solitary waves (EASWs) are studied in a collisionless and unmagnetized plasma consisting of cold background electrons, cold beam electrons, and two different temperature ion species. Using pseudopotential analysis, the properties of arbitrary amplitude EASWs are investigated. The present model supports compressive as well as rarefactive electron acoustic solitary structures. Furthermore, there is an interesting possibility of the coexistence of compressive and rarefactive solitary structures in a specific plasma parameter range. The application of our results in interpreting the salient features of the broadband electrostatic noise in the plasma sheet boundary layer is discussed.

INFLUENCE OF DUST MASS DISTRIBUTIONS ON GENERALIZED JEANS-BUNEMAN INSTABILITIES IN DUSTY PLASMAS

Abstract The linear dispersion law is given for a generalized Jeans-Buneman instability in the presence of a dust mass distribution. It is shown that this instability is easier to evoke when a reasonable power law mass distribution for the dust grains is assumed than for the mono-sized dust case. For Boltzmann distributed ions and electrons the dust-acoustic mode and the unstable Jeans mode are modified due to the self-gravitation and mass distribution. The frequency of the dust-acoustic mode is increased. For long wavelengths, a new stable mode occurs, due only to the dust mass distribution. The growth rate of the Jeans instability is increased, and the mode is extended beyond the usual wavelength domain. For high values of k a new instability arises, which is called the dust distribution instability.

Existence of bulk acoustic modes in pair plasmas

In view of applications to electron-positron and fullerene pair plasmas, a thorough discussion is given of the dispersion of linear electrostatic waves, before finding the parameter ranges in which stationary nonlinear electrostatic modes can exist, when there is a thermodynamic asymmetry between both constituents. Arguments for such an asymmetry can be found in the observed dispersion in fullerene pair plasma experiments, but point to small asymmetries. The existence of solitary modes is first discussed in general terms for various polytropic pressure-density relations, showing that the solitons are always compressive in both pair components. For large thermal asymmetries, there is at most a doubling of the densities, but small asymmetries lead to weakly nonlinear amplitudes, described by familiar Korteweg-de Vries solitons. Observations of an intermediate wave in the theoretical gap between the acoustic and Langmuir branches of the linear dispersion diagram might be accounted for, at least partially, by a train of weak solitons, as the difference between weak solitary modes and linear harmonic waves is rather difficult to ascertain experimentally.

Gas-dynamic description of electrostatic solitons

The nonlinear propagation of electrostatic solitary structures in unmagnetized multispecies plasmas is studied in the wave frame, where they are stationary. via the recently developed MeKenzie approach as an alternative to the more usual Saagdeev pseudo-potential method. This way of looking at the problem brings out the gas-dynamic aspects, which then allow a straightforward characterization of the solitary wave possibilities in terms of the species own sonic points and of the global charge neutral points. A qualitative discussion of ion-. dust- and electron-acoustic solitary waves is given in terms of these concepts and the results are contrasted with those obtained by other methods. Ion-acoustic solitons can be shown to always be compressive. without invoking simplifying assumptions such as cold ions or Boltzmann electrons. Beam-plasmas can also be studied, as in the electron-acoustic solitary wave model for the spiky structures of the broadband electrostatic noise observed in the auroral regions of the Earths magnetosphere. Such solitons always show a potential dip.