R. L. Mace

Comment on “Mathematical and physical aspects of Kappa velocity distribution” [Phys. Plasmas 14, 110702 (2007)]

A recent paper [L.-N. Hau and W.-Z. Fu, Phys. Plasmas 14, 110702 (2007)] deals with certain mathematical and physical properties of the kappa distribution. We comment on the authors’ use of a form of distribution function that is different from the “standard” form of the kappa distribution, and hence their results, inter alia for an expansion of the distribution function and for the associated number density in an electrostatic potential, do not fully reflect the dependence on κ that would be associated with the conventional kappa distribution. We note that their definition of the kappa distribution function is also different from a modified distribution based on the notion of nonextensive entropy.

Electron‐acoustic and cyclotron‐sound instabilities driven by field‐aligned hot‐electron streaming

We study the magnetized electron-acoustic instability in a three-component plasma comprising cool ions, cool electrons and a hot, drifting electron component. Whereas previous investigations of the electron-acoustic instability have usually been limited to the regime of strong magnetization, we have considered strong, intermediate, and weak magnetization regimes. In the weak to intermediate regime we identify an electron-cyclotron-sound instability which has lower threshold and larger growth rate than the weakly magnetized electron-acoustic instability for wave propagation angles quasi-parallel to the ambient magnetic field. The relationship between the cyclotron-sound and electron-acoustic instabilities is elucidated. In particular, we observe a “coupling” of the waves in weak magnetic fields, which becomes weaker and finally disappears with progressively larger magnetic field strengths. The relevance of this work to cusp auroral hiss and broadband electrostatic noise in the auroral magnetosphere is discussed.

Oblique propagation of electromagnetic waves in a kappa-Maxwellian plasma

Space plasmas are often observed to contain more particles in the high-energy tail than the usual Maxwellian distributions, and are well modeled by kappa distributions. The hybrid kappa-Maxwellian distribution and associated generalized plasma dispersion function ZκM were recently introduced to model magnetized space plasmas. The susceptibility tensor for a kappa-Maxwellian plasma component is derived, making use of ZκM. This enables one to make general studies of obliquely propagating electromagnetic waves in a magnetoplasma. The susceptibility and dielectric tensors reduce to the Maxwellian expressions in the limit κ→∞. As an illustration, the formalism is applied to the lower branch of the R mode and its off-parallel variant. For low κ values, low-wavenumber, low-frequency parallel whistler waves are shown to be stable, unlike the Maxwellian case, which is unstable if the perpendicular temperature exceeds the parallel temperature. A numerical study is made of the effects of the value of kappa, the prop...

A new formulation and simplified derivation of the dispersion function for a plasma with a kappa velocity distribution

A simplified derivation of the relationship between the dispersion function for a plasma with a kappa velocity distribution and the Gauss hypergeometric function is presented. This derivation relies on only a few standard integrals. It naturally leads to a new integral representation for the dispersion function, which readily yields the power and Laurent series for it. The new integral representation is shown to be closely related to the Gordeyev integral for a kappa distribution.

On the existence of ion-acoustic double layers in two-electron temperature plasmas

Earlier Sagdeev pseudopotential treatments of ion-acoustic double layers in plasmas with two electron populations were based on a model in which both electron densities were described by isothermal Boltzmann distributions. Using a more recent fluid-dynamical approach, with polytropic equations of state indices γj, one finds analytically that no double layers can be formed for γj⩾3∕2, due to total rarefaction of the cooler electrons or infinite compression of the ions. For γj<3∕2, rarefactive double layers occur, but, just below 3/2, at unrealistically small cool electron densities or large Mach numbers. As γj decreases towards 1, these constraints become less restrictive and go over smoothly to those known from Boltzmann studies. Contrary to what appears in the literature, very weak compressive double layers can also be found for Boltzmann electrons, but only for soliton conditions barely above the existence threshold; i.e., marginally super-ion-acoustic. Any slight increase in the critical Mach number de...

Solitons in dusty plasmas with positive dust grains

Although “typical” micrometer-sized dust grains in a space or laboratory plasma are often negatively charged because of collisions with the mobile electrons, there are environments in which grains may take on a positive charge. We consider a dusty plasma composed of electrons, positive ions and positive dust grains, and use the fluid dynamic paradigm to identify existence domains in parameter space for both dust-acoustic (DA) and dust-modified ion-acoustic (DIA) solitons. Only positive potential DA solitons are found. This represents an expected antisymmetry with the case of negative dust, where previously only negative solitons were reported. However, whereas for negative dust DIA solitons of either sign of potential may exist, we find that for the case of positive dust, DIA solitons are restricted to positive potentials only. The results for both positive and negative dust are consistent with an hypothesis that, in the absence of flows, the sign(s) of the soliton potential coincide(s) with the sign(s) o...

Conservation laws for steady flow and solitons in a multifluid plasma revisited

The conservation laws used in constructing the governing equations for planar solitons in multifluid plasmas are revisited. In particular, the concept of generalized vorticity facilitates the derivation of some general “Bernoulli theorems,” which reduce, in specific instances, to conservation laws previously deduced by other means. These theorems clarify the underlying physical principles that give rise to the conserved quantities. As an example of the usefulness of the techniques, even for relatively simple flows and progressive waves, the equations governing stationary nonlinear whistler waves propagating parallel to an ambient magnetic field are derived using generalized vorticity concepts.

Dual variational principles for nonlinear traveling waves in multifluid plasmas

A Hamiltonian description of nonlinear, obliquely propagating traveling waves in a charge neutral, electron-proton, multifluid plasma is developed. The governing equations are written as a dual spatial Hamiltonian system. In the first formulation, the Hamiltonian is identified with the longitudinal, x-momentum flux integral Px=const, in which the energy integral e=e0 acts as a constraint, and the Hamiltonian evolution operator is d∕dx, where x is the position coordinate in the wave frame. In the second Hamiltonian formulation, the Hamiltonian is proportional to the conserved energy integral e, in which the momentum integral Px=const acts as a constraint, and the Hamiltonian evolution operator d∕dτ=uxd∕dx is the Lagrangian time derivative where ux is the x component of the electron and proton fluids. The analysis is facilitated by using the de Hoffman–Teller frame of magnetohydrodynamic shock theory to simplify the transverse electron and proton momentum equations. The system is exactly integrable in cases...

Stopbands in the existence domains of acoustic solitons

A fully nonlinear Sagdeev pseudopotential approach is used to study the existence domain of fast mode ion-acoustic solitons in a three-species plasma composed of cold and warm adiabatic positive ion species and Boltzmann electrons. It is shown that for appropriate values of the cold-to-warm ion charge-to-mass ratio, μ, and the effective warm ion-to-electron temperature ratio, τ, there is a range in cold to warm ion charge density ratio, f, over which a stopband in soliton speed exists. Solitons do not propagate in the stopband, although they can occur for both higher and lower speeds. The stopbands are associated with a limiting curve of the existence domain that is double-valued in speed for a range of values of f. Analytical estimates of the upper and lower limits of τ and μ that support stopbands are found. It is suggested that, inter alia, the analysis should be applicable to the solar wind plasma.

Ion Bernstein waves in a plasma with a kappa velocity distribution

Using a Vlasov-Poisson model, a numerical investigation of the dispersion relation for ion Bernstein waves in a kappa-distributed plasma has been carried out. The dispersion relation is found to depend significantly on the spectral index of the ions, κi, the parameter whose smallness is a measure of the departure from thermal equilibrium of the distribution function. Over all cyclotron harmonics, the typical Bernstein wave curves are shifted to higher wavenumbers (k) if κi is reduced. For waves whose frequency lies above the lower hybrid frequency, ωLH, an increasing excess of superthermal particles (decreasing κi) reduces the frequency, ωpeak, of the characteristic peak at which the group velocity vanishes, while the associated kpeak is increased. As the ratio of ion plasma to cyclotron frequency (ωpi/ωci) is increased, the fall-off of ω at large k is smaller for lower κi and curves are shifted towards larger wavenumbers. In the lower hybrid frequency band and harmonic bands above it, the frequency in a ...