Wave propagation in pulsar magnetospheres - Dispersion relations and normal modes of plasmas in superstrong magnetic fields
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Arons, J.↗
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A space-time discretization procedure for wave propagation problems
Higher order compact algorithms are developed for the numerical simulation of wave propagation by using the concept of a discrete dispersion relation. The dispersion relation is the imprint of any linear operator in space-time. The discrete dispersion relation is derived from the continuous dispersion relation by examining the process by which locally plane waves propagate through a chosen grid. The exponential structure of the discrete dispersion relation suggests an efficient splitting of convective and diffusive terms for dissipative waves. Fourth- and eighth-order convection schemes are examined that involve only three or five spatial grid points. These algorithms are subject to the same restrictions that govern the use of dispersion relations in the constructions of asymptotic expansions to nonlinear evolution equations. A new eighth-order scheme is developed that is exact for Courant numbers of 1, 2, 3, and 4. Examples are given of a pulse and step wave with a small amount of physical diffusion.
Davis, Sanford↗
Symmetry relation in relaxation dispersions.
Symmetry relation between dispersion function of frequency variable and distribution function of relaxation time variable
RELAXATION TIME↗
Ten-moment fluid modeling of the Weibel instability
We investigate the one-dimensional non-relativistic Weibel instability through the capture of anisotropic pressure tensor dynamics using an implicit 10-moment fluid model that employs the electromagnetic Darwin approximation. The results obtained from the 10-moment model are compared with an implicit particle-in-cell simulation. The linear growth rates obtained from the numerical simulations are in good agreement with the theoretical fluid and kinetic dispersion relations. The fluid dispersion relations are derived using Maxwell’s equations and the Darwin approximation. We also show that the magnetohydrodynamic approximation can be used to model the Weibel instability if one accounts for an anisotropic pressure tensor and unsteady terms in the generalised Ohm’s law. In addition, we develop a preliminary theory for the saturation magnetic field strength of the Weibel instability, showing good agreement with the numerical results.
Kuldinow, D. A. (ORCID:0000000319730196)↗
Comments on absolute and convective instabilities
The paper puts into question the tenability of a critique by Oscarsson and Roennmark (1986) regarding the theory of absolute and convective instabilities. The space-time evolution of instabilities is reviewed with attention given to the two categories of time-asymptotic evolution. It is mentioned that the notion of time-asymptotics does not simply refer to t approaching infinity and that the evolution of the arbitrary initial perturbation at t = 0 is obtained by convolving the Green's function. The examples used in the previous critique describe instabilities that evolve in time only and are concluded to be nongeneric for continuous media, and the corresponding treatment of a time-asymptotic limit is characterized by imprecision. The original authors respond by suggesting that nondispersive waves are physically legitimate as in common plasma-wave modes and Alfven waves and can be described by their dispersion relation. A dispersive term is added to the relation so that it can be applied to ion-acoustic waves and other phenomena.
Ram, A. K.↗
Beyond Clausius-Mossotti - Wave propagation on a polarizable point lattice and the discrete dipole approximation
We derive the dispersion relation for electromagnetic waves propagating on a lattice of polarizable points. From this dispersion relation we obtain a prescription for choosing dipole polarizabilities so that an infinite lattice with finite lattice spacing will mimic a continuum with dielectric constant. The discrete dipole approximation is used to calculate scattering and absorption by a finite target by replacing the target with an array of point dipoles. We compare different prescriptions for determining the dipole polarizabilities. We show that the most accurate results are obtained when the lattice dispersion relation is used to set the polarizabilities.
Draine, B. T.↗
Theory of the current-driven ion cyclotron instability in the bottomside ionosphere
A comprehensive treatment of the theory of electrostatic ion cyclotron instability in the collisional bottomside ionosphere is given. The linear dispersion relations for the ion cyclotron instability (electron and ion collisions) are derived. Analytical solutions to the dispersion relation are obtained in three limits: collisionless; weakly collisional; and collisional. In addition, the linear dispersion relation is solved numerically, using parameters typical of the high-latitude bottomside ionosphere. It is pointed out that the linear growth rates in the bottomside collisional regime can be of the same order as the corresponding topside collisionless growth rates. A nonlinear saturation mechanism for the electrostatic ion cyclotron instability is proposed on the basis of Dupree's (1966) resonance broadening theory.
Satyanarayana, P.↗
Ion streaming instabilities with application to collisionless shock wave structure
The electromagnetic dispersion relation for two counterstreaming ion beams of arbitrary relative strength flowing parallel to a dc magnetic field is derived. The beams flow through a stationary electron background and the dispersion relation in the fluid approximation is unaffected by the electron thermal pressure. The dispersion relation is solved with a zero net current condition applied and the regions of instability in the k-U space (U is the relative velocity between the two ion beams) are presented. The parameters are then chosen to be applicable for parallel shocks. It was found that unstable waves with zero group velocity in the shock frame can exist near the leading edge of the shock for upstream Alfven Mach numbers greater than 5.5. It is suggested that this mechanism could generate sufficient turbulence within the shock layer to scatter the incoming ions and create the required dissipation for intermediate strength shocks.
Golden, K. I.↗
Ion streaming instabilities with application to collisionless shock wave structure
The electromagnetic dispersion relation for two counterstreaming ion beams of arbitrary relative strength flowing parallel to a dc magnetic field is derived. The beams flow through a stationary electron background and the dispersion relation in the fluid approximation is unaffected by the electron thermal pressure. Magnetic effects on the ion beams are included, but the electrons are treated as a magnetized fluid. The dispersion relation is solved with a zero net current condition applied and the regions of instability in the k-U space (U is the relative velocity between the two ion beams) are presented. These results are extensions of Kovner's analysis for weak beams. The parameters are then chosen to be applicable for parallel shocks. It is found that unstable waves with zero group velocity in the shock frame can exist near the leading edge of the shock for upstream Alfven Mach numbers greater than 5.5.
Golden, K. I.↗
Energy dependence of cosmic ray composition above 10(15) GeV/nucleus
It is argued that above 10 to the 5th power GeV/nucleus, in the range where charge-resolved spectra have not yet been determined, the appropriate measures of equal-energy composition are 1nA and 1nA , the mean value and dispersion relative to the mean value and dispersion relative to the mean of 1nA, where A is the mass number. Experimental data which are sensitive to changes in 1nA with increasing energy are examined. It is found that, taken as a whole, they show no change (+ or 0.5) between 10 to the 5th power and 10 to the 6th power GeV, and a decrease of 1.5 + or - 0.5 between 10 to the 6th power and 10 to the 8th power GeV, with no further change + or - 0.5) above 10 to the 8th power GeV. Taken as a whole, the various indirect estimates of the absolute value of 1nA above 10 to the 5th power GeV/nucleus are also consistent with this pattern. For a wide range of astrophysically plausible composition models the value of the other measure, 1nA is insensitive to changes in 1nA . Because of this the existing data on 1nA can likewise easily be reconciled with this pattern.
Linsley, J.↗
Finite ion temperature effects on electrostatic instabilities in partially magnetized plasmas
In this paper, the effects of warm ions on electrostatic, kinetic instabilities observed in partially magnetized plasmas, such as the electron cyclotron drift instability (ECDI) and modified two-stream instability (MTSI), are investigated. The kinetic dispersion relation that accounts for warm, non-magnetized ions and warm, magnetized electrons is solved using a complex root-finding technique [A. C. Denig and K. Hara, Phys. Plasmas 30, 032108 (2023)]. It is observed that finite ion temperature introduces ion Landau damping effects, decreasing the growth rate of most unstable modes. The high-frequency, short-wavelength ECDI modes are more strongly affected by ion Landau damping than the low-frequency, long-wavelength MTSI modes. The solutions of the kinetic dispersion relation for MTSI are compared with the fluid dispersion relation of MTSI, which was originally proposed by McBride et al. [Phys. Fluids 15 2367–2383 (1972)]. The differences in the dispersion characteristics between the kinetic and fluid MTSI limits are assessed, illustrating the effects of electron and ion Landau damping on kinetic instabilities in partially magnetized plasmas.
Denig, A. C. (ORCID:0000000253339572)↗
Contact solitons as spin pistons in one-dimensional ferromagnetic channels
Ferromagnetic channels subject to spin injection have been theoretically shown to sustain dissipative exchange flows (DEFs). In the strong injection regime, a soliton is stabilized at the injection site, which has been termed a contact soliton DEF or CS-DEF. Here, in this work, we investigate the modulation of CS-DEFs as a mechanism to inject magnons into a DEF. By varying the injection current, the parameters connecting the soliton with the DEF via a boundary layer are varied. These lead to a modification in the DEF which is interpreted as a spin piston. The injected magnons follow the expected dispersion relation of DEFs, akin to the Bogoliubov–de Gennes dispersion relation. As a result, this work demonstrates that changes in the injected current can pump magnons along a ferromagnetic channel via dissipative exchange flows.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Doubly diffusive magnetic buoyancy instability in the solar interior
An investigation of the buoyancy of diffuse magnetic fields has shown that in the presence of rotation, static equilibrium configurations of the toroidal magnetic field and ambient plasma can exist. In that case, the escape of toroidal magnetic flux from the solar interior may be determined by the growth of instabilities which the equilibrium configuration may be subject to. In connection with the present investigation, it is assumed that in the region of toroidal magnetic flux amplification, the magnetic field has not as yet filamented into flux ropes, and is therefore 'diffuse'. A study is conducted of the MHD stability of an electrically conducting and differentially rotating gas in the presence of a toroidal magnetic field, an external constant gravitational field, and radiance pressure. The full dispersion relation for the magnetic buoyancy problem is developed, and the solutions of the dispersion relation are discussed.
Schmitt, J. H. M. M.↗
Wave modes of the Io plasma torus
The corotating magnetospheric convection model is analyzed with the objective of deriving the fundamental wave modes present in the Io torus. The time-dependent equations of motion are linearized for the case of the absence of plasma mass and momentum sources. By separating the magnetosphere-ionosphere coupling equation into two equations and by adopting a specific analytic form for the equilibrium plasma density, a cubic equation is derived for the dispersion relation defining the angular frequencies of the fundamental wave modes. A detailed analysis of the dispersion relation yields three fundamental wave modes. One of the modes is identified as the previously studied inertial interchange (unstable) mode, while the other two are newly derived decaying modes. The results obtained are discussed in the context of plasma transport in the Io torus.
Summers, D.↗
The cosmic Doppler instability
The equations governing the behavior of perturbations of a mixture of nearly homogeneous and isotropic matter and radiation are derived, using a diffusion approximation where spatial perturbations in the radiation spectrum are allowed to vary with frequency. A simple model of line opacity leads to dispersion relations which display a new bulk instability. The model is used to derive an approximate dispersion relation for radiation interacting via resonance scattering opacity in atomic hydrogen at low density and low temperature. Possible applications to cosmology are briefly discussed.
Hogan, Craig J.↗
A revised parametrization of the dispersion constants for high dispersion IUE images
An economical system of parameterizing dispersion constants spectra is derived and applied to International Ultraviolet Explorer (IUE) spectra by equating specific terms to geometric coordinates of an echellogram. Because of the virtual property of the IUE camera pixels, several geometrical rectifications can be performed analytically before the dispersion relations are solved for line and sample position. This permits the relations to be decoupled and reduced to two terms apiece, the simplest representation possible. A generalization of these principles allows the dispersion relations to be determined neatly in other echelle systems having certain well understood distortions. Prismatic cross dispersion, S wave distortion, and optical aberrations are some areas in which this system can be used.
Smith, Myron A.↗
The radiation pressure-driven Rayleigh-Taylor instability - Analysis and application to QSO emission line clouds
The growth of perturbations in a photoionized gas slab accelerated by radiation pressure under conditions like those in QSO emission-line regions is analyzed. A linear dispersion relation is derived, and numerical radiation-transfer calculations are performed to evaluate the coefficients and roots of that dispersion relation for L-alpha optical depths between 0.1 and 10,000. The nonlinear growth of the waves is estimated, and it is concluded that complete dispersal of the clouds is likely. On the basis of qualitative arguments it is suggested that clouds of greater optical depth are linearly stable.
Krolik, J. H.↗
Beat, modulational, and decay instabilities of a circularly polarized Alfven wave
A circulary polarized low-frequency electomagnetic pump wave propoagating along an ambient magnetic field is known to be unstable to the growth of several parallel-propagating parametric instabilties. If ion-cyclotron effects are retained in a two-fluid description, the dispersion relation is a sixth-order polynomial. We present a series of new analytical approximations to this dispersion relation. We emphasize new results for the beat instability that occurs as an interaction of the forward prpagating upper sideband with the backward propagating lower sideband. The nature of the beat instabitlity depends on beta = (v(sub sound)/v(sub A)(exp 2) and on the sense of polarization of the pump wave. The beat and decay instabilities can occur together if the pump is left-handed (i.e., ion resonant) and if beta is less than or approximately 1, but they cannot occur together if the pump is right-handed. For a left-handed pump the beat mode is the only instability if beta is greater than or approximately 1. If the pump is right-handed and beta is greater than or approximately 1, then the beat instability exists only when the pump amplitude exceeds a threshold value, and the beat will be the only instability if the pump amplitude is large enough to stabilize the modulational instability. If the pump is left-handed and beta is less than or approximately 1, then the beat mode is stabilized when the pump amplitude becomes sufficiently large. The beat instability primarily produces a forward propagating transverse wave in the upper sideband. Thus if beta is greater than or approximately 1, the instabilities considered here do not produce the backward propagating waves which are thought to affect turbulence and the evolution of cross helicity in the solar wind. New analytical results are presented also for the decay and modulational instabilites when beta is approximately equal to 1.
Hollweg, Joseph V.↗