Propagation Of Small-amplitude Waves Research Articles

Wave propagation in a hot nonuniform magnetized plasma

A differential equation for small amplitude wave propagation in a hot nonuniform magnetized plasma is derived from the Vlasov equation by a perturbation expansion in the smallness of the Larmor radius compared to characteristic scale-lengths of the plasma. This equation is developed primarily to study the effects of strong plasma nonuniformities on propagation of waves which have counterparts in a uniform magnetized plasma. It consistently incorporates collisionless Landau-cyclotron damping effects in the wave propagation and is valid for wavelengths comparable to the scale-lengths of nonuniformities. Other features explicitly included in the equation are: (i) multiple ion species and (ii) weak nonlinear effects. An ordering has been established to evaluate the relative importance of finite Larmor radius effects and nonlinear effects.

Small amplitude wave propagation in stratified media

Four mutually connected first order linear differential equations for a system of two waves — constituting a set of mathematical models are developed. Small amplitude wave propagation through stratified media have been studied using the mathematical models. Limiting wave solutions are identified as WKB solutions.

Possibility of Landau damping of gravitational waves

There is considerable uncertainty in the literature concerning whether or not transverse traceless gravitational waves can Landau damp. Physically, the issue is whether particles of nonzero mass can comove with surfaces of constant wave phase, and therefore, loosely, whether gravitational waves can have phase speeds less than that of light. We approach the question of Landau damping in various ways. We consider first the propagation of small-amplitude gravitational waves in an ideal fluid-filled Robertson-Walker universe of zero spatial curvature. We argue that the principle of equivalence requires those modes to be lightlike. We show that a freely moving particle interacting only with the collective fields cannot comove with such waves if it has nonzero mass. The equation for gravitational waves in collisionless kinetic gases differs from that for fluid media only by terms so small that deviations from lightlike propagation are unmeasurable. Thus, we conclude that Landau damping of small-amplitude, transverse traceless gravitational waves is not possible.

The propagation of small amplitude waves in prestressed incompressible elastic cylinders

A study is made of the propagation of small amplitude waves in prestressed cylinders. The initial state of finite strain is assumed to be a pure homogeneous biaxial deformation and the cylinder composed of a Mooney material. The structure of the equations of motion is discussed and separable solutions of the equations of motion are constructed. These describe long wave solutions, rotationally symmetric modes, pure torsional modes (which collapse onto the classical solutions) and generally flexural/torsional modes. Dispersion relations for each of these cases are derived and their analytical and numerical properties are discussed.

A continuum approach to the second-sound effect

Standard techniques of continuum mechanics are used to describe the flow of certain microscopic excitations which are believed to give rise to the second-sound phenomena in some materials at low temperatures. Appropriate balance laws are formulated, and constitutive equations for an elastic solid are postulated. The propagation of small-amplitude second-sound waves is discussed and the results compared with those predicted by the theory of Lord and Shulman [1].

Acoustic wave propagation in liquid helium II

Elsewhere [1], using the framework of multipolar continuum mechanics, the authors have discussed a possible alternative to the two-fluid theories for liquid helium 11 and showed that, in the case when the fluid is assumed to be incompressible, second sound waves exist in both the stationary and rotating fluid. Here the constitutive theory presented in the paper cited is extended to include the effects of compressibility and viscosity and a study of these effects on the propagation of small-amplitude waves. 1t is found that the qualitative predictions agree with the experimental observations in helium II.

Heat-convection waves in a semi-infinite horizontal liquid layer with free boundaries

A solution is found for the complete problem of the propagation of small-amplitude heat-convection waves in a semi-infinite horizontal layer of a thermally compressible liquid. The waves are excited by a periodically varying temperature of a vertical side wall.

A Least Squares Version of Short Wave Asymptotics

The primary object of this paper is to point out, by the means of presenting a rational alternative, that the conventional progressive wave formalism is one of many possible asymptotic expansions. The conventional approach minimizes the algebraic difficulties, whereas in this paper we choose to minimize, in a least squares sense, the effect of truncating an asymptotic expansion. For waves with a profile whose derivative is not square integrable, the two approaches are shown to be in agreement both for free waves and for waves near an isolated caustic. The least squares procedure can be extended to more complicated problems, and equations are derived for the propagation of unsteady small amplitude waves on water of small depth.

Surface waves in uniaxially-stressed Mooney material

A theoretical investigation is made into the propagation of small-amplitude waves across the free surface of an elastic medium, whose strain-energy function is of Mooney form. The medium is taken to be semi-infinite in extent, and to be subjected to a large primary extension (or compression) in a direction lying in the free surface. The dispersion equation is derived and the general nature of its solutions is explored. Detailed numerical results are given for certain special cases.

Oscillating Progressive Shear Waves in Nonhomogeneous Viscoelastic Solids

The equations of motion for cylindrical and spherical shear waves in nonhomogeneous, isotropic, "standard", viscoelastic media with continuous radial variations are derived. Oscillatory shearing tractions are applied to the boundaries of cylindrical and spherical openings in unlimited viscoelastic media. The propagation of small-amplitude waves is studied, and formal asymptotic expansions of the solutions are obtained. In both cases (cylindrical and spherical), the leading term of the formal asymptotic expansion represents a modulated, oscillating, progressive wave propagating with variable velocity. The modulation depends on the moduli of rigidity and viscosity, whereas the velocity depends on the moduli of rigidity only. Application of our results to the propagation of shear waves in both finite and infinite viscoelastic plates is discussed.

Collisionless Damping of Hydromagnetic Waves in Relativistic Plasma. Weak Landau Damping

view Abstract Citations (35) References (39) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Collisionless Damping of Hydromagnetic Waves in Relativistic Plasma. Weak Landau Damping Barnes, Aaron ; Scargle, Jeffrey D. Abstract The propagation and damping of small-amplitude waves in a plasma of relativistic electrons and/ or protons is studied. As in the analogous nonrelativistic problem, the damping is found to be large except for particular angles of propagation. The results are applied, in the ultrarelativistic limit, to the problem of the heating of the high-energy electrons in the Crab Nebula. Some aspects of the morphology of the propagating disturbances near the center of the nebula can be understood in terms of the magnitude and angular dependence of the calculated damping. Subject headings: Crab Nebula - hydromagnetics - plasmas - relativity Publication: The Astrophysical Journal Pub Date: August 1973 DOI: 10.1086/152324 Bibcode: 1973ApJ...184..251B full text sources ADS |

Simple waves in nonconducting magnetizable medium: PMM vol. 37, n≗5, 1973, pp. 813–821

The propagation of small amplitude waves through a nonconducting, isotropically magnetizable medium is studied, and simple wave equations obtained. Simple waves in an ideal magnetizable gas are studied in detail. The problem of stability is considered for the ideal gas and a magnetizable fluid, and the parameter values for which the wave phase velocities become imaginary are determined.

Propagation of Hydromagnetic Waves in a Stochastic Magnetic Field

view Abstract Citations (20) References (18) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Propagation of Hydromagnetic Waves in a Stochastic Magnetic Field Valley, George C. Abstract The propagation of coherent small-amplitude hydromagnetic waves through a medium in which the magnetic field has a large-scale ordered component and a stationary random component is investigated. By neglecting third-order correlations between the random part of the wave and the stochastic field, dispersion relations which give the wavenumber as a function of frequency for the coherent part of the wave are obtained. From these dispersion relations, damping decrements are evaluated in several limits for the Alfve'n mode propagating parallel to the average field and for the fast magnetosonic mode prop agating perpendicular to the average field. In typical astrophysical systems these modes damp in 10-100 correlation lengths in a stochastic field; and since all other modes, and these modes at all other angles, undergo Landau damping, application to the solar wind and interstellar gas shows that no coherent hydromagnetic wave can propagate across the solar system or the Galaxy. Publication: The Astrophysical Journal Pub Date: September 1971 DOI: 10.1086/151080 Bibcode: 1971ApJ...168..251V full text sources ADS |

Wave-Wave Coupling in Ion Wave Propagation

Wave-wave coupling among ion waves is investigated, experimentally and theoretically. When two ion waves of different frequencies of f 1 and f 2 are excited by one grid, the signals of the harmonic (2 f 1 ) and f 1 – f 2 are detected by another grid. They are found to grow spatially in some region, on the contrary to those of f 1 and f 2 which decrease monotonously in the region. The growing regions of the harmonic and f 1 – f 2 are in accord with those obtained from the theory of the wave-wave coupling among ion waves. The propagation of small-amplitude wave under the large-amplitude wave and the propagation of ion wave with large-amplitude are also investigated.

Effects of Plasma Flow on Electrostatic Disturbances in a Q Machine

The evolution of a large discontinuity in density in a single-ended Q machine has been found to be adequately described by a free-streaming model of the ions modified by a density gradient electric field due to a finite electron temperature. As the electron temperature is increased through microwave heating at cyclotron resonance, the profile of the discontinuity is found to broaden spatially as predicted by the theoretical model. The plasma ion drift velocity along the magnetic field can be measured from the motion of the discontinuity and is found to be in close agreement with the drift velocity measured from the propagation of small-amplitude ion-acoustic waves. An estimate of the ion thermal velocity parallel to the magnetic field can also be obtained from the broadening of th discontinuity profile. The ion drift velocity exhibits systematic variation with changes in oven and ionizer temperatures which is attributable to the electron-ion balance in the region surrounding the hot ionizer.

Propagation of Sinusoidal Small-Amplitude Waves in a Deformed Viscoelastic Solid. I

The propagation of a sinusoidal wave of small amplitude in an initially isotropic viscoelastic solid, which is subjected to a static pure homogeneous deformation, is discussed. The secular equation for a plane wave propagating an arbitrary direction with respect to the principal directions of the static deformation is derived. The complex slownesses corresponding to propagation along the principal axes of the static strain are found. Relations are obtained between these and the principal stresses associated with the static deformation, which generalize earlier formulas obtained by Ericksen for elastic materials.

Wave Propagation in a Sandwich Ring

The propagation of small-amplitude free harmonic waves in an elastic sandwich ring is studied by using a Timoshenko-type theory, which takes into account the effects of radial shear deformation, rotatory inertia, and extension of the neutral axis. The form of the equations of motion is the same for both homogeneous and sandwich rings, but the range of values for the parameters involved in the latter case can lead to qualitative changes in the wave propagation characteristics of the system. It is shown that the ratio of the ring's extensional stiffness to its shear stiffness has an important influence on the frequencies and group velocities of sandwich rings. When this ratio becomes large, two of the three modes of wave propagation become less dispersive. Numerical examples are presented and discussed.

Negative ion detection in the ionosphere from effects on ELF waves

The theory for propagation of small-amplitude electromagnetic waves in a cold, homogeneous plasma including negative ions and immersed in a uniform, static magnetic field is developed. It is found that for longitudinal propagation each negative ion introduces a resonance at the negative ion cyclotron frequency, a concentration dependent cutoff frequency above the negative ion cyclotron frequency, and possibly a crossover frequency depending on the ion concentrations and charge-to-mass ratios. At both the cyclotron frequency and the cutoff frequency the group refractive index becomes infinite. Between these two frequencies there is a ‘nose’ frequency, for which the group refractive index is a minimum. Examples are given for a three-and five-component plasma. Application of this negative ion theory is made to propagation of negative ion whistlers in the ionosphere. It is found that for frequencies near the negative ion cyclotron frequencies the WKB approximation is valid above 300 km during the nighttime and 150 km during the daytime. Effects of collisions can be neglected above 150 km. An ideal experiment is proposed for observation of negative ion whistlers (1–1000 cps). Sample whistler, frequency-time spectrograms like those that would be observed with such an experiment are sketched. From the distinctive frequencies on these sample spectrograms, it is shown that the negative ion specie and concentration can be determined using the developed cold plasma expressions.

Small Amplitude Wave Propagation in Hot Ionized Gases

Radiative transfer effects on both the forced and the free small-amplitude wave propagation problem in an ordinary as well as an ionized gas have been investigated. The results predict an additional radiation induced mode. For an ionized medium, in the presence of a magnetic field, we have the Alfvén wave, adiabatic and isothermal magnetosonic, fast and slow waves. These investigations also show that the skin depth for the waves is proportional to the mean free path of the radiation and the lifetime to the time taken by a sound wave to travel a distance equal to the wavelength or radiation mean free path. The magnetic field seems to support the propagation of some modes, but oppose that of the radiation induced wave in an ionized medium.

Alfvén waves in inhomogeneous magnetic fields

A perfectly conducting, nonviscous fluid is assumed to be permeated by an inhomogeneous, time-independent external magnetic field. Propagation of small-amplitude hydromagnetic waves with the velocity vector satisfying div v = 0 is investigated in a curvilinear coordinate system in which the lines of the external magnetic field are chosen as coordinate lines. It is shown that, if the lines have no torsion and if the external magnetic field has a certain symmetry, such that the field intensity is independent of one of the curvilinear coordinates, there exist rigorous solutions of the linearized hydromagnetic equations describing waves which travel along the lines of the external magnetic field, with the velocity of the fluid motion directed everywhere along the binormal to the local magnetic line of force. The examples of magnetic fields of plane and axial symmetry are discussed.