Dispersion Relations Of Modes Research Articles

Anisotropy of Isobaric Instability in a Partially Ionized Plasma in a Magnetic Field

Linear equations describing the dynamics of small perturbations in partially ionized heat-releasing plasma in an external magnetic field with an arbitrary induction vector are obtained. Using these equations, a dispersion relation for condensation modes is derived, and their time increments are calculated in the case of isobaric instability in the presence of anisotropy of the plasma thermal conductivity.

Unstable electrostatic surface waves in a turbulent plasma containing streaming ions: transverse truncation approach

The unstable modes of surface waves propagating in a sharply bounded turbulent plasma containing streaming ions are investigated by employing the specular reflection condition and the transverse truncation method. We have found that the bounded turbulent plasma supports damping and growing modes. The damping mode propagates for all values of the ion streaming speed modes and their behavior is similar to the case of surface waves in a turbulent plasma without ion streaming. If the speed of ion streaming is larger than the ion-acoustic speed, growing mode exists for all values of the wave number. However, if the ion stream is slower than the ion acoustic speed, then the growing mode appears under a certain condition. We derive the dispersion relations for such modes of surface waves and investigate the condition for propagation.

Polaritonic contribution to the Casimir energy between two graphene layers

We study the role of surface polaritons in the zero-temperature Casimir effect between two graphene layers that are described by the Dirac model. A parametric approach allows us to accurately calculate the dispersion relations of the relevant modes and to evaluate their contribution to the total Casimir energy. The resulting force features a change of sign from attractive to repulsive as the distance between the layers increases. Contrary to similar calculations that have been performed for metallic plates, our asymptotic analysis demonstrates that at small separations the polaritonic contribution becomes negligible relative to the total energy.

Dispersion relations in non-relativistic two-dimensional materials from quasinormal modes in H\u01d2rava Gravity

We compute dispersion relations of non-hydrodynamic and hydrodynamic modes in a non-relativistic strongly coupled two-dimensional quantum field theory. This is achieved by numerically computing quasinormal modes (QNMs) of a particular analytically known black brane solution to 3+1-dimensional Hǒrava Gravity. Hǒrava Gravity is distinguished from Einstein Gravity by the presence of a scalar field, termed the khronon, defining a preferred time-foliation. Surprisingly, for this black brane solution, the khronon fluctuation numerically decouples from all others, having its own set of purely imaginary eigenfrequencies, for which we provide an analytic expression. All other Hǒrava Gravity QNMs are expressed analytically in terms of QNMs of Einstein Gravity, in units involving the khronon coupling constants and various horizons. Our numerical computation reproduces the analytically known momentum diffusion mode, and extends the analytic expression for the sound modes to a wide range of khronon coupling values. In the eikonal limit (large momentum limit), the analytically known dispersion of QNM frequencies with the momentum is reproduced by our numerics. We provide a parametrization of all QNM frequencies to fourth order in the momentum. We demonstrate perturbative stability in a wide range of coupling constants and momenta.

Longitudinal sound and diffusion in holographic massive gravity

We consider a simple class of holographic massive gravity models for which the dual field theories break translational invariance spontaneously. We study, in detail, the longitudinal sector of the quasi-normal modes at zero charge density. We identify three hydrodynamic modes in this sector: a pair of sound modes and one diffusion mode. We numerically compute the dispersion relations of the hydrodynamic modes. The obtained speed and the attenuation of the sound modes are in agreement with the hydrodynamic predictions. On the contrary, we surprisingly find disagreement in the case of the diffusive mode; its diffusion constant extracted from the quasi-normal mode data does not agree with the expectations from hydrodynamics. We confirm our numerical results using ana- lytic tools in the decoupling limit and we comment on some possible reasons behind the disagreement. Finally, we extend the analysis of the collective longitudinal modes beyond the hydrodynamic limit by displaying the dynamics of the higher quasi-normal modes at large frequencies and momenta.

Linear Analysis of 2-D Sheet Beam Cyclotron Maser With Metallic Grating Structures

Based on a kinetic model, a linear theory of the 2-D sheet beam metallic grating cyclotron maser has been derived and analyzed numerically. The TE mode dispersion relation and the periodicity of the normalized amplitudes of spatial harmonics of the cyclotron maser with rectangular gratings are obtained. Through numerical calculations, the dependence of the growth rate on the gap distance between the metallic grating surface and the beam, the external magnetic field strength, the beam current, the transverse-to-axial velocity ratio, the axial velocity spread, and the beam voltage are analyzed. This article presents an analysis of interaction using the fundamental TE mode in the 2-D metallic grating sheet beam system. The fundamental TE mode in the 2-D metallic rectangular waveguide grating structure is the fundamental TMx mode in the 3-D rectangular waveguide grating structure and this method can be extended to the practical 3-D interaction system that operates at other TMx modes and has a good potential for the study of the combined resonances in cyclotron masers with grating structures.

Fast neutrino flavor conversion: collective motion vs. decoherence

In an interacting neutrino gas, flavor coherence becomes dynamical and can propagate as a collective mode. In particular, tachyonic instabilities can appear, leading to “fast flavor conversion” that is independent of neutrino masses and mixing angles. On the other hand, without neutrino-neutrino interaction, a prepared wave packet of flavor coherence simply dissipates by kinematical decoherence of infinitely many non-collective modes. We reexamine the dispersion relation for fast flavor modes and show that for any wavenumber, there exists a continuum of non-collective modes besides a few discrete collective ones. So for any initial wave packet, both decoherence and collective motion occurs, although the latter typically dominates for a sufficiently dense gas. We derive explicit eigenfunctions for both collective and non-collective modes. If the angular mode distribution of electron-lepton number crosses between positive and negative values, two non-collective modes can merge to become a tachyonic collective mode. We explicitly calculate the interaction strength for this critical point. As a corollary we find that a single crossing always leads to a tachyonic instability. For an even number of crossings, no instability needs to occur.

Bubbly Water as a Natural Metamaterial of Negative Bulk-Modulus

In this study, an oscillator model of bubble-in-water is proposed to analyze the effective modulus of low-concentration bubbly water. We show that in a wide range of wave frequency the bubbly water acquires a negative effective modulus, while the effective density of the medium is still positive. These two properties imply the existence of a wide acoustic gap in which the propagation of acoustic waves in this medium is prohibited. The dispersion relation for the acoustic modes in this medium follows Lorentz type dispersion, which is of the same form as that of the phonon-polariton in an ionic crystal. Numerical results of the gap edge frequencies and the dispersion relation in the long-wavelength regime based on this effective theory are consistent with the sonic band results calculated with the plane-wave expansion method (PWEM). Our theory provides a simple mechanism for explaining the long-wavelength behavior of the bubbly water medium. Therefore, phenomena such as the high attenuation rate of sound or acoustic Anderson localization in bubbly water can be understood more intuitively. The effects of damping are also briefly discussed. This effective modulus theory may be generalized and applied to other bubble-in-soft-medium type sonic systems.

Spin Pinning and Spin-Wave Dispersion in Nanoscopic Ferromagnetic Waveguides

Spin waves are investigated in yttrium iron garnet waveguides with a thickness of 39nm and widths ranging down to 50nm, i.e., with an aspect ratio thickness over width approaching unity, using Brillouin light scattering spectroscopy. The experimental results are verified by a semianalytical theory and micromagnetic simulations. A critical width is found, below which the exchange interaction suppresses the dipolar pinning phenomenon. This changes the quantization criterion for the spin-wave eigenmodes and results in a pronounced modification of the spin-wave characteristics. The presented semianalytical theory allows for the calculation of spin-wave mode profiles and dispersion relations in nanostructures.

Wave dispersion in pulsar plasma. Part 1. Plasma rest frame

Wave dispersion in a pulsar plasma (a one-dimensional, strongly magnetized, pair plasma streaming highly relativistically with a large spread in Lorentz factors in its rest frame) is discussed, motivated by interest in beam-driven wave turbulence and the pulsar radio emission mechanism. In the rest frame of the pulsar plasma there are three wave modes in the low-frequency, non-gyrotropic approximation. For parallel propagation (wave angle$\unicode[STIX]{x1D703}=0$) these are referred to as the X, A and L modes, with the X and A modes having dispersion relation$|z|=z_{\text{A}}\approx 1-1/2\unicode[STIX]{x1D6FD}_{\text{A}}^{2}$, where$z=\unicode[STIX]{x1D714}/k_{\Vert }c$is the phase speed and$\unicode[STIX]{x1D6FD}_{\text{A}}c$is the Alfvén speed. The L mode dispersion relation is determined by a relativistic plasma dispersion function,$z^{2}W(z)$, which is negative for$|z|<z_{0}$and has a sharp maximum at$|z|=z_{\text{m}}$, with$1-z_{\text{m}}<1-z_{0}\ll 1$. We give numerical estimates for the maximum of$z^{2}W(z)$and for$z_{\text{m}}$and$z_{0}$for a one-dimensional Jüttner distribution. The L and A modes reconnect, for$z_{\text{A}}>z_{0}$, to form the O and Alfvén modes for oblique propagation ($\unicode[STIX]{x1D703}\neq 0$). For$z_{\text{A}}<z_{0}$the Alfvén and O mode curves reconnect forming a new mode that exists only for$\tan ^{2}\unicode[STIX]{x1D703}\gtrsim z_{0}^{2}-z_{\text{A}}^{2}$. The L mode is the nearest counterpart to Langmuir waves in a non-relativistic plasma, but we argue that there are no ‘Langmuir-like’ waves in a pulsar plasma, identifying three features of the L mode (dispersion relation, ratio of electric to total energy and group speed) that are not Langmuir like. A beam-driven instability requires a beam speed equal to the phase speed of the wave. This resonance condition can be satisfied for the O mode, but only for an implausibly energetic beam and only for a tiny range of angles for the O mode around$\unicode[STIX]{x1D703}\approx 0$. The resonance is also possible for the Alfvén mode but only near a turnover frequency that has no counterpart for Alfvén waves in a non-relativistic plasma.

Response to “Comment on ‘Symmetry in electron and ion dispersion in 1D Vlasov-Poisson plasma’” [Phys. Plasmas 26, 064701 (2019)

Treating electron and ion kinetics on the same physics footing or in a symmetric framework, dispersion relations (ωr, k) for ion and electron modes in a 1D Vlasov-Poisson (VP) plasma were obtained in the limit of weak flattening of the electron and ion distributions. Using this information of (ωr, k), a nonlinear VP solver with a low amplitude, harmonic external forcing has been solved. A possibility of simultaneous excitation of all the electrostatic normal modes was demonstrated in Trivedi et al. [Phys. Plasmas 25, 112102 (2018)]. The main focus of the paper is on the excitation of normal modes by applying a small amplitude external, monochromatic, electric field drive. In order to drive as well as to identify Phase Space Vortices (i.e., Bernstein-Greene-Kruskal/Cnoidal modes, etc.) formed out of the driven nonlinear VP system, assuming local flattening of electron and ion distributions, the real part of the plasma dispersion function for arbitrary ratios of ion to electron masses and temperatures is solved, which is known to be accurate in the low amplitude, harmonic limit, as pointed out by Schamel [Phys. Plasmas 19, 020501 (2012)].

Interface-phonon–electron interaction potentials and dispersion relations in III-nitride-based structures

In dimensionally confined multilayer heterostructures, phonons that are joint modes of the materials composed of these heterostructures are known to exist over specific frequency ranges. These modes, known as interface phonons, can exhibit phonon-electron interactions that are enhanced as the thicknesses of the layers of the heterostructure are reduced in size to about 10 nm or less. These modes have been shown to be important in phonon engineering and have been applied in optoelectronic and electronic devices, primarily for semiconductor heterostructures with underlying cubic lattices, with few studies existing for heterostructures based on wurtzite III-nitride. Motivated by applications of interface modes in ternary-based nitride structures, such as heat transport, this paper presents generalized expressions for the phonon-electron Fröhlich interactions as well as the dispersion relations for these joint modes for the technologically important case of III-nitride materials. Frequency conditions are found to restrict the existence of interface modes as illustrated through several structures.

Electromagnetic Viscous-Resistive-Drift-Wave Instability in Burning Plasma

Drift wave instabilities (DWI) might be take a part for anomalous transport in modern day tokamaks due to contributions of edge turbulence and zonal flows. Experimentally, it is found that micro-level turbulence (associated with two-fluid dynamics) braced with macro-level (associated with single-fluid dynamics) magnetohydrodynamics-type processes. In this paper, additional two-fluid effect viz. ion viscosity on the electromagnetic (EM) linear resistive drift wave instability is analyzed by using a two-fluid MHD model. A modify dispersion relation for EM drift modes in a nonuniform magnetized plasma is derived, taken into account equilibrium pressure gradients, effect of finite ion-sound gyro-radius associated with electron–ion decoupling and viscous effect due to ions. The dispersion relation is then analyzed both analytically as well as numerically. It is shown, how additional two-fluid effects modify the growth rate for DWI in different regimes. The standard resistive drift-Alfven mode is reproduced in the cold ion case. Moreover, it is estimated that these effects provide the possibility of novel effects on EM instabilities in a nonuniform magnetized plasma. The results should be useful in the interpretation of EM fluctuations in nonuniform magneto-plasmas in which resistivity is a key element in calculations of dissipative drift instabilities.

Electromagnetic wave propagation in a superconducting parallel-plate waveguide filled with an indefinite medium

Abstract The electromagnetic wave propagation is analysed in a superconducting parallel-plate waveguide filled with an indefinite medium. The dispersion relations of transverse electric and transverse magnetic wave modes are derived by using the Meissner boundary conditions. The different cases of these wave modes are discussed by choosing the appropriate signs of the anisotropic parameters of the indefinite medium. In this connection, the regions of propagation/non-propagation are numerically analysed by plotting the phase velocity versus propagation frequency.

Optimization of Spin-Wave Propagation with Enhanced Group Velocities by Exchange-Coupled Ferrimagnet-Ferromagnet Bilayers

We report broadband spectroscopy and numerical analysis by which we explore propagating spin waves in a magnetic bilayer consisting of a 23 nm thick permalloy film deposited on 130 nm thick $Y_{3}Fe_{5}O_{12}$. In the bilayer, we observe a characteristic mode that exhibits a considerably larger group velocity at small in-plane magnetic field than both the magnetostatic and perpendicular standing spin waves. Using the finite element method, we confirm the observations by simulating the mode profiles and dispersion relations. They illustrate the hybridization of spin wave modes due to exchange coupling at the interface. The high-speed propagating mode found in the bilayer can be utilized to configure multi-frequency spin wave channels enhancing the performance of spin wave based logic devices.

Holographic response of electron clouds

In order to make progress towards more realistic models of holographic fermion physics, we use gauge/gravity duality to compute the dispersion relations for quasinormal modes and collective modes for the electron cloud background, i.e. the non-zero temperature version of the electron star. The results are compared to the corresponding results for the Schwarzschild and Reissner-Nordström black hole backgrounds, and the qualitative differences are highlighted and discussed.

Temperature-dependent ultraviolet Raman scattering and anomalous Raman phenomenon of AlGaN/GaN heterostructure.

Temperature-dependent ultraviolet (UV) Raman scattering from AlGaN/GaN heterostructure is investigated. Compared to the visible Raman spectrum, four new peaks at 600, 700, 780, and 840 cm-1 are observed in the UV Raman spectrum. The peak at 780 cm-1 is from the AlGaN A1(LO) mode. According to the calculated dispersion relations of the interface phonon modes in the AlGaN/GaN heterostructure, the peaks at 600 and 840 cm-1 correspond to interface phonon modes. Meanwhile, the peak at 700 cm-1 is attributed to the disorder-active mode near the 2DEG interface. Due to the near-resonant enhancement effect, the intensities of the GaN A1(LO) mode, interface phonon modes, disorder active mode and the AlGaN A1(LO) mode exhibit different temperature dependence. Furthermore, the frequencies of the interface phonon modes and the disorder active mode show anomalous temperature dependence, which can be attributed to the strong built-in electric field near the 2DEG interface.

Exotic holographic dispersion

For strongly interacting systems, where perturbation theory is not applicable, holographic duality is a powerful framework for computing e.g. dispersion relations. Using the standard Reissner-Nordström black hole as a holographic model for a (strange) metal, we obtain exotic dispersion relations for both plasmon modes and quasinormal modes for certain intermediate values of the charge of the black hole.The obtained dispersion relations show dissipative behavior which we compare to the generic expectations from the Caldeira-Leggett model for quantum dissipation. Based on these considerations, we investigate how holography can predict higher order corrections for strongly coupled physics.

Direct detection of multiple backward volume modes in yttrium iron garnet at micron scale wavelengths

Using a set of wave-vector-specific multielement antennas, we have characterized the dispersion of spin waves in an yttrium iron garnet film at submicron lengths and resolved the dispersion relations of multiple backward volume modes, particularly in the region of their minima. The techniques developed now facilitate the characterization of spin waves at length scales limited only by available lithography and at a spectral resolution that generally exceeds that of Brillouin scattering. The data obtained are in excellent agreement with theoretical predictions based on a model Hamiltonian.

Infrared stability of ground states of spin-orbit coupled Bose–Einstein condensates

We proved that the spin-1 Bose–Einstein condensate with one-dimensional spin-orbit coupling at the tricritical point is stable against excitations of Goldstone modes. The dispersion relations of these modes are anisotropic and cubic in some directions in the momentum space, which are much softer than the ordinary ones with linear form. A particular scaling form of the quantum depletions fraction on spin-orbit coupling strength is found, which is due to the special form of the dispersion relations of the Goldstone modes.