Surface Eigenmodes Research Articles

Magnetospheric “magic” frequencies as magnetopause surface eigenmodes

The persistent so‐called “magic” magnetospheric frequencies are thought to be either directly driven by monochromatic solar wind pressure fluctuations or resonantly excited global (cavity/waveguide) or magnetopause surface eigenmodes. We distinguish between these cases by statistically investigating, using simultaneous observations, the magnetospheric response to jets in the subsolar magnetosheath. The broadband jets do not exhibit discrete frequencies but do drive waves at the discrete magic frequencies, with both direct and resonant driving. We show that the expected fundamental frequencies of magnetopause surface eigenmodes have two preferential values over a wide range of upstream conditions, corresponding to fast and slow solar wind, and that their harmonics are in good agreement with the magic frequencies. We also show that the waves are largely inconsistent with global modes outside the plasmasphere. Thus, we conclude that these magic frequencies are most likely due to magnetopause surface eigenmodes.

Eigenanalysis of Electromagnetic Structures Based on the Finite Element Method

This article presents a review of our research effort on the eigenanalysis of open radiating waveguides and closed resonating structures. A two dimensional (2-D) hybrid Finite Element method in conjunction with a cylindrical harmonics expansion is established to formulate the open waveguide generalized eigenvalue problem. The key element of this approach refers to the adoption of a vector Dirichlet-to-Neumann map to rigorously enforce the continuity of the two field expansions along a truncation surface. The resulting algorithm was able to evaluate both surface and leaky eigenmodes. The eigenanalysis of three dimensional (3-D) structures involves vast research challenges, especially when they are electrically large and open-radiating. The effort herein is focused on the electrically large case including the losses due to the finite conductivity of metallic walls and objects as well as the loading material losses. The former is introduced through impedance or Leontovich boundary condition, resulting to a non-linear-polynomial generalized eigenvalue problem. A straightforward linearization solution is adopted along with a more efficient alternative technique which mimics analytical approaches. For this one the linear eigenproblem formulated assuming metals as perfect electric conductors is initially solved and their finite conductivity is accounted through impedance boundary conditions enforced locally on the resulting eigenvectors. Finally, some numerical results are presented to verify the performance of these methodologies along with a discussion on their possibilities for extension to open 3D structures as well as to characteristic modes eigenanalysis.

Torus in a magnetic field: curvature-induced surface states

We study the quantum dynamics of a particle bound on a torus in the presence of an external magnetic field. We derive and discuss the effective Schrödinger equation for the surface eigenmodes and the corresponding quantum effective potential which is periodic and exhibits quantum anti-centrifugal force for non-vanishing angular momentum quantum numbers. An energy band structure of pure geometrical origin emerges naturally which can be tested experimentally in semiconducting as well as carbon nanotori.

Possibility of excitation of azimuthal surface waves in a magnetized plasma by annular ion beams

Excitation of the azimuthal surface eigenmodes with the extraordinary polarization for the ion plasma component is shown to be possible in cylindrical waveguides with metal walls, filled partially by a cold magnetoactive neon plasma. The interaction of the oscillations with the flows of alpha particles rotating around the plasma column in a narrow layer that separates the plasma from the waveguide walls is studied. If the external magnetic field is strong enough, the resonance interaction of the beam with the waves can be realized for three minimum values of the azimuthal mode number when the wave frequency normalized by neon ion cyclotron frequency is close to the factor of five (mNe/mHe ≈ 5).

Surface plasmon polaritons in attenuated total reflection systems with metamaterials: homogeneous problem

In this work we study the propagation characteristics of surface plasmon polaritons (surface eigenmodes) of Kretschmann attenuated total reflection structures with metamaterials. Contrary to the conventional case, in which surface polaritons with positive phase velocity appear at the boundary of a metallic guide, we consider a case where surface polaritons propagate along the boundary of a transparent metamaterial guide with negative refractive index. Depending on the choice of the metamaterial constitutive parameters, these polaritons can have either positive (forward) or negative (backward) phase velocity. For both situations we show numerical examples that illustrate the variation of the real and imaginary parts of the propagation constant with the guide width and the spatial distributions of energy.

Whistler eigenmodes of magnetic flux tubes in a magnetoplasma

Guided propagation of whistler waves along cylindrical non-uniformities of a dc magnetic field is studied within the framework of a full-wave approach. Conditions are revealed under which such guiding structures, commonly known as magnetic flux tubes, can support volume and surface eigenmodes in the whistler range. The dispersion properties and field structures of whistler eigenmodes guided by flux tubes with an enhanced magnetic field are calculated and analysed for plasma parameters typical of laboratory experiments. The results obtained are useful in understanding the basic features of whistler wave guidance by magnetic flux tubes and can be applied to interpreting the data of the relevant experiments.

Whistler waves guided by density depletion ducts in a magnetoplasma

The guided propagation of whistler waves along cylindrical density depletion ducts in a magneto-plasma is studied. It is shown that, under certain conditions, such ducts can support volume and surface eigenmodes. The dispersion properties and field structure of whistler modes guided by density depletion ducts are analyzed. The effect of collisional losses in the plasma on the properties of modes is discussed.

Smith–Purcell frequency multiplier with synchronization of radiation from a wide electron beam

An orotronlike feedback can provide a significant increase in the selectivity and power of frequency-multiplied Smith–Purcell radiation of the electron bunches formed in the course of self-excitation of a grating surface eigenmode. This method looks promising for efficient terahertz generation from both weakly and mildly relativistic electron beams.

Resonant effect of the noncircular shape of the plasma surface on the dispersion properties of extraordinary azimuthal surface modes in magnetoactive waveguides

A theoretical study is made of the resonant effect of the shape of the cross section of the plasma column on the propagation of a packet of extraordinary electromagnetic waves with a zero axial wavenumber in a circular-cross-section cylindrical metal waveguide in an axial magnetic field. The waveguide is assumed to be partially filled with a plasma. The effect of the noncircular shape of the plasma cross section on the dispersion properties of surface eigenmodes propagating strictly transverse to the external magnetic field is investigated by the method of successive approximations for the case in which the angular period of the wave perturbations is twice the ripple period of the interface between the plasma and the dielectric. In this resonant case, the fields and eigenfrequencies of the eigenmodes are determined to second order in the small parameter describing the rippling of the plasma-dielectric interface.

Surface plasmon-like modes on structured perfectly conducting surfaces

Surface plasmon-like (SPL) modes are the electromagnetic surface eigenmodes supported by the structured perfectly conducting surfaces. The standard eigenvalue-solving method is adopted to solve these SPL modes. The field patterns of the SPL modes in the square holes for in-plane wavevectors k(x) = 2pi / 2d and k(x) = 2pi /d are TE(10)-like and TE(11), respectively. However, the field patterns can no longer be identified as any particular waveguide mode for other in-plane wavevectors. The dispersion relations of the SPL modes are obtained numerically. The change in mode character with wavevector prevents the dispersion relation from being derived by assuming only the fundamental mode in the holes. On a thin perfect conductor perforated with structures, the SPL mode splits into a high-frequency anti-symmetric mode and a low-frequency symmetric mode, which is caused by the mutual interaction of the electromagnetic evanescent fields on both sides.

A plasmaspheric cavity resonance in a longitudinally non-uniform plasmasphere

Power spectra of a plasmaspheric cavity resonance (strictly, a plasmaspheric virtual resonance) in a longitudinally non-uniform plasmasphere are calculated. It is shown that the spectra depend on longitude. Therefore, a cavity resonance mode can have local time depending spectra when the plasmasphere is non-uniform in a longitudinal direction. This fact concludes that the local time dependent peak frequencies of the mid- and low-latitude Pi2 pulsations discussed by Kosaka et al. (2002) are also explained by the cavity resonance model. We also discuss that the surface eigenmode can be a possible generation mechanism for Pi2 pulsations localized in a longitudinal direction.

More concerning the anelastic and subseismic approximations for low-frequency modes in stars

Two approximations, namely the subseismic approximation and the anelastic approximation, are used to filter out the acoustic modes when computing low-frequency modes of a star (gravity modes or inertial modes). In a previous paper, we observed that the anelastic approximation gave eigenfrequencies much closer to the exact ones than the subseismic approximation. Here, we try to clarify this behaviour and show that it is a result of the different physical approach taken by each approximation. On the one hand, the subseismic approximation considers the low-frequency part of the spectrum of (say) gravity modes and turns out to be valid only in the central region of a star; on the other hand, the anelastic approximation considers the Brunt–Vaisala frequency to be asymptotically small and makes no assumption concerning the order of the modes. Both approximations fail to describe the modes in the surface layers but eigenmodes issued from the anelastic approximation are closer to those including acoustic effects than their subseismic equivalent. We conclude that, as far as stellar eigenvalue problems are concerned, the anelastic approximation is better suited for simplifying the eigenvalue problem when low-frequency modes of a star are considered, while the subseismic approximation is a useful concept when analytic solutions of high-order low-frequency modes are needed in the central region of a star.

3D multispecies nonlinear perturbative particle simulations of collective processes in intense particle beams for heavy ion fusion

Collective processes in intense charged particle beams for heavy ion fusion are studied using a 3D multispecies nonlinear perturbative particle simulation method, which solves self-consistently the nonlinear Vlasov–Maxwell equations. The newly-developed Beam Equilibrium Stability and Transport code is used to simulate the nonlinear stability properties of intense beam propagation, surface and body eigenmodes in a high-intensity beam, and the electron-ion two-stream instability, which occurs when a small population of (unwanted) electrons is present in the system.

Three-dimensional multispecies nonlinear perturbative particle simulations of collective processes in intense particle beams

Collective processes in intense charged particle beams described self-consistently by the Vlasov-Maxwell equations are studied using a 3D multispecies nonlinear perturbative particle simulation method. The newly developed beam equilibrium, stability, and transport (BEST) code is used to simulate the nonlinear stability properties of intense beam propagation, surface eigenmodes in a high-intensity beam, and the electron-proton ($e\ensuremath{-}p$) two-stream instability observed in the Proton Storage Ring (PSR) experiment. Detailed simulations in a parameter regime characteristic of the PSR experiment show that the dipole-mode two-stream instability is stabilized by a modest spread (about 0.1%) in axial momentum of the beam particles.

3D nonlinear perturbative particle simulations of two-stream collective processes in intense particle beams

Collective processes in intense charged particle beams described self-consistently by the Vlasov–Maxwell equations are studied using a 3D multispecies nonlinear perturbative particle simulation method. The newly-developed Beam Equilibrium Stability and Transport (BEST) code has been used to simulate the nonlinear stability properties of intense beam propagation, surface eigenmodes in a high-intensity beam, and the electron–proton (e–p) two-stream instability observed in the Proton Storage Ring (PSR).

Magnetoelastic waves in a bicrystalline gap structure under a bias magnetic field

SH acoustic fields in transversely isotropic media with magnetoelastic coupling due to a linearized magnetostriction are considered for a bicristalline structure with a gap. The surface and pseudosurface eigenmodes and the conditions of their existence are described. A study is carried out of the resonant excitation of the surface wave in one crystallite by means of a pumping bulk wave in the other crystallite. The potentialities of a control of wave parameters by means of the bias magnetic field are considered.

Instabilities in localized non-uniform charged dust streams in cold plasmas

Surface eigenmodes in a dusty plasma, where the dust is confined to a particular region, modelled as a uniform slab with non-uniform smooth boundary layers, are discussed. Inside this region, electron depletion occurs, while outside it, the plasma is just a normal uncontaminated plasma. In addition, the dust component can flow with respect to the background plasma, as a first approximation to cometary tails, where there is a notable difference between the fast flowing solar wind and the slow moving dust tail, viewed in the comet frame. The equilibrium densities and flow are non-uniform and the description involves a space-dependent dielectric function, which indicates the possibility of singular points, where eigenmodes resonate with local plasma oscillations. Surface eigenmodes on the slab are obtained analytically in the limit of long wavelengths, and these give rise to two distinct frequency domains, both having three different wave solutions. One of these refers to plasma surface waves, unaffected by the dust flow. The other two lead to convective surface modes, which become unstable for large flow speeds, akin to Buneman-type instabilities. A detailed study is made of the resonant processes in the boundary layers, including damping and growth rates.

Energy loss functions for electron energy loss spectroscopy

Losses to surface excitations affect experimental data in several different kinds of spectroscopies and have been considered in detail by various workers. We discuss and compare calculations using commonly assumed response functions. The boundary (begrenzung) effect, originating in the orthogonality of surface and bulk eigenmodes, manifests interesting interference in the loss functions. The variation of static electron density in the selvage of a metal is known to affect the dispersion of surface excitations. The effect of this structure on energy loss spectra is studied. Analytical forms of the kind studied can be employed in practical data analysis if parameterized to correspond with more rigorous, but time-consuming, numerical results such as those found from density functional methods.

Surface Trapped X Rays: Whispering-Gallery Modes atλ=0.7Å

X-ray bound states trapped on a curved surface are realized by coupling subangstrom photons at grazing angles into a bent silicon wafer with adjustable radius. At small radii of curvature the usual ray approximation breaks down and new phenomena associated with wave optical behavior of x-ray surface eigenmodes are revealed. For such samples, tunneling is shown to extinguish all but the ground state surface eigenmode, whose presence may be detected after extremely long distances of propagation along the surface.

The three‐dimensional seismological model a priori constrained: Confrontation with seismic data

We compare the predictions of an a priori model of the upper mantle with seismic observations of surface waves and eigenmodes. The 3‐Dimensional Seismological Model A Priori Constrained (3SMAC) has been developed by Nataf and Ricard [1996]. It is based on the interpretation by geodynamicists of the near surface layers of the Earth; on distributions of temperature, pressure, and composition as a function of depth; and then on estimates of seismic parameters (density, velocities, attenuations) from solid state laboratory measurements as a function of temperature and pressure. The 3SMAC predictions are confronted with observations consisting of phase velocities for Love and Rayleigh waves in the period range of 70–250 s [Montagner and Tanimoto, 1990]. We first show that tomographic inversions applied to 3SMAC synthetics induce a strong smoothing of the heterogeneities. This casts doubt on the meaning of the spectra of mantle heterogeneities revealed by tomography. We then show that most of the Love and Rayleigh fundamental mode observations for periods less than 200 s are satisfactorily predicted by 3SMAC. The major differences come from the seismic velocities under the Red Sea and Southeast China, which are much slower than what is estimated from 3SMAC, as well as those under Greenland, which are not as fast as the other cratonic areas. Because the lithosphere is thinner than 100 km under oceans and thinner than 300 km under continents in 3SMAC, we suggest that the existence of deeper lithospheric anomalies as proposed in many tomographic models is mostly due to a spurious effect of the inversion rather than implied by surface wave data. Half of the variance of the degree 2 anomaly mapped by low‐degree eigenmode observations can be explained by lithospheric velocity structures. The other half is highly correlated with the distribution of deep slabs, but its amplitude is a factor of 3 or 4 larger than that predicted by 3SMAC. The lithospheric anomalies present a degree 6 pattern well correlated with the distribution of hotspots even when the thermal anomalies that could be associated with plumes are not included in 3SMAC. Our results emphasize the importance of giving very close attention to “surface corrections” in tomographic models.