Radial Wavenumber Research Articles

Electromagnetic effects on geodesic acoustic modes

By using the full electromagnetic drift kinetic equations for electrons and ions, the general dispersion relation for geodesic acoustic modes (GAMs) is derived incorporating the electromagnetic effects. It is shown that m = 1 harmonic of the GAM mode has a finite electromagnetic component. The electromagnetic corrections appear for finite values of the radial wave numbers and modify the GAM frequency. The effects of plasma pressure βe, the safety factor q, and the temperature ratio τ on GAM dispersion are analyzed.

3D cosmic shear: cosmology from CFHTLenS

This paper presents the first application of 3D cosmic shear to a wide-field weak lensing survey. 3D cosmic shear is a technique that analyses weak lensing in three dimensions using a spherical harmonic approach, and does not bin data in the redshift direction. This is applied to CFHTLenS, a 154 square degree imaging survey with a median redshift of 0.7 and an effective number density of 11 galaxies per square arcminute usable for weak lensing. To account for survey masks we apply a 3D pseudo-Cl approach on weak lensing data, and to avoid uncertainties in the highly non-linear regime, we separately analyse radial wave numbers k<=1.5h/Mpc and k<=5.0h/Mpc, and angular wavenumbers l~400-5000. We show how one can recover 2D and tomographic power spectra from the full 3D cosmic shear power spectra and present a measurement of the 2D cosmic shear power spectrum, and measurements of a set of 2-bin and 6-bin cosmic shear tomographic power spectra; in doing so we find that using the 3D power in the calculation of such 2D and tomographic power spectra from data naturally accounts for a minimum scale in the matter power spectrum. We use 3D cosmic shear to constrain cosmologies with parameters OmegaM, OmegaB, sigma8, h, ns, w0, wa. For a non-evolving dark energy equation of state, and assuming a flat cosmology, lensing combined with WMAP7 results in h=0.78+/-0.12, OmegaM=0.252+/-0.079, sigma8=0.88+/-0.23 and w=-1.16+/-0.38 using only scales k<=1.5h/Mpc. We also present results of lensing combined with first year Planck results, where we find no tension with the results from this analysis, but we also find no significant improvement over the Planck results alone. We find evidence of a suppression of power compared to LCDM on small scales 1.5 < k < 5.0 h/Mpc in the lensing data, which is consistent with predictions of the effect of baryonic feedback on the matter power spectrum.

Reconstructing the thermal Sunyaev–Zel'dovich effect in 3D

The thermal Sunyaev-Zel'dovich (tSZ) effect measures the line-of-sight projection of the thermal pressure of free electrons and lacks any redshift information. By cross correlating the tSZ effect with an external cosmological tracer we can recover a good fraction of this lost information. Weak lensing (WL) is thought to provide an unbiased probe of the dark Universe, with many WL surveys having sky coverage that overlaps with tSZ surveys. Generalising the tomographic approach, we advocate the use of the spherical Fourier-Bessel (sFB) expansion to perform an analysis of the cross-correlation between the projected (2D) tSZ Compton $y$-parameter maps and 3D weak lensing convergence maps. We use redshift dependent linear biasing and the halo model as a tool to investigate the tSZ-WL cross-correlations in 3D. We use the Press-Schechter (PS) and the Sheth-Tormen (ST) mass-functions in our calculations, finding that the results are quite sensitive to detailed modelling. We provide detailed analysis of surveys with photometric and spectroscopic redshifts. The signal-to-noise (S/N) of the cross-spectra $\mathcal{C}_{\ell} (k)$ for individual 3D modes, defined by the radial and tangential wave numbers $(k;\ell)$, remains comparable to, but below, unity though optimal binning is expected to improve this. The results presented can be generalised to analyse other CMB secondaries, such as the kinetic Sunyaev-Zel'dovich (kSZ) effect.

Short wavelength turbulence generated by shear in the quiescent H-mode edge on DIII–D

A region of turbulence with large radial wavenumber (krρs&amp;gt;1) is found in the high-shear portion of the plasma edge in Quiescent H-mode (QH-mode) on DIII–D using the Phase Contrast Imaging (PCI) diagnostic. At its peak outside the minimum of the Er well, the turbulence exhibits large amplitude ñ/n∼40%, with large radial wavenumber |k¯r/k¯θ|∼11 and short radial correlation length Lr/ρi∼0.2. The turbulence inside the Er well minimum is characterized by the opposite sign in radial wavenumber from that of turbulence outside the minimum, consistent with the expected effects of velocity shear. The PCI diagnostic provides a line-integrated measurement of density fluctuations, so data are taken during a scan of plasma position at constant parameters to allow the PCI to sample a range in kr/kθ. Analysis of the Doppler shift and plasma geometry allows the turbulence to be localized to a narrow region 3 mm inside the last closed flux surface, outside the minimum of the Er well. The turbulence amplitude and radial wavenumber and correlation length are determined by fitting the PCI results with a simple non-isotropic turbulence model with two regions of turbulence. These PCI observations, made in QH-mode, are qualitatively similar to those made in standard edge localized modes (ELM)-free H-mode and between ELMs, suggesting a similar role for large kr turbulence there.

Electromagnetic gyrokinetic turbulence in finite-beta helical plasmas

A saturation mechanism for microturbulence in a regime of weak zonal flow generation is investigated by means of electromagnetic gyrokinetic simulations. The study identifies a new saturation process of the kinetic ballooning mode (KBM) turbulence originating from the spatial structure of the KBM instabilities in a finite-beta Large Helical Device (LHD) plasma. Specifically, the most unstable KBM in LHD has an inclined mode structure with respect to the mid-plane of a torus, i.e., it has a finite radial wave-number in flux tube coordinates, in contrast to KBMs in tokamaks as well as ion-temperature gradient modes in tokamaks and helical systems. The simulations reveal that the growth of KBMs in LHD is saturated by nonlinear interactions of oppositely inclined convection cells through mutual shearing as well as by the zonal flow. The saturation mechanism is quantitatively investigated by analysis of the nonlinear entropy transfer that shows not only the mutual shearing but also a self-interaction with an elongated mode structure along the magnetic field line.

Dipole-Exchange Spin Waves in a Ferromagnetic Nanotube

Spin waves in a cylindrical ferromagnetic nanotube are studied. A nanotube with an external magnetic field applied parallel to its symmetry axis is considered. A linearized Landau–Lifshitz equation in the magnetostatic approximation is used with regard for the magnetic dipole-dipole interaction, exchange interaction, and anisotropy effects. As a result, the dispersion relation and the radial wavenumber spectrum for spin waves in the above-described nanotube are found. From the radial wavenumber spectrum, limitations on the transverse-angular modes are defined.

Local stability of a gravitating filament: a dispersion relation

Filamentary structures are ubiquitous in astrophysics and are observed at various scales. On a cosmological scale, matter is usually distributed along filaments, and filaments are also typical features of the interstellar medium. Within a cosmic filament, matter can contract and form galaxies, whereas an interstellar gas filament can clump into a series of bead-like structures which can then turn into stars. To investigate the growth of such instabilities, we derive a local dispersion relation for an idealized self-gravitating filament, and study some of its properties. Our idealized picture consists of an infinite self-gravitating and rotating cylinder with pressure and density related by a polytropic equation of state. We assume no specific density distribution, treat matter as a fluid, and use hydrodynamics to derive the linearized equations that govern the local perturbations. We obtain a dispersion relation for axisymmetric perturbations and study its properties in the (k_R, k_z) phase space, where k_R and k_z are respectively the radial and longitudinal wavenumbers. While the boundary between the stable and unstable regimes is symmetrical in k_R and k_z and analogous to the Jeans criterion, the most unstable mode displays an asymmetry that could constrain the shape of the structures that form within the filament. Here the results are applied to a fiducial interstellar filament, but could be extended for more astrophysical systems such as cosmological filaments and tidal tails.

THE STABILITY OF TIDALLY DEFORMED NEUTRON STARS TO THREE- AND FOUR-MODE COUPLING

It has recently been suggested that the tidal deformation of a neutron star excites daughter p- and g-modes to large amplitudes via a quasi-static instability. This would remove energy from the tidal bulge, resulting in dissipation and possibly affecting the phase evolution of inspiralling binary neutron stars and hence the extraction of binary parameters from gravitational wave observations. This instability appears to arise because of a large three-mode interaction among the tidal mode and high-order p- and g-modes of similar radial wavenumber. We show that additional four-mode interactions enter into the analysis at the same order as the three-mode terms previously considered. We compute these four-mode couplings by finding a volume-preserving coordinate transformation that relates the energy of a tidally deformed star to that of a radially perturbed spherical star. Using this method, we relate the four-mode coupling to three-mode couplings and show that there is a near-exact cancellation between the destabilizing effect of the three-mode interactions and the stabilizing effect of the four-mode interaction. We then show that the equilibrium tide is stable against the quasi-static decay into daughter p- and g-modes to leading order. The leading deviation from the quasi-static approximation due to orbital motion of the binary is considered; while it may slightly spoil the near-cancellation, any resulting instability timescale is at least of order the gravitational-wave inspiral time. We conclude that the p-/g-mode coupling does not lead to a quasi-static instability, and does not impact the phase evolution of gravitational waves from binary neutron stars.

Spin-wave spectra and stability of the in-plane vortex state in two-dimensional magnetic nanorings

We study theoretically two-dimensional nanorings assumed to have the in-plane vortex magnetic configuration. Using a discrete dipole model we examine the spectrum of normal spin-wave modes vs. the dipolar-to-exchange interaction ratio. We systematize the spin-wave excitations by their azimuthal and radial wave numbers. The lowest-frequency mode, the fundamental (quasiuniform) mode, and the mode hybridization are analyzed; the discussion of the influence of effective pinning at the ring boundaries is provided as well. We study the stability of the in-plane vortex state and discuss the role of the size of the ring and the type of lattice arrangement of the magnetic moments within it. To facilitate comparison with our results we provide the relationships between microscopic parameters, used in our model, and those used in the case of continuous medium.

Efficient Computation of the Coupling Between a Vertical Line Source and a Slot

A novel spectral formulation is proposed here for the coupling integral between a cylindrical wave with arbitrary radial wavenumber and azimuthal dependence, and a slot placed on a plane orthogonal to the wavefront. Such a kind of integral is massively encountered in electromagnetic modeling of stratified structures comprising slots and vertical pins or vias. The twofold spatial integral defining the coupling is transformed into an equivalent onefold spectral integral, the integration path of which is selected to obtain Gaussian decay of the integrand. Both propagating and evanescent cylindrical modes are considered. An arbitrary stratification orthogonal to the slot plane can be considered, as well as an arbitrary current on the slot. Numerical comparisons against the standard spatial approach are shown to validate the new formulation, and its advantage in terms of computation cost is investigated in depth.

Geodesic acoustic mode excitation by drift waves in tokamak plasmas with toroidal rotation

Nonlinear excitation of geodesic acoustic mode by drift waves is investigated in toroidally rotating tokamak plasmas using the ideal magnetohydrodynamic equations. It is found that both the radial wave number and the nonlinear growth rate of the driven geodesic acoustic mode increase with the speed of the toroidal rotation, where the decisive factor is the frequency shift of the geodesic acoustic mode induced by the toroidal rotation. The additional nonlinear terms induced by the toroidal rotation velocity make little effect, even though they promote the nonlinear excitation at all times.

Combining a Kinematic Fractal Source Model with Hybrid Green's Functions to Model Broadband Strong Ground Motion

Abstract A hybrid empirical method is proposed to simulate broadband strong ground motion that combines a kinematic complex source model with both numerical and empirical Green’s functions. The kinematic approach is based on a composite source model description where subevents are generated using a fractal distribution of sizes. The subevents are set up with a size‐dependent rise time. Each elementary source is described as a crack‐type slip model that starts radiating when the rupture front reaches the nucleation point located randomly inside a size‐dependent nucleation region. The synthetic acceleration spectra follow the ω 2 model, and the spectral amplitudes are scaled by a frequency‐dependent directivity coefficient. In this study, the hypothesis of constant stress drop of subevents is released to better model the high‐frequency level radiated by the source. Taking advantage of small‐magnitude events, synthetic seismograms are computed using hybrid Green’s functions (HGF) to model the impulsive response of the medium. The procedure computes HGF for each subfault combining the numerical low‐frequency and the empirical high‐frequency Green’s functions with appropriate amplitude and phase correction (geometrical spreading and time delays due to the S ‐wave travel‐time propagation). This methodology is applied to simulate the strong ground motions recorded during the 1997 M w 5.9 Yamaguchi‐Ken, Hokubu, Japan, earthquake. Some of the finite‐source rupture parameters (e.g., rupture velocity, asperity size, and seismic moment) were chosen according to previously published studies conducted on this event. Only random generation of k −2 composite slip distributions was allowed ( k being the radial wavenumber), to model heterogeneous slip while mimicking the main asperity size and location imaged. Comparisons of predicted and observed strong‐motion characteristics show that predictions are largely improved, when both HGF and variable stress drop of subevents are used.

A new paradigm for E × B velocity shear suppression of gyro-kinetic turbulence and the momentum pinch

Detailed studies of the non-linear radial wavenumber spectrum of electric potential fluctuations in gyro-kinetic plasma turbulence simulations have led to a new paradigm that is capable of computing the momentum pinch quasilinearly. It is found that shear in the E × B velocity Doppler shift suppresses turbulence by inducing a shift in the peak of the radial wavenumber spectrum, and a reduction in the amplitude. An analytic model of the process is used to understand the roles of the sheared velocity and the non-linear mode coupling. The analytic model leads to a simple formula that fits the non-linear spectrum and only depends on the spectral average shift in the radial wavenumber. This ‘spectral shift’ model is a new paradigm that radial parity breaking is the fundamental mechanism that suppresses the turbulence through a radial wavenumber shift. The E × B velocity shear is one of a number of radial parity breaking mechanisms. Using a model of the spectral shift the toroidal Reynolds stress due to the E × B velocity shear can be computed for the first time with a quasilinear model. It is shown that, when diamagnetic and neoclassical contributions to the parallel flows are included, the E × B velocity shear term in the toroidal Reynolds stress allows the sign of the intrinsic toroidal rotation to change. Simulations of the co-current and balanced neutral beam injection phase of a DIII-D discharge using the quasilinear model show good agreement with experiment.

Observation of nonlinear couplings between coexisting kinetic geodesic acoustic modes in the edge plasmas of the HT-7 tokamak

Coexisting multi-geodesic acoustic modes (GAMs), especially coexisting dual GAMs, are observed and studied through Langmuir probe arrays at the edge plasmas of the HT-7 tokamak with lithium-coated walls. The dual GAMs are named a low-frequency GAM (LFGAM) and a high-frequency GAM (HFGAM), and it is found that within the measuring range, the HFGAM propagates outwards while the LFGAM propagates both inwards and outwards with their central frequencies nearly unchanged, and both modes have maximum amplitudes at positions with radial wavenumbers close to zero; meanwhile, the two positions happen to be where the continuum GAM frequency is closest to the central frequencies of the LFGAM and the HFGAM. These characteristics are consistent with those of a kinetic GAM converted from a continuum GAM. The nonlinear couplings between the LFGAM and the HFGAM are also analysed. In this study, we observed not only the interaction between the LFGAM and the HFGAM, but also the self-coupling of the GAM with the beat frequency between them, as well as the coupling between the LFGAM and an unknown mode at ∼50 kHz. These nonlinear interactions may play important roles during the saturation process of GAMs. Additionally, amplitude correlation analyses of multi-GAMs indicate that second harmonic GAMs are probably generated from the self-interaction of fundamental GAMs.

On Sound Generation in Cylindrical Flow Ducts with Non-Uniform Wall Impedance

The use of acoustic liners is a common means of noise reduction in jet engine exhausts. The quest for more effective sound absorption mechanisms in cylindrical ducts has led to the consideration of non-uniform liners, with impedance varying circumferentially, axially, or in both directions. The present paper is based on the theory of mode coupling in a non-uniformly lined cylindrical duct and considers the complementary problem of generation of sound or excitation of coupled modes by a source distribution. The sound field due to an arbitrary source distribution is obtained as a superposition of eigenfunctions corresponding to complex eigenvalues for the radial wavenumbers and natural frequencies taking into account that the radial, axial and azimuthal modes are coupled by the non-uniform wall impedance, and including resonant and non-resonant cases. The waveforms are illustrated for point monopole, dipole and quadrupole sources and a continuous monopole distribution. It is shown that a non-uniform liner provides a greater attenuation than a uniform liner with the same average impedance if it is ‘well-matched’ to the sound field, that is, if it has higher impedance at the peaks and lower at the nodes of the standing modes.

Dispersion analysis of leaky guided waves in fluid-loaded waveguides of generic shape

A fully coupled 2.5D formulation is proposed to compute the dispersive parameters of waveguides with arbitrary cross-section immersed in infinite inviscid fluids.The discretization of the waveguide is performed by means of a Semi-Analytical Finite Element (SAFE) approach, whereas a 2.5D BEM formulation is used to model the impedance of the surrounding infinite fluid. The kernels of the boundary integrals contain the fundamental solutions of the space Fourier-transformed Helmholtz equation, which governs the wave propagation process in the fluid domain. Numerical difficulties related to the evaluation of singular integrals are avoided by using a regularization procedure. To improve the numerical stability of the discretized boundary integral equations for the external Helmholtz problem, the so called CHIEF method is used.The discrete wave equation results in a nonlinear eigenvalue problem in the complex axial wavenumbers that is solved at the frequencies of interest by means of a contour integral algorithm. In order to separate physical from non-physical solutions and to fulfill the requirement of holomorphicity of the dynamic stiffness matrix inside the complex wavenumber contour, the phase of the radial bulk wavenumber is uniquely defined by enforcing the Snell–Descartes law at the fluid–waveguide interface.Three numerical applications are presented. The computed dispersion curves for a circular bar immersed in oil are in agreement with those extracted using the Global Matrix Method. Novel results are presented for viscoelastic steel bars of square and L-shaped cross-section immersed in water.

Time evolution of the exponential wavenumber spectra of turbulence upon helium injection into a hydrogen discharge at the FT-2 tokamak

The effect of variations in the key parameter of short-wavelength turbulence—the ion-acoustic Larmor radius ρs, which determines the position of the maximum of the drift instability growth rate over poloidal wavenumbers—was studied experimentally at the FT-2 tokamak. For this purpose, helium was injected to hydrogen plasma, which resulted in a change in the electron temperature at the plasma edge. The universality of the exponential shape of the turbulence spectra over radial wavenumbers q and a substantial excess of the characteristic turbulence scale L over the ion-acoustic Larmor radius was confirmed with the help of correlative diagnostics of enhanced scattering. This excess at the discharge periphery reaches a value of 3–5 at a low electron temperature, apparently, due to an increase in the dissipation of drift waves upon their cascade transfer toward short scale-lengths.

Numerical modelling of tokamak plasma micro turbulence wave number spectrum reconstruction using radial correlation reflectometry data

Radial correlation reflectometry (RCR) is used technique providing information on the tokamak plasma micro turbulence. The data interpretation in this technique using for probing simultaneously different frequencies is based on the hypothesis of high measurements localization. In essence, it is similar to that used in probe correlation method where the signal cross-correlation function (CCF) is identified with the turbulence CCF. Unfortunately according to a strict theoretical analysis, both numerical and analytical, this assumption is incorrect; nevertheless the analytical theory proposed here shows that it is possible to reconstruct the turbulence radial wave number spectra using the RCR experimental data. It is also demonstrated that the turbulence CCF is reconstructed more precisely than spectra. It is illustrated by numerical computations for FT-2 (Russian Federation) and Tore Supra (France) tokamaks. Capabilities of spatial inhomogeneous micro turbulence spectra reconstruction is investigated as the transport barrier characterization for example. Information is also reported on the limitations of this method.

New Paradigm for Suppression of Gyrokinetic Turbulence by Velocity Shear

The shear in the mean field velocity Doppler shift is shown to suppress the amplitude of electric potential fluctuations by inducing a shift in the peak of the radial wave number spectrum. An analytic model of the process shows that the fluctuation spectrum shifts in the direction where the velocity shear is linearly destabilizing but that nonlinear mixing causes a recentering of the spectrum about a shifted radial wave number at reduced amplitude A model for the 2D nonlinear spectrum is used in a quasilinear calculation of the transport that is shown to accurately reproduce the suppression of energy and particle transport and the Reynolds stress due to the velocity shear.

Gyrokinetic simulations of entropy transfer in high ion temperature LHD plasmas

Gyrokinetic simulations of the ion temperature gradient (ITG) turbulence in non-axisymmetric configurations modeled on the Large Helical Device (LHD) are performed with the entropy transfer analysis (Nakata et al 2012 Phys. Plasmas 19 022303). It is clarified that a fluctuation spectrum elongated in the radial wavenumber direction is formed in a neoclassically optimized field configuration with the inward-shifted magnetic axis position, where the zonal flows are more effectively generated than in the standard case. The strong interaction between zonal flows and turbulence causes the successive entropy transfer from low to high radial wavenumber space and the spectral broadening of ITG turbulence.