Frequencies Of Acoustic Modes Research Articles

Observations of zonal flows in electrode biasing experiments on the Joint Texas Experimental tokamak

Zonal flows (ZFs) are observed during the electrode biasing (EB) high confinement mode (H-mode) using Langmuir probe arrays on the edge of J-TEXT tokamak. The long-distance correlation characteristics of floating potentials and interactions with turbulence are studied. During positive biasing H-mode, either the geodesic acoustic mode or low frequency ZF increases. Strong suppression of radial transport by ZFs is found in the low frequency region. The components of the radial particle flux without and with EB are compared in the frequency domain. The interaction between ZFs and ambient turbulence is also discussed. The results show that the rate of ZFs' shear is comparable with that of E×B shear, suggesting that ZFs could be the trigger of the biasing H-mode.

Comparison of experiment and models of geodesic acoustic mode frequency and amplitude geometric scaling in ASDEX Upgrade

In a set of dedicated ASDEX Upgrade shape-scan experiments, the influence of plasma geometry on the frequency and amplitude behaviour of the geodesic acoustic mode (GAM), measured by Doppler reflectometry, is studied. In both limiter and divertor configurations, the plasma elongation was varied between circular and highly elongated states (). Also, the edge safety factor was scanned between 3 < q < 5. The GAM frequency and amplitude are used to test several models (heuristic, fluid and gyrokinetic based), which incorporate various plasma geometry effects. The experimentally observed effect of decreasing with increasing κ is predicted by most models. Other geometric factors, such as inverse aspect ratio ε and Shafranov shift gradient are also seen to be influential in determining a reliable lower boundary. The GAM amplitude is found to vary with boundary elongation and safety factor q. The collisional damping is compared to multiple models for the collisionless damping. Collisional damping appears to play a stronger role in the divertor configuration, while collisional and collisionless damping both may contribute to the GAM amplitude in the limiter configuration.

Classical ferroelectriclike behavior of highly orderedPb(Sc1/2Nb1/2)O3studied by dielectric and Brillouin scattering spectroscopy

The ferroelectric phase transition behavior in the highly ordered $\mathrm{Pb}(\mathrm{S}{\mathrm{c}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}){\mathrm{O}}_{3}$ has been investigated by the dielectric and Brillouin spectroscopy. The dielectric permittivity ${\ensuremath{\varepsilon}}_{r}$ exhibits a sharp maximum without any frequency dispersion at its Curie temperature ${T}_{c}$. In the temperature range far above ${T}_{c}$, it was noted that the dielectric permittivity exhibits a noticeable deviation from the Curie-Weiss law below the characteristic intermediate temperature ${T}^{*}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}500\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, which is common to most of the Pb-based oxide perovskite relaxors. Upon cooling, the frequency of the longitudinal acoustic phonon mode exhibits a remarkable softening towards ${T}_{c}$. The relaxation time of the order parameter calculated using the Landau-Khalatnikov approach was determined to be more than one order of magnitude lower than that of the disordered $\mathrm{Pb}(\mathrm{S}{\mathrm{c}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}){\mathrm{O}}_{3}$ and is very close to that observed in the paraelectric phase of the classical ferroelectric, $\mathrm{BaTi}{\mathrm{O}}_{3}$. The observed dielectric and relaxation features are qualitatively discussed in terms of the difference in the strength of the random electric fields.

Observation of 20–400 kHz fluctuations in the U-3M torsatron

First observations of quasi-coherent fluctuations in the frequency range of 20–400 kHz in Alfvén-wave-heated plasmas of the U-3M torsatron are presented. The excitation conditions of these modes depend on the radio frequency antenna type and the plasma density, the appearance of the modes correlating with the presence of both suprathermal electrons and high-energy ions in the plasma, which supports our opinion that the modes are excited by energetic particles. Complicated evolution of the mode frequencies with abrupt changes at the instants of plasma confinement transitions is observed at the initial stage of each discharge. The frequencies become stable at the stage of the plasma current flattop. Raw estimates show that toroidicity-induced Alfvén eigenmodes could be responsible for the 150–400 kHz fluctuations. Low-frequency 20–70 kHz bursts are observed during plasma confinement transitions. The poloidal mode number of one of these bursts with the frequency of 20 kHz burst was determined to be m = 2. This mode rotated in the electron diamagnetic rotation direction with a frequency lower than the geodesic acoustic mode frequency and can be identified as a drift-sound-type mode.

Strong Destabilization of Stable Modes with a Half-Frequency Associated with Chirping Geodesic Acoustic Modes in the Large Helical Device.

Abrupt and strong excitation of a mode has been observed when the frequency of a chirping energetic-particle driven geodesic acoustic mode (EGAM) reaches twice the geodesic acoustic mode (GAM) frequency. The frequency of the secondary mode is the GAM frequency, which is a half-frequency of the primary EGAM. Based on the analysis of spatial structures, the secondary mode is identified as a GAM. The phase relation between the secondary mode and the primary EGAM is locked, and the evolution of the growth rate of the secondary mode indicates nonlinear excitation. The results suggest that the primary mode (EGAM) contributes to nonlinear destabilization of a subcritical mode.

LES Study of Transverse Acoustic Instabilities in a Swirled Kerosene/Air Combustion Chamber

LES is used to study self-excited transverse modes in an atmospheric, square combustor (p = 1 bar). Simulations over a range of different mass flow rates show that transverse modes are present for all cases and exhibit varying RMS pressure amplitudes up to 0.4 bar. Analysis of LES results shows that transverse modes are due to a lock-in mechanism between an hydrodynamic unstable mode typical of swirling flows (the PVC mode or Processing Vortex Core) and the cavity modes. A control method using damping compliant walls (named DCWs) is applied to control the acoustic mode in the LES and to characterize the PVC in the absence of acoustic forcing. This method shows that the highest pressure oscillations appear when the PVC frequency is close to the frequency of the first transverse acoustic mode. A 3D Helmholtz solver is then used to predict the stability limits obtained by 3D LES. To capture transverse modes, a new flame transfer function (FTF) formulation is derived where local heat release perturbations are controlled by the orthoradial acoustic velocity fluctuations. The FTF is measured in the LES and when it is included in the Helmholtz solver, it allows to recover the stability zones observed in the LES.

VARIATIONS IN HIGH DEGREE ACOUSTIC MODE FREQUENCIES OF THE SUN DURING SOLAR CYCLES 23 AND 24

We examine continuous measurements of the high-degree acoustic mode frequencies of the Sun covering the period from 2001 July to June 2014. These are obtained through the ring-diagram technique applied to the full-disk Doppler observations made by the Global Oscillation Network Group (GONG). The frequency shifts in the degree range of 180-1200 are correlated with different proxies of solar activity e.g. 10.7 cm radio flux, the International Sunspot Number and the strength of the local magnetic field. In general, a good agreement is found between the shifts and activity indices, and the correlation coefficients are found to be comparable with intermediate degree mode frequencies. Analyzing the frequency shifts separately for the two cycles, we find that cycle 24 is weaker than cycle 23. Since the magnetic activity is known to be different in the two hemisphere, for the first time, we compute the frequency shifts over the two hemispheres separately and find that the shifts also display hemispheric asymmetry; the amplitude of shifts in the northern hemisphere peaked during late 2011, more than two years earlier than the south. We further correlate the hemispheric frequency shifts with the hemispheric sunspot number and mean magnetic activity index. Since the frequency shifts and the hemispheric activity indices are found to be significantly correlated, we suggest that the shifts be used as an indicator of hemispheric activity since not many indices are measured over the two hemispheres separately. We also investigate the variation at different latitudinal bands and conclude that the shifts in active latitudes correlate well with the local magnetic activity index.

Test of a virtual cylindrical acoustic resonator for determining the Boltzmann constant

We report progress toward determining the Boltzmann constant kB using the concept of a virtual acoustic resonator, a hypothetical resonator that is mathematically equivalent to a cylindrical cavity with periodic boundary conditions. We derived the virtual resonator by combining the measured frequencies of the longitudinal acoustic modes of two argon-filled, cylindrical cavity resonators in such a way to minimize the effects of the cavities’ ends, including transducers and ducts attached to the ends. The cavities had lengths of 80 mm and 160 mm and were operated in their longitudinal (ℓ,0,0) modes. We explored virtual resonators that combine modes of the two resonators that have nearly the same frequencies. The virtual resonator formed from the (2,0,0) mode of the 80 mm resonator combined with the (4,0,0) mode of the 160 mm resonator yielded a value for kB that is, fractionally, only (0.2 ± 1.5) × 10−6 larger than the 2010 CODATA-recommended value of kB. (The estimated uncertainty is one standard uncertainty corresponding to a 68% confidence level.) The same virtual resonator yielded values of the pressure derivatives of the speed of sound c in argon, (∂c2/∂p)T and (∂c2/∂p2)T, that differed from literature values by 1% and 2%, respectively. By comparison, when each cavity was considered separately, the values of kB, (∂c2/∂p)T, and (∂c2/∂p2)T differed from literature values by up to 7 ppm, 10%, and 5%, respectively. However, combining the results from the (3,0,0) or (4,0,0) modes of shorter resonator with the results from the (6,0,0) or (8,0,0) modes of the longer resonator yielded incorrect values of kB that varied from run-to-run. We speculate that these puzzling results originated in an unmodeled coupling, either between the two cavities (that resonated at nearly identical resonance frequencies in the same pressure vessel) or between the cavities and modes of the pressure vessel.

Helium signature in red giant oscillation patterns observed byKepler

The space-borne missions CoRoT and Kepler have provided a large amount of precise photometric data. Among the stars observed, red giants show a rich oscillation pattern that allows their precise characterization. Long-duration observations allow for investigating the fine structure of this oscillation pattern. A common pattern of oscillation frequency was observed in red giant stars, which corresponds to the second-order development of the asymptotic theory. This pattern, called the universal red giant oscillation pattern, describes the frequencies of stellar acoustic modes. We aim to investigate the deviations observed from this universal pattern, thereby characterizing them in terms of the location of the second ionization zone of helium. We also show how this seismic signature depends on stellar evolution. We measured the frequencies of radial modes with a maximum likelihood estimator method, then we identified a modulation corresponding to the departure from the universal oscillation pattern. We identify the modulation component of the radial mode frequency spacings in more than five hundred red giants. The variation in the modulation that we observe at different evolutionary states brings new constraints on the interior models for these stars. We also derive an updated form of the universal pattern that accounts for the modulation and provides highly precise radial frequencies.

Comparison of collision operators for the geodesic acoustic mode

The collisional damping rate and real frequency of the geodesic acoustic mode (GAM) are solved from a drift kinetic model with different collision operators. As the ion collision rate increases, the damping rate increases at low collision rate but decays at high ion collision rate. Different collision operators do not change the overall trend but influence the magnitude of the damping rate. The collision damping is much overestimated with the number-conserving-only Krook operator; on the other hand, using the Lorentz operator with a constant collision rate, the damping is overestimated at low collision rate but underestimated at high collision rate. The results from the Krook operator with both number and energy conservation terms, the Lorentz operator with an energy-dependent collision rate and the full Hirshman–Sigmar–Clarke collision operator are very close. Meanwhile, as the ion collision rate increases, the GAM frequency decreases from the collisionless value, , to for the number-conserving-only Krook operator, but to for the other four operators, which conserve both number and energy, where τ, vti and R are the ratio of electron temperature to ion temperature, the ion thermal velocity and the major radius, respectively. The results imply that the property of energy conservation of the collision operator is important to the dynamics of the GAM as well as that of number conservation, which may provide guidance in choosing collision operators in further study of the zonal flow (ZF) dynamics, such as the nonlinear simulation of the ZF-turbulence system.

Collective excitation interferometry with a toroidal Bose-Einstein condensate

The precision of compact inertial sensing schemes using trapped- and guided-atom interferometers has been limited by uncontrolled phase errors caused by trapping potentials and interactions. Here, we propose an acoustic interferometer that uses sound waves in a toroidal Bose-Einstein condensate to measure rotation, and we demonstrate experimentally several key aspects of this type of interferometer. We use spatially patterned light beams to excite counter-propagating sound waves within the condensate and use \emph{in situ} absorption imaging to characterize their evolution. We present an analysis technique by which we extract separately the oscillation frequencies of the standing-wave acoustic modes, the frequency splitting caused by static imperfections in the trapping potential, and the characteristic precession of the standing-wave pattern due to rotation. Supported by analytic and numerical calculations, we interpret the noise in our measurements, which is dominated by atom shot noise, in terms of rotation noise. While the noise of our acoustic interferometric sensor, at the level of $\sim \mbox{rad}\, \mbox{s}^{-1}/\sqrt{\mbox{Hz}}$, is high owing to rapid acoustic damping and the small radius of the trap, the proof-of-concept device does operate at $10^4 - 10^6$ times higher density and in a volume $10^9$ times smaller than free-falling atom interferometers.

Radial homogeneity of geodesic acoustic modes in ohmic discharges with low B in the T-10 tokamak

The electric potential oscillations in the hot plasma zone have been measured directly using a heavy ion beam probe at the frequencies of geodesic acoustic modes in the T-10 tokamak (the major and minor radii are R = 1.5 m and a = 0.3 m, respectively, and the toroidal magnetic field is B = 1.5–2.5 T). In discharges with the lowered magnetic field B = 1.55 T, the diagnostic beam can probe a rather wide radial plasma region (0.06 < r < 0.28 m). This made it possible to study the radial structure of geodesic acoustic modes. It has been shown that the frequency and amplitude of geodesic acoustic modes in the region under study are constant over the radius in the whole region of observation. Thus, it has been shown experimentally that the observed frequency of geodesic acoustic modes may not correspond to the predictions of the local theory (f∼ √Te) in a wide radial range comparable with the plasma minor radius. The numerical simulation of the turbulence dynamics using the solution of Braginskii magnetohydrodynamic equations for a peripheral plasma has showed the formation of geodesic acoustic modes in the observed frequency range owing to the nonlinear interaction between broadband turbulence modes.

Stress effects on the elastic properties of amorphous polymeric materials.

Brillouin light scattering measurements have been used to study the stress induced modification in the elastic properties of two glass forming polymers: polybutadiene and epoxy-amine resin, prototypes of linear and network polymers, respectively. Following the usual thermodynamic path to the glass transition, polybutadiene has been studied as a function of temperature from the liquid well into the glassy phase. In the epoxy resin, the experiments took advantage of the system ability to reach the glass both via the chemical vitrification route, i.e., by increasing the number of covalent bonds among the constituent molecules, as well as via the physical thermal route, i.e., by decreasing the temperature. Independently from the particular way chosen to reach the glassy phase, the measurements reveal the signature of long range tensile stresses development in the glass. The stress presence modifies both the value of the sound velocities and their mutual relationship, so as to break the generalized Cauchy-like relation. In particular, when long range stresses, by improvise sample cracking, are released, the frequency of longitudinal acoustic modes increases more than 10% in polybutadiene and ∼4% in the epoxy resin. The data analysis suggests the presence of at least two different mechanisms acting on different length scales which strongly affect the overall elastic behaviour of the systems: (i) the development of tensile stress acting as a negative pressure and (ii) the development of anisotropy which increases its importance deeper and deeper in the glassy state.

Turbulence and zonal flow structures in the core and L-mode pedestal of tokamak plasmas

Zonal flows (ZF) play a crucial role in regulating ion temperature gradient (ITG) turbulence. In previous global gyrokinetic simulations [1] using the ORB5 code with the adiabatic electron model, it was observed that long-lived ZF structures, leading to a corrugated transport and temperature gradient pattern, could develop in shaped tokamak plasmas much more than in circular shaped plasmas, resulting in reduced transport. These studies are extended to a hybrid electron model in which trapped electrons are kinetic while passing electrons are assumed to have a Boltzmann response for a case dominated by ITG modes. These confirm the results of the fully adiabatic electron model. Simulations done in "gradient-driven" mode, with a Krook-like relaxation towards a given profile, result in non-realistic corrugated heat source/sink profiles. However, after switching off completely the heat source/sink, it is shown that the ZF and transport corrugation remains. Thus the heat source corrugation is merely a consequence, not a cause, of the zonal structures and related radial transport pattern. Considering then core profiles with constant logarithmic gradients and pedestal profiles with linear gradients for L-mode plasmas, as in Ref.[2], we analyze how ITG transport and zonal structures react by independently varying the logarithmic gradients in the core and the linear gradients in the pedestal, using the adiabatic electron model. Results show the presence of large radial zones straddling the core-pedestal transition region. Avalanche-like events propagate over the radial zone at constant speed and repeat with a well defined frequency somewhat below the local geodesic acoustic mode (GAM) frequency. These avalanches are observed on the E × B ZFs, effective heat diffusivity and heat flux, thus a change of gradient in the core affects transport in the pedestal and vice versa. In spite of these non-local effects, attempt is made to characterize transport, and in particular its stiffness, quasi-locally. Global simulation results show that with increased input power the logarithmic gradient in the core is only slightly increased while the linear gradient in the pedestal is substantially enhanced.

Overstability of acoustic waves in strongly magnetized anisotropic magnetohydrodynamic shear flows

We present a linear stability analysis of the perturbation modes in anisotropic magnetohydrodynamic (MHD) flows with velocity shear and strong magnetic field. Collisionless or weakly collisional plasma is described within the 16-momentum MHD fluid closure model that takes into account not only the effect of pressure anisotropy but also the effect of anisotropic heat fluxes. In this model, the low frequency acoustic wave is revealed into a standard acoustic mode and higher frequency fast thermo-acoustic and lower frequency slow thermo-acoustic waves. It is shown that thermo-acoustic waves become unstable and grow exponentially when the heat flux parameter exceeds some critical value. It seems that velocity shear makes thermo-acoustic waves overstable even at subcritical heat flux parameters. Thus, when the effect of heat fluxes is not profound acoustic waves will grow due to the velocity shear, while at supercritical heat fluxes the flow reveals compressible thermal instability. Anisotropic thermal instability should be also important in astrophysical environments, where it will limit the maximal value of magnetic field that a low density ionized anisotropic flow can sustain.

Temperature-induced electron[sbnd]phonon coupling behaviour of AgGaS2 probed by Brillouin spectroscopy

Low-temperature Brillouin scattering studies on Chalcopyrite AgGaS2 have been carried out between the temperatures ranges 20300K. We observe the Brillouin modes for AgGaS2 as follows: for crossed polarization (VH) the two modes are around 5.4 and 18GHz, labelled as RSW1 (Rayleigh surface mode), LA (longitudinal) modes and for parallel polarization (HH), we see the modes are around 4.5 and 11GHz, labelled as RSW2, TA (transverse acoustic). According to this acoustic phonon mode behaviour with temperature, we do see phase transition at 80K for AgGaS2. The phase change observed at 80K is attributed to a strong electronphonon coupling between the acoustic modes, which modulates the acoustic mode frequency 1015%. The strong electronphonon coupling between acoustic modes (LA and TA), which is seen from the anomalous behaviour below 80K, shows the electronic transition to be of the type direct to indirect band gap. The sound velocity and elastic constants have been calculated using Brillouin modes, which are in good agreement with previous reports.

Elastic anomalies associated with the antiferroelectric phase transitions of PbHfO3 single crystals

The temperature dependence of the elastic properties of antiferroelectric PbHfO3 was investigated by using Brillouin scattering. The two structural phase transitions of antiferroelectricantiferroelectric-paraelectric phases were clearly identified from the discontinuous changes in the acoustic mode frequencies and the hypersonic damping. The substantial softening of the mode frequency, along with the remarkable increase in the acoustic damping observed in the paraelectric phase, indicated the formation of precursor noncentrosymmetric (polar) clusters and their coupling to the acoustic waves. This was corroborated by the observation of quasi-elastic central peaks, the intensity of which grew upon cooling toward the Curie point. The obtained relaxation time exhibited a slowing-down behavior, suggesting that the dynamics of the precursor clusters became more sluggish on approaching the phase transition temperature.

Nonlinear magneto-electric effects in ferromagnetic-piezoelectric composites

Theory and results of a systematic study on the nature of nonlinear magnetoelectric (ME) interactions in layered ferromagnetic and ferroelectric composites are discussed. The model that considers the nonlinearity associated with magnetostriction of the ferromagnet is to result in (i) a dc component and (ii) frequency doubling when the composite is subjected to an ac magnetic field. In the presence of two ac magnetic fields of different frequencies, nonlinear effects give rise to generation of ME voltages at the sum and difference of the fields frequencies. The efficiencies of nonlinear ME interactions are shown to be a function of the second derivative of the magnetostriction with respect to the bias magnetic field. The predictions of the model are compared with data for bilayers of lead zirconate titanate (PZT) and ferromagnetic layers with wide variations in saturation magnetostrictions and saturation magnetic fields, i.e., an amorphous ferromagnetic (AF) alloy, Ni, or permendur. Under linear excitation conditions an enhancement in the ME voltage is measured when the ac magnetic field is applied at the acoustic mode frequencies. Under nonlinear excitation conditions the mechanical deformation and the ME response occur at twice the excitation frequency and the AF-PZT composite shows a much higher nonlinear ME effects. In addition, the AF-PZT shows an efficient frequency mixing than the samples with Ni or permendur when subjected to two ac magnetic fields. The frequency mixing is shown to be of importance for magnetic field sensor applications.

THE SURFACE NITROGEN ABUNDANCE OF A MASSIVE STAR IN RELATION TO ITS OSCILLATIONS, ROTATION, AND MAGNETIC FIELD

We have composed a sample of 68 massive stars in our galaxy whose projected rotational velocity, effective temperature and gravity are available from high-precision spectroscopic measurements. The additional seven observed variables considered here are their surface nitrogen abundance, rotational frequency, magnetic field strength, and the amplitude and frequency of their dominant acoustic and gravity mode of oscillation. Multiple linear regression to estimate the nitrogen abundance combined with principal components analysis, after addressing the incomplete and truncated nature of the data, reveals that the effective temperature and the frequency of the dominant acoustic oscillation mode are the only two significant predictors for the nitrogen abundance, while the projected rotational velocity and the rotational frequency have no predictive power. The dominant gravity mode and the magnetic field strength are correlated with the effective temperature but have no predictive power for the nitrogen abundance. Our findings are completely based on observations and their proper statistical treatment and call for a new strategy in evaluating the outcome of stellar evolution computations.

Non-radial oscillations in rotating giant planets with solid cores: Application to Saturn and its rings

Recent observations have revealed evidence for the global acoustic oscillations of Jupiter and Saturn. Such oscillations can potentially provide a new window into the interior structure of giant planets. Motivated by these observations, we study the non-radial oscillation modes of giant planets containing a solid core. Our calculations include the elastic response of the core and consider a wide range of possible values of the core shear modulus. While the elasticity of the core only slightly changes the frequencies of acoustic modes (including the f-modes), which reside mostly in the fluid envelope, it adds two new classes of shear modes that are largely confined to the core. We also calculate the effects of the Coriolis force on the planetary oscillation modes. In addition to changing the mode frequencies, the Coriolis force can cause the shear modes to mix with the f-modes. Such mixing occurs when the frequencies of the shear mode and the f-mode are close to each other, and results in “mixed modes” that have similarly large surface displacements and gravitational potential perturbations, but are slightly split in frequency. We discuss our results in light of the recent work by Hedman and Nicholson (Hedman, M., Nicholson, P. [2013]. arXiv:1304.3735), which revealed the presence of density waves in Saturn’s C-ring that appear to be excited by the gravitational perturbations associated with the f-mode oscillations within Saturn. We find that the fine splitting in wave frequencies observed in the rings can in principle be explained by the rotation-induced mixing between core shear modes and f-modes, possibly indicating the presence of a solid core within Saturn. However, in our current calculations, which assume rigid-body rotation and include only first-order rotational effects, significant fine-tuning in the planetary model parameters is needed in order to achieve these mode mixings and to explain the observed fine frequency splitting. We briefly discuss other effects that may modify the f-modes and facilitate mode mixing.