Slow-mode Waves Research Articles

Characterization of Co-Planar Silicon Transmission Lines With and Without Slow-Wave Effect

Co-planar lines on silicon substrates with and without slow-wave effect are characterized using time-domain reflectometry (TDR) and vector network analyzer (VNA) measurements, and simulated using a proposed nonphysical resistance-inductance-conductance-capacitance (RLGC) model. The silicon co-planar lines are characterized based on comparison to package transmission lines. Co-planar silicon lines without slow-wave mode are modeled in the same way as package transmission lines, but co-planar lines with slow-wave mode are modeled in a different way from package transmission lines. Hence, a nonphysical RLGC model including slow-wave mode is proposed along with the extraction method from VNA measurements. Simulation results correlate well with time- and frequency-domain measurements for the co-planar silicon lines.

Effects of the Thin-Film Metal Ground Embedded in On-Chip Microstrip Lines

This letter studies the influence of embedded thin-film metallization layers, normally designed as ground planes, upon the dispersive characteristics of multilayer microstrip lines. The spectral domain approach is used to analyze the effects of the metallization thickness as a design parameter in two structures: the thin-film microstrip line and metal-insulator-metal-insulator line. Numerical results indicate that the thin metallization layer can excite the slow-wave mode and change significantly the dispersive characteristics. Moreover, at low frequencies a local minimal attenuation can be achieved with certain metallization thickness. Thus, it is necessary to take into account this thin-film metal ground to achieve reliable numerical simulation from dc to millimeter-wave frequencies

Bayesian estimation of the underlying bone properties from mixed fast and slow mode ultrasonic signals

We recently proposed that the observed apparent negative dispersion in bone can arise from the interference between fast wave and slow wave modes, each exhibiting positive dispersion [Marutyan et al., J. Acoust. Soc. Am. 120, EL55-EL61 (2006)]. In the current study, we applied Bayesian probability theory to solve the inverse problem: extracting the underlying properties of bone. Simulated mixed mode signals were analyzed using Bayesian probability. The calculations were implemented using the Markov chain Monte Carlo with simulated annealing to draw samples from the marginal posterior probability for each parameter.

Toward bone quality assessment: Interference of fast and slow wave modes with positive dispersion can account for the apparent negative dispersion

The goal of this work was to show that apparently negative dispersion in bone can arise from interference between fast wave and slow wave longitudinal modes, each of positive dispersion. Simulations were carried out using two approaches, one based on the Biot-Johnson model and the second independent of that model. The resulting propagating fast wave and slow wave modes accumulated phase and suffered loss with distance traveled. Results of both types of simulation served as the input into a phase and magnitude spectroscopy algorithm (previously validated with experimental data) in order to determine the phase velocity as a function of frequency. Results based on both methods of simulation were mutually consistent. Depending upon the relative magnitudes and time relationships between the fast and slow wave modes, the apparent phase velocities as functions of frequency demonstrated either negative or positive dispersions. These results appear to account for measurements from many laboratories that report that the phase velocity of ultrasonic waves propagating in cancellous bone decreases with increasing frequency (negative dispersion) in about 90% of specimens but increases with frequency in about 10%. [Work supported in part by Grant NIH R37HL40302.]

Reflection and transmission of waves in composite porous media: A quantification of energy conversions involving slow waves

This paper studies the reflection and transmission of plane elastic waves at interfaces in fluid-saturated poroviscoelastic media in which the solid matrix is composed of two weakly coupled solids. The analysis of this problem, not formally performed before, is based on a theory recently developed by some of the authors, which allows us to derive expressions for the reflection and transmission coefficients at a plane interface within this kind of media and their relationship with the energy flux (Umov-Poynting) vector. The results of the present derivation were applied to study the energy splitting that takes place when a plane fast compressional wave strikes obliquely an interface defined by a change in ice content within a sample of water saturated partially frozen sandstone. The numerical results show wave mode conversions from fast to slow compressional and shear waves, with maximum energy conversion on the order of 20% from fast to slow wave modes near the critical angle. This phenomenon was observed at frequencies lying from the seismic to the ultrasonic range, showing that the role of the slow waves must be taken into account when considering wave propagation in this type of media.

Experimental study and direct numerical simulation of the evolution of disturbances in a viscous shock layer on a flat plate

The evolution of disturbances in a hypersonic viscous shock layer on a flat plate excited by slow-mode acoustic waves is considered numerically and experimentally. The parameters measured in the experiments performed with a free-stream Mach number M∞ = 21 and Reynolds number ReL = 1.44 · 105 are the transverse profiles of the mean density and Mach number, the spectra of density fluctuations, and growth rates of natural disturbances. Direct numerical simulation of propagation of disturbances is performed by solving the Navier-Stokes equations with a high-order shock-capturing scheme. The numerical and experimental data characterizing the mean flow field, intensity of density fluctuations, and their growth rates are found to be in good agreement. Possible mechanisms of disturbance generation and evolution in the shock layer at hypersonic velocities are discussed.

The generation of dense cores and substructure within them by MHD waves

AbstractBy using 2D simulations, we examine the generation of dense cores and substructures by magnetosonic waves. We find that the excitation of slow-mode waves by fast-mode waves produces these high-density structures.

Petschek‐Type Reconnection Exhausts in the Solar Wind Well beyond 1 AU:Ulysses

We have identified 91 Petschek-type exhausts associated with local, quasi-stationary magnetic reconnection in the solar wind in plasma and magnetic field data from the Ulysses spacecraft obtained over a wide range of heliocentric distances (1.4-5.4 AU) and latitudes (S79°-N65°). The characteristic signature of an exhaust was a brief (minutes) interval of accelerated or decelerated plasma flow within a bifurcated current sheet in which changes in magnetic field and flow velocity were correlated at one edge and anticorrelated at the other. Transitions from outside to inside the exhausts were always slow-mode-like, the exhausts appearing to an observer as encounters with closely spaced, forward-reverse, slow-mode wave (shock) pairs. The exhausts almost universally occurred in low-speed or interplanetary coronal mass ejection plasma having low proton β (<1 and often 1) at relatively large shears (90°-180°) in the heliospheric magnetic field. Magnetic field strength decreases within the exhausts were highly variable from event to event and were roughly correlated with the magnitude of the local magnetic shears; this indicates the presence of substantial guide fields in at least some of these events. Many of the exhausts occurred at current sheets separating plasma having distinctly different Alfven speeds and were thus asymmetric. Local exhaust widths at Ulysses varied up to a maximum of ~2 × 106 km but statistically did not vary significantly with heliocentric distance. We offer several possible explanations of this observation.

Viscous Damping of Non-Adiabatic MHD Waves in an Unbounded Solar Coronal Plasma

The damping of MHD waves in solar coronal magnetic field is studied taking into account thermal conduction and compressive viscosity as dissipative mechanisms. We consider viscous homogeneous unbounded solar coronal plasma permeated by a uniform magnetic field. A general fifth-order dispersion relation for MHD waves has been derived and solved numerically for different solar coronal regimes. The dispersion relation results three wave modes: slow, fast, and thermal modes. Damping time and damping per periods for slow- and fast-mode waves determined from dispersion relation show that the slow-mode waves are heavily damped in comparison with fast-mode waves in prominences, prominence–corona transition regions (PCTR), and corona. In PCTRs and coronal active regions, wave instabilities appear for considered heating mechanisms. For same heating mechanisms in different prominences the behavior of damping time and damping per period changes significantly from small to large wavenumbers. In all PCTRs and corona, damping time always decreases linearly with increase in wavenumber indicate sharp damping of slow- and fast-mode waves.

Spatiotemporal pore pressure evolution due to fluid-mass point sources in dynamic poroelasticity

SUMMARY The spatiotemporal behaviours of pore pressure induced by a fluid mass point source in quasi-static and dynamic poroelasticity are compared and contrasted. Explicit results for the pore pressure in time domain are derived using the known fundamental solution of dynamic poroelasticity in frequency domain. Depending on the frequency content of the source function, different regimes can be identified. First, the diffusive regime where only the diffusive slow wave exists; the latter is equivalent to the process of pore pressure diffusion. Second, there is the propagation–diffusion regime where slow and fast wave modes coexist. It is shown that the amount of induced pore pressure due to the diffusive slow wave is different for quasi-static loadings (e.g. fluid injection experiments) and transient loads (e.g. propagating low-frequency seismic waves). The results are discussed in the context of fluid injection experiments where short-term fluctuations of the injection rate can create both, the fast compressional wave and the slow diffusive wave. The results can be used in order to generate synthetic seismograms and validate numerical schemes for pressure disturbances in dynamic poroelasticity.

Characteristics of Solar Flare Doppler‐Shift Oscillations Observed with the Bragg Crystal Spectrometer onYohkoh

This paper reports the results of a survey of Doppler shift oscillations measured during solar flares in emission lines of S XV and Ca XIX with the Bragg Crystal Spectrometer (BCS) on Yohkoh. Data from 20 flares that show oscillatory behavior in the measured Doppler shifts have been fitted to determine the properties of the oscillations. Results from both BCS channels show average oscillation periods of 5.5 +/- 2.7 minutes, decay times of 5.0 +/-2.5 minutes, amplitudes of 17.1 +/- 17.0 km/s, and inferred displacements of 1070 +/- 1710 km, where the listed errors are the standard deviations of the sample means. For some of the flares, intensity fluctuations are also observed. These lag the Doppler shift oscillations by 1/4 period, strongly suggesting that the oscillations are standing slow mode waves. The relationship between the oscillation period and the decay time is consistent with conductive damping of the oscillations.

Slow mode waves and mirror instability in gyrotropic Hall magnetohydrodynamic model

Recently the nonlinear magnetohydrodynamic (MHD) model corrected by pressure anisotropy and Hall current arising from the ion inertia is applied to construct slow or mirror mode structures and compare with the observation in the Earth’s magnetosphere [K. Stasiewicz, Phys. Rev. Lett. 93, 125004 (2004)]. A serious issue is also raised of whether the Hall MHD model is appropriate for describing the high beta plasma and is capable of reproducing the wave dispersion found in kinetic theory [O. Pokhotelov et al., Phys. Rev. Lett. 95, 129501 (2005)]. In this paper we give an overview of the characteristics of linear slow mode waves and mirror instability within the context of the gyrotropic Hall MHD model closed with various energy equations. The properties examined include the phase speed, the compressibility of plasma density and magnetic field, the magnetic polarization of slow mode waves, as well as the criteria for mirror instability and their dependences on pressure anisotropy, plasma beta, propagation angle, and energy closures. The analyses help to clarify the applicability and limitation with applying the gyrotropic Hall MHD model to the observed slow or mirror mode structures.

Erratum: The chemistry of transient molecular cloud cores

We assume that some, but not all, of the structure observed in molecular clouds is associated with transient features which are not bound by self-gravity. We investigate the chemistry of a transient density fluctuation, with properties similar to those of a core within a molecular cloud. We run a multipoint chemical code through a core's condensation from a diffuse medium to its eventual dispersion, over a period of ∼1 Myr. The dynamical description adopted for our study is based on an understanding of a particular mechanism, involving slow-mode wave excitation, for transient structure formation which so far has been studied in detail only with plane-parallel models in which self-gravity has not been included. We find a significant enhancement of the chemical composition of the core material on its return to diffuse conditions, whilst the expansion of the core as it disperses moves this material out to large distances from the core centre. This process transports molecular species formed in the high-density regions out into the diffuse medium. Chemical enrichment of the cloud as a whole also occurs, as other cores of various sizes, life-spans and separations evolve throughout. Enrichment is strongly affected by freeze-out on to dust grains, which takes place in high-density, high visual extinction regions. As the core disperses after reaching its peak density and the visual extinction drops below a critical value, grain mantles are evaporated back into the gas phase, initiating more chemistry. The influence of the sizes, masses and cycle periods of cores will be large both for the level of chemical enrichment of a dark cloud and ultimately for the low-mass star formation rate. The cores in which stars form are almost certainly bound by their self-gravity and are not transient in the sense that the cores on which most of our study is focused are transient. Obviously, enrichment of the chemistry of low-density material will not take place if self-gravity prevents the re-expansion of a core. We also consider the case of a self-gravitating core, by holding its peak density conditions for a further 0.4 Myr. We find that the differences near the peak densities between transient and gravitationally bound cores are generally small, and the resultant column densities for objects near the peak densities do not provide definitive criteria for discriminating between transient and bound cores. However, increases in fractional abundances due to reinjection of mantle-borne species may provide a criterion for detection of a non-bound core.

The first observed stellar X-ray flare oscillation: Constraints on the flare loop length and the magnetic field

We present the first X-ray observation of an oscillation during a stellar flare. The flare occurred on the active M-type dwarf AT Mic and was observed with XMM-Newton. The soft X-ray light curve (0.2-12 keV) is investigated with wavelet analysis. The flare's extended, flat peak shows clear evidence for a damped oscillation with a period of around 750 s, an exponential damping time of around 2000 s, and an initial, relative peak-to-peak amplitude of around 15%. We suggest that the oscillation is a standing magneto-acoustic wave tied to the flare loop, and find that the most likely interpretation is a longitudinal, slow-mode wave, with a resulting loop length of (2.5 +- 0.2) e10 cm. The local magnetic field strength is found to be (105 +- 50) G. These values are consistent with (oscillation-independent) flare cooling time models and pressure balance scaling laws. Such a flare oscillation provides an excellent opportunity to obtain coronal properties like the size of a flare loop or the local magnetic field strength for the otherwise spatially-unresolved star.

Initiation of hot coronal loop oscillations: Spectral features

We explore the excitation of hot loop oscillations observed with the SUMER spectrograph on SOHO by analysing and spectral line profiles in the initial phase of the events. We investigate all 54 Doppler shift oscillations in 27 flare-like events, whose physical parameters have been measured so far. In nearly 50% of the cases, the spectral evolution reveals the presence of two spectral components, one of them almost undisturbed, the other highly shifted. We find that the shifted component reaches maximum Doppler shift (on the order of 100-300 km s-1) and peak intensity almost simultaneously. The velocity amplitude of the shifted component has no correlation with the oscillation amplitudes. These features imply that in these events the initial shifts are not caused by the locally oscillating plasma (or waves), but most likely by a pulse of hot plasma travelling along the loop through the slit position. This interpretation is also supported by several examples showing that standing slow mode waves are set up immediately after the initial line shift pulse (standing slow mode waves are inferred from the 1/4-period phase relationship between the velocity and intensity oscillations). We re-measure the physical parameters of the 54 Doppler oscillations by fitting the time profiles excluding the first peak, and find that the periods are almost unchanged, damping times are shorter by 5%, and amplitudes are smaller by 37% than measured when the first peak is included. We also measure the velocity of the net (background) flow during the oscillations, which is found to be nearly zero. Our result of initial hot flows supports the model of single footpoint (asymmetric) excitation, but contradicts chromospheric evaporation as the trigger.

The effect of dissipation on the generation of density structure by magnetohydrodynamic waves

Observations of absorption lines in diffuse interstellar clouds may indicate that significant fluctuations in physical conditions exist on scales comparable to, or even smaller than, the dissipation length associated with ambipolar diffusion. Here we describe the results of simulations of magnetohydrodynamic (MHD) wave evolution in which ambipolar diffusion plays a major role. We find that ambipolar diffusion affects the evolution of waves with wavelengths up to about a thousand times the dissipation length-scale, which means that these results are relevant to both molecular and atomic interstellar clouds. The initial conditions consist of a uniform background upon which is superposed a non-linear fast-mode ideal MHD wave with a density contrast comparable to unity or less. The ratio, β, of the thermal pressure to the magnetic pressure is assumed to be small. For initial disturbances that have wavelengths that are very large compared to the dissipation length, the generation of structures with high-density contrast is due to the excitation of slow-mode waves by non-linear steepening of the fast-mode wave. In this case, collisions between the resulting structures lead to additional density enhancement for some ranges of the initial wave amplitude. For initial disturbances that have wavelengths such that dissipation is significant, slow-mode waves are also produced by ambipolar diffusion and this can generate higher density contrasts than those found in the corresponding cases in which dissipation is negligible. Large density contrasts on scales comparable to the dissipation length are found only when the wavelength of the initial perturbation is comparatively small. Because such waves do not propagate far before they are dissipated, we suggest that the variations in absorption features with time-scales ≃10 yr can only be generated by waves if they are located at the surfaces of clouds and are excited by external disturbances such as stellar winds, supernovae, etc. In order to produce the highest density contrasts that have been detected, the waves must have even larger amplitudes than those we have examined. This places severe restrictions on the properties of waves that could produce the kind of microstructure that some believe to be responsible for the rapid variations of absorption features.

Plasma depletion layer: the role of the slow mode waves

Abstract. The plasma depletion layer (PDL) is a layer on the sunward side of the magnetopause with lower plasma density and higher magnetic field compared to their corresponding values in the upstream magnetosheath. The depletion layer usually occurs during northward (IMF) conditions with low magnetic shear across the magnetopause. We have previously validated the Raeder global model by comparing the computed formation of a magnetosheath density depletion with in-situ observations. We also have performed a detailed force analysis and found the varying roles that different MHD forces play along the path of a plasma parcel flowing around the magnetopause. That study resulted in a new description of the behavior of magnetosheath magnetic flux tubes which better explains the plasma depletion along a flux tube. The slow mode waves have been observed in the magnetosheath and have been used to explain the formation of the PDL in some of the important PDL models. In this study, we extend our former work by investigating the possible role of the slow mode waves for the formation of the PDL, using global MHD model simulations. We propose a new technique to test where a possible slow mode front may occur in the magnetosheath by comparing the slow mode group velocity with the local flow velocity. We find that the slow mode fronts can exist in certain regions in the magnetosheath under certain solar wind conditions. The existence and location of such fronts clearly depend on the IMF. We do not see from our global simulation results either the sharpening of the slow mode front into a slow mode shock or noticeable changes of the flow and field in the magnetosheath across the slow mode front, which implies that the slow mode front is not likely responsible for the formation of the PDL, at least for the stable solar wind conditions used in these simulations. Also, we do not see the two-layered slow mode structures shown in some observations and proposed in certain PDL models. Instead, we see only a one-layered spatial PDL structure under the stable solar wind conditions used in this study.

The strange physics of low frequency mirror mode turbulence in the high temperature plasma of the magnetosheath

Abstract. Mirror mode turbulence is the lowest frequency perpendicular magnetic excitation in magnetized plasma proposed already about half a century ago by Rudakov and Sagdeev (1958) and Chandrasekhar et al. (1958) from fluid theory. Its experimental verification required a relatively long time. It was early recognized that mirror modes for being excited require a transverse pressure (or temperature) anisotropy. In principle mirror modes are some version of slow mode waves. Fluid theory, however, does not give a correct physical picture of the mirror mode. The linear infinitesimally small amplitude physics is described correctly only by including the full kinetic theory and is modified by existing spatial gradients of the plasma parameters which attribute a small finite frequency to the mode. In addition, the mode is propagating only very slowly in plasma such that convective transport is the main cause of flow in it. As the lowest frequency mode it can be expected that mirror modes serve as one of the dominant energy inputs into plasma. This is however true only when the mode grows to large amplitude leaving the linear stage. At such low frequencies, on the other hand, quasilinear theory does not apply as a valid saturation mechanism. Probably the dominant processes are related to the generation of gradients in the plasma which serve as the cause of drift modes thus transferring energy to shorter wavelength propagating waves of higher nonzero frequency. This kind of theory has not yet been developed as it has not yet been understood why mirror modes in spite of their slow growth rate usually are of very large amplitudes indeed of the order of |B/B0|2~O(1). It is thus highly reasonable to assume that mirror modes are instrumental for the development of stationary turbulence in high temperature plasma. Moreover, since the magnetic field in mirror turbulence forms extended though slightly oblique magnetic bottles, low parallel energy particles can be trapped in mirror modes and redistribute energy (cf. for instance, Chisham et al. 1998). Such trapped electrons excite banded whistler wave emission known under the name of lion roars and indicating that the mirror modes contain a trapped particle component while leading to the splitting of particle distributions (see Baumjohann et al., 1999) into trapped and passing particles. The most amazing fact about mirror modes is, however, that they evolve in the practically fully collisionless regime of high temperature plasma where it is on thermodynamic reasons entirely impossible to expel any magnetic field from the plasma. The fact that magnetic fields are indeed locally extracted makes mirror modes similar to "superconducting" structures in matter as known only at extremely low temperatures. Of course, microscopic quantum effects do not play a role in mirror modes. However, it seems that all mirror structures have typical scales of the order of the ion inertial length which implies that mirrors evolve in a regime where the transverse ion and electron motions decouple. In this case the Hall kinetics comes into play. We estimate that in the marginally stationary nonlinear state of the evolution of mirror modes the modes become stretched along the magnetic field with k||=0 and that a small number the order of a few percent of the particle density is responsible only for the screening of the field from the interior of the mirror bubbles.

Chromospheric Waves Observed in the HeiSpectral Line (λ = 10830 A): A Closer Look

Although Moreton waves have historically been observed in Hα data, more recently waves have also been observed in chromospheric He I (λ = 10830 A) images. In a previous study, we found that chromospheric waves observed in He I data (from the Mauna Loa Solar Observatory) in two events (occurring on 2000 November 25 and 2001 January 20) are cospatial with the corresponding coronal waves observed by EIT (Fe XII λ = 195 A). In an effort to better understand the nature of chromospheric waves, we focus on these two wave events observed in He I in which two interesting phenomena occur: the waves are visible in the He I velocity data, and multiple waves are observed for each event. We suggest that the velocity signal is a result of slow-mode wave compression followed by a slow-mode wave rarefaction propagating downward from the corona into the upper chromosphere. We also suggest that the observed multiple waves indicate that more than one driving mechanism may be involved.

Observed and simulated depletion layers with southward IMF

Abstract. We present observations from the Polar satellite that confirm the existence of two types of depletion layers predicted under southward interplanetary magnetic field (IMF) conditions in magnetohydrodynamic simulations. The first depletion type occurs along the stagnation line when IMF BX and/or dipole tilt are/is present. Magnetic merging occurred away from the equator (Maynard et al., 2003) and flux pile-ups developed while the field lines drape to the high-latitude merging sites. This high-shear type of depletion is consistent with the depletion layer model suggested by Zwan and Wolf (1976) for low-shear northward IMF conditions. Expected sites for depletion layers are associated with places where IMF tubes of force first impinge upon the magnetopause. The second depletion type develops poleward of the cusp. Under strongly driven conditions, magnetic fields from Region 1 current closure over the lobes (Siscoe et al., 2002c) cause the high-latitude magnetopause to bulge outward, creating a shoulder above the cusp. These shoulders present the initial obstacle with which the IMF interacts. Flow is impeded, causing local flux pile-ups and low-shear depletion layers to form poleward of the cusps. Merging at the high-shear dayside magnetopause is consequently delayed. In both low- and high-shear cases, we show that the depletion layer structure is part of a slow mode wave standing in front of the magnetopause. As suggested by Southwood and Kivelson (1995), the depletions are rarefactions on the magnetopause side of slow-mode density compressions. While highly sheared magnetic fields are often used as proxies for ongoing local magnetic merging, depletion layers are prohibited at merging locations. Therefore, the existence of a depletion layer is evidence that the location of merging must be remote relative to the observation.