Measurement Method for Evaluating the Probability Distribution of the Quality Factor of Mode-Stirred Reverberation Chambers

An original experimental method for determining the empirical probability distribution function (PDF) of the quality factor (Q) of a mode-stirred reverberation chamber is presented. Spectral averaging of S-parameters across a relatively narrow frequency interval at a single pair of locations for the transmitting and receiving antennas is applied to estimate the stored and dissipated energy in the cavity, avoiding the need for spatial scanning to obtain spatial volume or surface averages. The effective number of simultaneously excited cavity modes per stir state, M, can be estimated by fitting the empirical distribution to the parametrized theoretical distribution. The measured results support a previously developed theoretical model for the PDF of Q and show that spectral averaging over a bandwidth as small as a few hundred kHz is sufficient to obtain accurate results.Comment: submitted for publicatio

Notes on simplicial rook graphs

The simplicial rook graph ${\rm SR}(m,n)$ is the graph of which the vertices are the sequences of nonnegative integers of length $m$ summing to $n$, where two such sequences are adjacent when they differ in precisely two places. We show that ${\rm SR}(m,n)$ has integral eigenvalues, and smallest eigenvalue $s = \max (-n, -{m \choose 2})$, and that this graph has a large part of its spectrum in common with the Johnson graph $J(m+n-1,n)$. We determine the automorphism group and several other properties

Non-axisymmetric oscillations of stratified coronal magnetic loops with elliptical cross-sections

We study non-axisymmetric oscillations of a straight magnetic tube with an elliptic cross-section and density varying along the tube. The governing equations for kink and fluting modes in the thin tube approximation are derived. We found that there are two kink modes, polarised along the large and small axes of the elliptic cross-section. We have shown that the ratio of frequencies of the first overtone and fundamental harmonic is the same for both kink modes and independent of the ratio of the ellipse axes. On the basis of this result we concluded that the estimates of the atmospheric scale height obtained using simultaneous observations of the fundamental harmonic and first overtone of the coronal loop kink oscillations are independent of the ellipticity of the loop cross-section

Resonant Alfven waves in partially ionized plasmas of the solar atmosphere

Context. Magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere. In magnetic waveguides resonant absorption due to plasma inhomogeneity naturally transfers wave energy from large-scale motions to small-scale motions. In the cooler parts of the solar atmosphere as, e.g., the chromosphere, effects due to partial ionization may be relevant for wave dynamics and heating. Aims. We study resonant Alfven waves in partially ionized plasmas. Methods. We use the multifluid equations in the cold plasma approximation. We investigate propagating resonant MHD waves in partially ionized flux tubes. We use approximate analytical theory based on normal modes in the thin tube and thin boundary approximations along with numerical eigenvalue computations. Results. We find that the jumps of the wave perturbations across the resonant layer are the same as in fully ionized plasmas. The damping length due to resonant absorption is inversely proportional to the frequency, while that due to ion-neutral collisions is inversely proportional to the square of the frequency. For observed frequencies in the solar atmosphere, the amplitude of MHD kink waves is more efficiently damped by resonant absorption than by ion-neutral collisions. Conclusions. Most of the energy carried by chromospheric kink waves is converted into localized azimuthal Alfven waves that can deposit energy in the coronal medium. The dissipation of wave energy in the chromosphere due to ion-neutral collisions is only effective for high-frequency waves. The chromosphere acts as a filter for kink waves with periods shorter than 10 s

Three-dimensional coronal slow modes: toward three-dimensional seismology

On 2008 January 10, the twin Solar Terrestrial Relations Observatory (STEREO) A and B spacecraft conducted a high time cadence study of the solar corona with the Extreme UltraViolet Imager (EUVI) instruments with the aim of investigating coronal dynamics. Observations of the three-dimensional propagation of waves within active region coronal loops and a measurement of the true coronal slow mode speed are obtained. Intensity oscillations with a period of approximately 12 minutes are observed to propagate outwards from the base of a loop system, consistent with the slow magnetoacoustic mode. A novel analysis technique is applied to measure the wave phase velocity in the observations of the A and B spacecraft. These stereoscopic observations are used to infer the three-dimensional velocity vector of the wave propagation, with an inclination of 37 +- 6 deg to the local normal and a magnitude of 132 +- 9 and 132 +- 11 km s-1, giving the first measurement of the true coronal longitudinal slow mode speed, and an inferred temperature of 0.84 +- 12 MK and 0.84 +- 15 MK

Kink oscillations of flowing threads in solar prominences

Recent observations by Hinode/SOT show that MHD waves and mass flows are simultaneously present in the fine structure of solar prominences. We investigate standing kink magnetohydrodynamic (MHD) waves in flowing prominence threads from a theoretical point of view. We model a prominence fine structure as a cylindrical magnetic tube embedded in the solar corona with its ends line-tied in the photosphere. The magnetic cylinder is composed of a region with dense prominence plasma, which is flowing along the magnetic tube, whereas the rest of the flux tube is occupied by coronal plasma. We use the WKB approximation to obtain analytical expressions for the period and the amplitude of the fundamental mode as functions of the flow velocity. In addition, we solve the full problem numerically by means of time-dependent simulations. We find that both the period and the amplitude of the standing MHD waves vary in time as the prominence thread flows along the magnetic structure. The fundamental kink mode is a good description for the time-dependent evolution of the oscillations, and the analytical expressions in the WKB approximation are in agreement with the full numerical results. The presence of flow modifies the period of the oscillations with respect to the static case. However, for realistic flow velocities this effect might fall within the error bars of the observations. The variation of the amplitude due to the flow leads to apparent damping or amplification of the oscillations, which could modify the real rate of attenuation caused by an additional damping mechanism.Comment: Accepted for publication in A&

THE INFLUENCE OF STATIC STRETCHING ON THE VISC0ELASTIC PROPERTIES OF M. TRICEPS SURAE

Though the practice of stretching is widely used in sports, general fitness and physiotherapy, there is still a lack of basic research in this area. This study describes the viscoelastic properties of m. triceps surae and investigates the influence of static stretching. 20 males and 11 females, without a history of ankle injury, participated in this experiment. Each testee completed two sessions of seven measurements on an active omnikinetic dynamometer (PROMETT-system). The velocity of the leverarm has been kept constant during all tests (lO°/s). An interactive loop determines the stretching amplitude depending on the force exerted on this lever. The subject was fixated in an adjustable chair, the right leg extended and sustained, the left leg maximally bended in the hip to stabilize the pelvis. Further on, wooden plates were placed between the back of the chair and the pelvis to avoid any hip displacements while exerting force on the foot. After aligning the ankle axis with the axis of the dynamometer, the leverarm was manipulated to determine the moment (Mcrit) and the angle associated with a stretch just short of causing pain. The first and last measurement,of each session was an isokinetic stretch up to Mcrit (Stretch). After a short hold (200 me) in this extreme position (Hold) the same isokinetic movement, but in opposite direction, was used to relax the muscle (Relax). Between-these two 'control measurements' five identic static stretches were performed. These stretches were varied among subgroups regarding the intensity of the Stretch (90% or 100% of Mcrit) and the duration of the Hold (10s or 30 a). Netto joint moments were calculated and expressed relatively as a function of the stretching amplitude. Eighty parameters were selected in order to describe the strain-stretch curves during Stretch and Relax phases and the stress-time curves during the Hold phases. Results obtained by comparing those parameters from first and last control measurements reveal a very stable intra-individual viscoelastic behaviour of the muscle. Though, significant differences in stretching amplitude, creep and parameters describing the shape of the relax curves were observed. Differences between subgroups show a stronger influence of the intensity to the result of the static stretch compared to the influence of a longer Hold phase. In this study females had a significant smaller stretching amplitude then males. They also had less advantages of static stretching

Coronal magnetic field measurement using loop oscillations observed by Hinode/EIS

We report the first spectroscopic detection of a kink MHD oscillation of a solar coronal structure by the Extreme-Ultraviolet Imaging Spectrometer (EIS) on the Japanese Hinode satellite. The detected oscillation has an amplitude of 1 kms−1 in the Doppler shift of the FeXII 195 Å spectral line (1.3 MK), and a period of 296 s. The unique combination of EIS’s spectroscopic and imaging abilities enables us to measure simultaneously the mass density and length of the oscillating loop. This enables us to measure directly the magnitude of the local magnetic field, the fundamental coronal plasma parameter, as 39 ± 8 G, with unprecedented accuracy. This proof of concept makes EIS an exclusive instrument for the full scale implementation of the MHD coronal seismological technique

Kelvin-Helmholtz instability in coronal magnetic flux tubes due to azimuthal shear flows

Transverse oscillations of coronal loops are often observed and have been theoretically interpreted as kink magnetohydrodynamic (MHD) modes. Numerical simulations by Terradas et al. (2008, ApJ 687, L115) suggest that shear flows generated at the loop boundary during kink oscillations could give rise to a Kelvin-Helmholtz instability (KHI). Here, we investigate the linear stage of the KHI in a cylindrical magnetic flux tube in the presence of azimuthal shear motions. We consider the basic, linearized MHD equations in the beta = 0 approximation, and apply them to a straight and homogeneous cylindrical flux tube model embedded in a coronal environment. Azimuthal shear flows with a sharp jump of the velocity at the cylinder boundary are included in the model. We obtain an analytical expression for the dispersion relation of the unstable MHD modes supported by the configuration, and compute analytical approximations of the critical velocity shear and the KHI growth rate in the thin tube limit. A parametric study of the KHI growth rates is performed by numerically solving the full dispersion relation. We find that fluting-like modes can develop a KHI in time-scales comparable to the period of kink oscillations of the flux tube. The KHI growth rates increase with the value of the azimuthal wavenumber and decrease with the longitudinal wavenumber. However, the presence of a small azimuthal component of the magnetic field can suppress the KHI. Azimuthal motions related to kink oscillations of untwisted coronal loops may trigger a KHI, but this phenomenon has not been observed to date. We propose that the azimuthal component of the magnetic field is responsible for suppressing the KHI in a stable coronal loop. The required twist is small enough to prevent the development of the pinch instability.Comment: Submitted in Ap

Nonlinear Instability of kink oscillations due to shear motions

First results from a high-resolution three-dimensional nonlinear numerical study of the kink oscillation are presented. We show in detail the development of a shear instability in an untwisted line-tied magnetic flux tube. The instability produces significant deformations of the tube boundary. An extended transition layer may naturally evolve as a result of the shear instability at a sharp transition between the flux tube and the external medium. We also discuss the possible effects of the instability on the process of resonant absorption when an inhomogeneous layer is included in the model. One of the implications of these results is that the azimuthal component of the magnetic field of a stable flux tube in the solar corona, needed to prevent the shear instability, is probably constrained to be in a very specific range