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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Extension of Low Dissipative High Order Hydrodynamics Schemes for MHD Equations

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD (magnetohydrodynamic) equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls to limit the amount and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvi-linear grids. The three features of the present MHD scheme over existing schemes in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion magnetized flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike existing schemes for the conservative MHD equations which suffer from ill-conditioned eigen-decompositions, the present scheme makes use of a well-conditioned eigen-decomposition to solve the conservative form of the MHD equations. This is due to, partly. the fact that the divergence of the magnetic field condition is a different type of constraint from its incompressible Navier-Stokes cousin. Third, a new approach to minimize the numerical error of the divergence free magnetic condition for high order scheme is introduced.

Yee, H. C.↗
NASA NTRS1998

Global MHD Simulation of Mesoscale Structures at the Magnetospheric Boundary

The research carried out for this protocol was focused on the study of mesoscales structures at the magnetospheric boundary. We investigated three areas: (1) the structure of the magnetospheric boundary for steady solar wind conditions; (2) the dynamics of the dayside magnetospheric boundary and (3) the dynamics of the distant tail magnetospheric boundary. Our approach was to use high resolution three-dimensional global magnetohydrodynamic (MHD) simulations of the interaction of the solar wind with the Earth's magnetosphere. We first considered simple variations of the interplanetary conditions to obtain generic cases that helped us in establishing the basic cause and effect relationships for steady solar wind conditions. Subsequently, we used actual solar wind plasma and magnetic field parameters measured by an upstream spacecraft as input to the simulations and compared the simulation results with sequences of events observed by another or several other spacecraft located downstream the bow shock. In particular we compared results with observations made when spacecraft crossed the magnetospheric boundary.

Berchem, Jean↗
NASA NTRS2023

Modeling the Formation and Eruption of Coronal Structures by Linking Data-Driven Magnetofrictional and MHD Simulations for AR 12673

Context .The data-driven and time-dependent modeling of coronal magnetic fields is crucial for understanding solar eruptions. These efforts are complicated by the challenges of finding a balance between physical realism and computing efficiency. One possible technique is to couple two modeling approaches. Aims . Our aim here is to showcase our progress in using time-dependent magnetofrictional model (TMFM) results as input to dynamical magnetohydrodynamic (MHD) simulations. However, due to the different evolution processes in these two models, using TMFM snapshots in an MHD simulation is nontrivial. We address these issues, both physically and numerically, discuss the incompatibility of the TMFM output to serve as the initial condition in MHD simulations, and show our methods of mitigating this. The evolution of the flux systems and the cause of the eruption are investigated. Methods . TMFM is a prevalent approach that has proven to be a very useful tool in the study of the formation of unstable structures in the solar corona. In particular, it is capable of incorporating observational data as initial and boundary conditions and requires shorter computational time compared to MHD simulations. To leverage the efficiency of data-driven TMFM and also to simulate eruptive events in the MHD framework, one can apply TMFM up to a certain time before the expected eruption(s) and then proceed with the simulation in the full or ideal MHD regime in order to more accurately capture the eruption process. Results . We show the results of a benchmark test case with a linked TMFM and MHD simulation to study the evolution of NOAA active region 12673. A rise of a twisted flux bundle through the MHD simulation domain is observed, but we find that the rate of the rise and the altitude reached depends on the time of the TMFM snapshot that was used to initialize the MHD simulation and the helicity injected into the system. The analysis suggested that torus instability and slip-running reconnection could play an important role in the eruption. Conclusions . The results show that the linkage of TMFM and zero-β MHD models can be successfully used to model the eruptive coronal magnetic fields.

F. Daei↗
NASA NTRS2022

How a Realistic Magnetosphere Alters the Polarizations of Surface, Fast Magnetosonic, and Alfvén Waves

System-scale magnetohydrodynamic (MHD) waves within Earth's magnetosphere are often understood theoretically using box models. While these have been highly instructive in understanding many fundamental features of the various wave modes present, they neglect the complexities of geospace such as the inhomogeneities and curvilinear geometries present. Here, we show global MHD simulations of resonant waves impulsively excited by a solar wind pressure pulse. Although many aspects of the surface, fast magnetosonic (cavity/waveguide), and Alfvén modes present agree with the box and axially symmetric dipole models, we find some predictions for large-scale waves are significantly altered in a realistic magnetosphere. The radial ordering of fast mode turning points and Alfvén resonant locations may be reversed even with monotonic wave speeds. Additional nodes along field lines that are not present in the displacement/velocity occur in both the perpendicular and compressional components of the magnetic field. Close to the magnetopause, the perpendicular oscillations of the magnetic field have the opposite handedness to the velocity. Finally, widely used detection techniques for standing waves, both across and along the field, can fail to identify their presence. We explain how all these features arise from the MHD equations when accounting for a non-uniform background field and propose modified methods that might be applied to spacecraft observations.

ULF Waves↗
NASA NTRS2017

Electron Drift Resonance in the MHD-Coupled Comprehensive Inner Magnetosphere-Ionosphere Model

Relativistic electrons in the outer radiation belt are highly dynamic and respond to interplanetary solar wind structures interacting with the Earth's magnetic field. A known mechanism dictating electron dynamics is the drift-resonant interaction with ultralow frequency (ULF) waves. The present work simulates the ring current and radiation belt electron populations in the bounce-averaged, kinetic Comprehensive Inner Magnetosphere-Ionosphere model coupled with the Block Adaptive Tree Solar Wind Roe-type Upwind Scheme global magnetospheric magnetohydrodynamic (MHD) code using an idealized ULF wave solar wind density driver. ULF waves generated with 10 min periods (at 1.67 mHz frequencies) in the MHD model are characterized and the corresponding energization of electrons and radial transport of electron phase space density is presented. The drift-resonant electron energy is determined in the simulation and is consistent with the electron resonance conditions in dipolar magnetic fields. The present results will be an important component of understanding inner magnetospheric dynamics and how these inner magnetospheric populations interact with ULF waves resulting from interplanetary solar wind structures.

Komar, C. M.↗
NASA NTRS2003

Dayside Proton Aurora: Comparisons between Global MHD Simulations and Image Observations

The IMAGE mission provides a unique opportunity to evaluate the accuracy of current global models of the solar wind interaction with the Earth's magnetosphere. In particular, images of proton auroras from the Far Ultraviolet Instrument (FUV) onboard the IMAGE spacecraft are well suited to support investigations of the response of the Earth's magnetosphere to interplanetary disturbances. Accordingly, we have modeled two events that occurred on June 8 and July 28, 2000, using plasma and magnetic field parameters measured upstream of the bow shock as input to three-dimensional magnetohydrodynamic (MHD) simulations. This paper begins with a discussion of images of proton auroras from the FUV SI-12 instrument in comparison with the simulation results. The comparison showed a very good agreement between intensifications in the auroral emissions measured by FUV SI-12 and the enhancement of plasma flows into the dayside ionosphere predicted by the global simulations. Subsequently, the IMAGE observations are analyzed in the context of the dayside magnetosphere's topological changes in magnetic field and plasma flows inferred from the simulation results. Finding include that the global dynamics of the auroral proton precipitation patterns observed by IMAGE are consistent with magnetic field reconnection occurring as a continuous process while the iMF changes in direction and the solar wind dynamic pressure varies. The global simulations also indicate that some of the transient patterns observed by IMAGE are consistent with sporadic reconnection processes. Global merging patterns found in the simulations agree with the antiparallel merging model. though locally component merging might broaden the merging region, especially in the region where shocked solar wind discontinuities first reach the magnetopause. Finally, the simulations predict the accretion of plasma near the bow shock in the regions threaded by newly open field lines on which plasma flows into the dayside ionosphere are enhanced. Overall the results of these initial comparisons between global MHD simulation results and IMAGE observations emphasize the interplay between reconnection and dynamic pressure processes at the dayside magnetopause. as well as the intricate connection between the bow shock and the auroral region.

Berchem, J.↗
NASA NTRS2011

Detection of Ionospheric Alfven Resonator Signatures Onboard C/NOFS: Implications for IRI Modeling

The 2008-2009 long-lasting solar minimum activity has been the one of its kind since the dawn of space age, offering exceptional conditions for investigating space weather in the near-Earth environment. First ever detection of Ionospheric Alfven Resonator (IAR) signatures in orbit offers new means for investigating ionospheric electrodynamics, namely MHD (MagnetoHydroDynamics) wave propagation, aeronomy processes, ionospheric dynamics, and Sun-Earth connection mechanisms at a local scale. Local and global plasma density heterogeneities in the ionosphere and magnetosphere allow for formation of waveguides and resonators where magnetosonic and shear Alfven waves propagate. The ionospheric magnetosonic waveguide results from complete magnetosonic wave reflection about the ionospheric F-region peak, where the Alfven index of refraction presents a maximum. MHD waves can also be partially trapped in the vertical direction between the lower boundary of the ionosphere and the magnetosphere, a resonance mechanism known as IAR. In this work we present C/NOFS (Communications/Navigation Outage Forecasting System) Extremely Low Frequency (ELF) electric field measurements related to IAR signatures, discuss the resonance and wave propagation mechanisms in the ionosphere, and address the electromagnetic inverse problem from which electron/ion distributions can be derived. These peculiar IAR electric field measurements provide new, complementary methodologies for inferring ionospheric electron and ion density profiles, and also contribute for the investigation of ionosphere dynamics and space weather monitoring. Specifically, IAR spectral signatures measured by C/NOFS contribute for improving the International Reference Ionosphere (IRI) model, namely electron density and ion composition.

Simoes, F.↗
NASA NTRS2012

Statistical Theory of the Ideal MHD Geodynamo

A statistical theory of geodynamo action is developed, using a mathematical model of the geodynamo as a rotating outer core containing an ideal (i.e., no dissipation), incompressible, turbulent, convecting magnetofluid. On the concentric inner and outer spherical bounding surfaces the normal components of the velocity, magnetic field, vorticity and electric current are zero, as is the temperature fluctuation. This allows the use of a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity, current and the temperature fluctuation. The resulting dynamical system, based on the Boussinesq form of the magnetohydrodynamic (MHD) equations, represents MHD turbulence in a spherical domain. These basic equations (minus the temperature equation) and boundary conditions have been used previously in numerical simulations of forced, decaying MHD turbulence inside a sphere [1,2]. Here, the ideal case is studied through statistical analysis and leads to a prediction that an ideal coherent structure will be found in the form of a large-scale quasistationary magnetic field that results from broken ergodicity, an effect that has been previously studied both analytically and numerically for homogeneous MHD turbulence [3,4]. The axial dipole component becomes prominent when there is a relatively large magnetic helicity (proportional to the global correlation of magnetic vector potential and magnetic field) and a stationary, nonzero cross helicity (proportional to the global correlation of velocity and magnetic field). The expected angle of the dipole moment vector with respect to the rotation axis is found to decrease to a minimum as the average cross helicity increases for a fixed value of magnetic helicity and then to increase again when average cross helicity approaches its maximum possible value. Only a relatively small value of cross helicity is needed to produce a dipole moment vector that is aligned at approx.10deg with the rotation axis.

Shebalin, J. V.↗
NASA NTRS2016

CME Flux Rope and Shock Identifications and Locations: Comparison of White Light Data, Graduated Cylindrical Shell Model, and MHD Simulations

Coronal mass ejections (CMEs) are major transient phenomena in the solar corona that are observed with ground-based and spacecraft-based coronagraphs in white light or with in situ measurements by spacecraft. CMEs transport mass and momentum and often drive shocks. In order to derive the CME and shock trajectories with high precision, we apply the graduated cylindrical shell (GCS) model to fit a flux rope to the CME directed toward STEREO A after about 19:00 UT on 29 November 2013 and check the quality of the heliocentric distance-time evaluations by carrying out a three-dimensional magnetohydrodynamic (MHD) simulation of the same CME with the Block Adaptive Tree Solar-Wind Roe Upwind Scheme (BATS-R-US) code. Heliocentric distances of the CME and shock leading edges are determined from the simulated white light images and magnetic field strength data. We find very good agreement between the predicted and observed heliocentric distances, showing that the GCS model and the BATS-R-US simulation approach work very well and are consistent. In order to assess the validity of CME and shock identification criteria in coronagraph images, we also compute synthetic white light images of the CME and shock. We find that the outer edge of a cloud-like illuminated area in the observed and predicted images in fact coincides with the leading edge of the CME flux rope and that the outer edge of a faint illuminated band in front of the CME leading edge coincides with the CME-driven shock front.

Schmidt, J. M.↗
NASA NTRS2014

Onset of Reconnection in the near Magnetotail: PIC Simulations

Using 2.5-dimensional particle-in-cell (PIC) simulations of magnetotail dynamics, we investigate the onset of reconnection in two-dimensional tail configurations with finite Bz. Reconnection onset is preceded by a driven phase, during which magnetic flux is added to the tail at the high-latitude boundaries, followed by a relaxation phase, during which the configuration continues to respond to the driving. We found a clear distinction between stable and unstable cases, dependent on deformation amplitude and ion/electron mass ratio. The threshold appears consistent with electron tearing. The evolution prior to onset, as well as the evolution of stable cases, are largely independent of the mass ratio, governed by integral flux tube entropy conservation as imposed in MHD (magnetohydrodynamics). This suggests that ballooning instability in the tail should not be expected prior to the onset of tearing and reconnection. The onset time and other onset properties depend on the mass ratio, consistent with expectations for electron tearing. At onset,we found electron anisotropies T⊥⁄ T∥ (bottom tail divided by parallel tail) equals 1.1-1.3, raising growth rates and wavenumbers. Our simulations have provided a quantitative onset criterion that is easily evaluated in MHD simulations, provided the spatial resolution is sufficient. The evolution prior to onset and after the formation of a neutral line does not depend on the electron physics, which should permit an approximation by MHD simulations with appropriate dissipation terms.

PIC↗
NASA NTRS2006

The Latitudinal Excursion of Coronal Magnetic Field Lines in Response to Differential Rotation: MHD Simulations

Solar energetic particles, which are believed to originate from corotating interacting regions (CIRS) at low heliographic latitude, were observed by the Ulysses spacecraft even as it passed over the Sun's poles. One interpretation of this result is that high-latitude field lines intercepted by Ulysses connect to low-latitude CIRs at much larger heliocentric distances. The Fisk model explains the latitudinal excursion of magnetic field lines in the solar corona and heliosphere as the inevitable consequence of the interaction of a tilted dipole in a differentially rotating photosphere with rigidly rotating coronal holes. We use a time-dependent three-dimensional magnetohydrodynamic (MHD) algorithm to follow the evolution of a simple model of the solar corona in response to the differential rotation of the photospheric magnetic flux. We examine the changes of the coronal-hole boundaries, the redistribution of the line-of-sight magnetic field, and the precession of field lines in the corona. Our results confirm the basic idea of the Fisk model, that differential rotation leads to changes in the heliographic latitude of magnetic field lines. However, the latitudinal excursion of magnetic field lines in this simple "tilted dipole" model is too small to explain the Ulysses observations. Although coronal holes in our model rotate more rigidly than do photospheric features (in general agreement with observations), they do not rotate strictly rigidly as assumed by Fisk. This basic difference between our model and Fisk's will be explored in the future by considering more realistic magnetic flux distributions, as observed during Ulysses polar excursions.

Lionello, Roberto↗
NASA NTRS2016

Fast Ionized X-Ray Absorbers in AGNs

We investigate the physics of the X-ray ionized absorbers often identified as warm absorbers (WAs) and ultra-fast outflows (UFOs) in Seyfert AGNs from spectroscopic studies in the context of magnetically-driven accretion-disk wind scenario. Launched and accelerated by the action of a global magnetic field anchored to an underlying accretion disk around a black hole, outflowing plasma is irradiated and ionized by an AGN radiation field characterized by its spectral energy density (SED). By numerically solving the Grad-Shafranov equation in the magnetohydrodynamic (MHD) framework, the physical property of the magnetized disk-wind is determined by a wind parameter set, which is then incorporated into radiative transfer calculations with xstar photoionization code under heating-cooling equilibrium state to compute the absorber's properties such as column density N(sub H), line-of-sight (LoS) velocity v, ionization parameter xi, among others. Assuming that the wind density scales as n varies as r(exp. -1), we calculate theoretical absorption measure distribution (AMD) for various ions seen in AGNs as well as line spectra especially for the Fe K alpha absorption feature by focusing on a bright quasar PG 1211+143 as a case study and show the model's plausibility. In this note we demonstrate that the proposed MHD-driven disk-wind scenario is not only consistent with the observed X-ray data, but also help better constrain the underlying nature of the AGN environment in a close proximity to a central engine.

accretion↗
NASA NTRS1992

Role of inductive electric fields in substorm development

A study discussing and investigating the role of inductive electric fields in substorm development is presented. It is common to use the scalar potential phi to calculate the electrostatic field E(sup ES)-(inverted Delta)(phi). However, vector potential A has not been extensively used to analyze results by the relation for the inductive electric field E(sup IND)-delta A/delta t. Because of the weak dependence in distance (1/r) these potentials show the effect of distant sources, unlike MHD (Magnetohydrodynamic) theory which is strictly local. The two can be separated by the choice of the Coulomb (transverse) gauge. It is proper to consider that the plasma polarizes to counteract the activation of the inductive electric field; this is a matter of cause and effect. However, such polarization produces a curl free electrostatic field and thus cannot alter the electromotive force due to induction. This idea has some interesting consequences for plasma physics, including violations of MHD theory, creation of the substorm current diversion, and a fresh look at dayside merging via plasma transfer events.

Heikkila, Walter J.↗
NASA NTRS2016

Do We Know the Actual Magnetopause Position for Typical Solar Wind Conditions?

We compare predicted magnetopause positions at the subsolar point and four reference points in the terminator plane obtained from several empirical and numerical MHD (magnetohydrodynamics) models. Empirical models using various sets of magnetopause crossings and making different assumptions about the magnetopause shape predict significantly different magnetopause positions (with a scatter greater than 1 Earth radius (R (sub E)) even at the subsolar point. Axisymmetric magnetopause models cannot reproduce the cusp indentations or the changes related to the dipole tilt effect, and most of them predict the magnetopause closer to the Earth than non axisymmetric models for typical solar wind conditions and zero tilt angle. Predictions of two global non axisymmetric models do not match each other, and the models need additional verification. MHD models often predict the magnetopause closer to the Earth than the non axisymmetric empirical models, but the predictions of MHD simulations may need corrections for the ring current effect and decreases of the solar wind pressure that occur in the foreshock. Comparing MHD models in which the ring current magnetic field is taken into account with the empirical Lin et al. model, we find that the differences in the reference point positions predicted by these models are relatively small for B (sub z) equals 0 (note: B (sub z) is when the Earth's magnetic field points north versus Sun's magnetic field pointing south). Therefore, we assume that these predictions indicate the actual magnetopause position, but future investigations are still needed.

Samsonov, A. A.↗
NASA NTRS2002

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes for the compressible Euler and Navier-Stokes equations has been developed and verified by the authors and collaborators. These schemes are suitable for the problems in question. Basically, the scheme consists of sixth-order or higher non-dissipative spatial difference operators as the base scheme. To control the amount of numerical dissipation, multiresolution wavelets are used as sensors to adaptively limit the amount and to aid the selection and/or blending of the appropriate types of numerical dissipation to be used. Magnetohydrodynamics (MHD) waves play a key role in drag reduction in highly maneuverable high speed combat aircraft, in space weather forecasting, and in the understanding of the dynamics of the evolution of our solar system and the main sequence stars. Although there exist a few well-studied second and third-order high-resolution shock-capturing schemes for the MHD in the literature, these schemes are too diffusive and not practical for turbulence/combustion MHD flows. On the other hand, extension of higher than third-order high-resolution schemes to the MHD system of equations is not straightforward. Unlike the hydrodynamic equations, the inviscid MHD system is non-strictly hyperbolic with non-convex fluxes. The wave structures and shock types are different from their hydrodynamic counterparts. Many of the non-traditional hydrodynamic shocks are not fully understood. Consequently, reliable and highly accurate numerical schemes for multiscale MHD equations pose a great challenge to algorithm development. In addition, controlling the numerical error of the divergence free condition of the magnetic fields for high order methods has been a stumbling block. Lower order methods are not practical for the astrophysical problems in question. We propose to extend our hydrodynamics schemes to the MHD equations with several desired properties over commonly used MHD schemes.

Sjoegreen, Bjoern↗
NASA NTRS2013

A Simple GPU-Accelerated Two-Dimensional MUSCL-Hancock Solver for Ideal Magnetohydrodynamics

We describe our experience using NVIDIA's CUDA (Compute Unified Device Architecture) C programming environment to implement a two-dimensional second-order MUSCL-Hancock ideal magnetohydrodynamics (MHD) solver on a GTX 480 Graphics Processing Unit (GPU). Taking a simple approach in which the MHD variables are stored exclusively in the global memory of the GTX 480 and accessed in a cache-friendly manner (without further optimizing memory access by, for example, staging data in the GPU's faster shared memory), we achieved a maximum speed-up of approx. = 126 for a sq 1024 grid relative to the sequential C code running on a single Intel Nehalem (2.8 GHz) core. This speedup is consistent with simple estimates based on the known floating point performance, memory throughput and parallel processing capacity of the GTX 480.

graphics processing units↗
NASA NTRS1995

Numerical magetohydrodynamics in astronphysics: Algorithm and tests for one-dimensional flow`

We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the total variation diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. We also describe a non-linear Riemann solver for ideal MHD, which includes rarefractions as well as shocks. The numerical code and the Riemann solver have been used to test each other. Extensive tests encompassing all the possible ideal MHD structures with planar symmetries (i.e., one-dimensional flows) are presented. These include those for which the field structure is two dimensional (i.e., those flows often called '1 + 1/2 dimensional') as well as those for which the magnetic field plane rotates (i.e., those flows often called '1 + 1/2 + 1/2 dimensional'). Results indicate that the code can resolve strong fast, slow, and magnetosonic shocks within two to four cells, but more cells are required if shocks become weak. With proper steepening, we could resolve rotational discontinuities within three to five cells. However, without successful implementation of steepening, contact discontinuities are resolved with approximately 10 cells and tangential discountinuities are resolved with approximately 15 cells. Out tests confirm that slow compound structures with tow-dimensional magnetic fields are composed of intermediate shocks (so-called 2-4 intermediate shocks) followed by slow rarefaction waves. Finally, tests demostrate that in two-dimensional magnetohydrodynamics, fast compound structures, which are composed of intermediate shocks (so-called 1-3 intermediate shocks) preceeded by fast rarefaction waves, are also possible.

Ryu, Dongsu↗
NASA NTRS1986

Impulsively generated fast coronal pulsations

Rapid oscillations in the corona are discussed from a theoretical standpoint, developing some previous work on ducted, fast magnetoacoustic waves in an inhomogeneous medium. In the theory, impulsively (e.g., flare) generated mhd (magnetohydrodynamic) waves are ducted by regions of low Alfven speed (high density) such as coronal loops. Wave propagation in such ducts is strongly dispersive and closely akin to the behavior of Love waves in seismology, Pekeris waves in oceanography and guided waves in fiber optics. Such flare-generated magnetoacoustic waves possess distinctive temporal signatures consisting of periodic, quasi-periodic and decay phases. The quasi-periodic phase possesses the strongest amplitudes and the shortest time scales. Time scales are typically of the order of a second for inhomogeneities (coronal loop width) of 1000 km and Alfven speeds of 1000/kms, and pulse duration times are of tens of seconds. Quasi-periodic signatures have been observed in radio wavelengths for over a decade and more recently by SMM. It is hoped that the theoretical ideas outlined may be successfully related to these observations and thus aid the interpretation of oscillatory signatures recorded by SMM. Such signatures may also provide a diagnostic of coronal conditions. New aspects of the ducted mhd waves, for example their behavior in smoothly varying as opposed to tube-like inhomogeneities, are currently under investigation. The theory is not restricted to loops but applied equally to open field regions.

Edwin, P. M.↗