Propagation Of Hydromagnetic Waves Research Articles

Propagation of Hydromagnetic Disturbance Waves and Gravitational Instability in a Magnetized Rotating Heat-Conducting Anisotropic Plasma

Propagation of Hydromagnetic Disturbance Waves and Gravitational Instability in a Magnetized Rotating Heat-Conducting Anisotropic Plasma

A taxonomy of simulated geomagnetic jerks

SUMMARYGeomagnetic jerks—abrupt changes in the acceleration of Earth’s magnetic field that punctuate geomagnetic records— have been richly documented over the past decades by taking advantage of the complementary strengths of ground observatory and satellite measurements. It has recently been proposed that these events originate from the interplay and timescale separation between slow convection and rapid hydromagnetic wave propagation in Earth’s outer core, with these latter waves playing a key role in the generation of jerk signals. To assess the generality of this explanation, here we analyse a catalogue of 14 events obtained during a 14 000-yr-long temporal sequence from a numerical geodynamo simulation that is the closest to date to Earth’s core conditions regarding timescale separation. Events are classified according to their dynamic origin and the depth at which they are triggered in the outer core. The majority of jerk events are found to arise from intermittent local disruptions of the leading-order force balance between the pressure, Coriolis, buoyancy and Lorentz forces (the QG-MAC balance), that leads to an inertial compensation through the emission of rapid, non-axisymmetric, quasi-geostrophic Alfvén waves from the region where this force balance is disrupted. Jerk events of moderate strength arise from the arrival at low latitudes at the core surface of hydromagnetic wave packets emitted from convective plumes rooted at the inner core boundary. As in an earlier simulation, these account well for jerk features that have recently been documented by satellite and ground observations. The more realistic timescales in the simulation reported here allow further details to be distinguished, such as multiple temporal alternations of geomagnetic acceleration pulses at low latitudes, long-range synchronization of pulse foci in space and rapid longitudinal drift of these foci at the core surface. The strongest events in the catalogue arise from disruption of the leading-order force balance near or at the core surface, from the combined influence of the arrival of buoyancy plumes and magnetic field rearrangement. The hydromagnetic waves that are sent laterally and downwards generate signals that clearly illustrate the presence of nearly synchronous ‘V-shaped’ magnetic variation patterns over a wide portion of Earth’s surface and also at mid to high latitudes, despite the source being confined to low latitudes at the core surface. Other well-known characteristics of strong geomagnetic jerks such as surges in the intensity of the secular variation and inflexions in the length-of-day variations are also reproduced in these events. Irrespectively of the event strength, our results support the hypothesis of a single physical root cause—the emission of magneto-inertial waves following a disruption of the QG-MAC balance—for jerks observed throughout the geomagnetic record.

The Propagation of Hydromagnetic Cylindrical Shock Waves in Weak Magnetic Field, With A Self-Gravitating Gas

<p>The effects of overtaking disturbances behind the flow on the propagation of diverging cylindrical shock Waves through an ideal gas in presence of a magnetic field having =constant= and an Initial density distribution where is a constant, is the density at the plane / exes of symmetry: The analytical formula for flow variables representing both the position form viz; weak and strong cases at shock waves have been obtained. Their numerical estimates at permissible shock front locations have been obtained.</p> <p>There numerical estimates at permissible shock front location's have been Calculated and compared with earlier result describing in Free Propagation through figures. After inclusion of E.O.D. noted that there is no change at flow variable with parameters and . However, the trends of variation with propagation distance r, for shock strength, shock velocity and particle velocity are not change in case of weak shock with work Magnetic field<strong>(wswmf).</strong></p>

SPATIAL STRUCTURE OF AZIMUTHALLY SMALL-SCALE MHD WAVES IN ONE-DIMENSIONALLY INHOMOGENEOUS FINITE PRESSURE PLASMA WITH CURVED FIELD LINES

We have studied propagation of hydromagnetic (MHD) waves in one-dimensionally inhomogeneous finite pressure plasma with curved field lines. Magnetic surfaces are considered to be concentric cylinders, where the cylinder’s radius models the radial coordinate in Earth’s magnetosphere. The waves are supposed to be azimuthally small-scale. In this approximation there are only two MHD modes — Alfvén and slow magnetosonic (SMS). We have derived an ordinary differential equation for the spatial structure of the wave field in this model. We have examined the character of the singularity on the surface of Alfvén and SMS resonances and the influence of field line curvature on them. We have determined wave transparent regions. The SMS transparent region was found to essentially broaden as compared to the straight field line case. The very existence of the Alfvén transparent region is caused by the field line curvature and finite plasma pressure; otherwise, the wave structure is represented by a localized resonance.

Пространственная структура азимутально-мелкомасштабных МГД-волн в одномерно-неоднородной плазме конечного давления с кривыми силовыми линиями

We have studied propagation of hydromagnetic (MHD) waves in one-dimensionally inhomogeneous finite pressure plasma with curved field lines. Magnetic surfaces are considered to be concentric cylinders, where the cylinder’s radius models the radial coordinate in Earth’s magnetosphere. The waves are supposed to be azimuthally small-scale. In this approximation there are only two MHD modes — Alfvén and slow magnetosonic (SMS). We have derived an ordinary differential equation for the spatial structure of the wave field in this model. We have examined the character of the singularity on the surface of Alfvén and SMS resonances and the influence of field line curvature on them. We have determined wave transparent regions. The SMS transparent region was found to essentially broaden as compared to the straight field line case. The very existence of the Alfvén transparent region is caused by the field line curvature and finite plasma pressure; otherwise, the wave structure is represented by a localized resonance.

Hydromagnetic waves and current relaxation: Damping at short wavelengths and small conductivity

AbstractInertial and diffusive effects on the propagation of hydromagnetic waves in plasmas of finite conductivity are explored by assuming a finite relaxation time for the current density. The domain of validity of the hydromagnetic approximation is determined by defining a lower limit for the perturbative wavelength. Three independent dispersion relations are obtained. At short wavelengths, it is found that the longitudinal component of the perturbative magnetic field damps out at a finite rate, which is determined fully by the relaxation time of the current density. In the same limit, it is shown that Alfvén waves can propagate through conductive plasmas with a null group speed. It is also shown that strong inertial and diffusive effects on magnetosonic waves can be discussed by defining suitably a perturbative parameter with the dimension of speed. It is argued that relevant corrections to space and time scales describing the reconnection of magnetic field lines are expected by applying the results presented here at sufficiently high frequencies.

On the propagation of hydromagnetic waves in a plasma of thermal and suprathermal components

The propagation of MHD waves is studied when two ideal fluids, thermal and suprathermal gases, coupled by magnetic field are moving with the steady flow velocity. The fluids move independently in a direction perpendicular to the magnetic field but gets coupled along the field. Due to the presence of flow in suprathermal and thermal fluids there appears forward and backward waves. All the forward and backward modes propagate in such a way that their rate of change of phase speed with the thermal Mach number is same. It is also found that besides the usual hydromagnetic modes there appears a suprathermal mode which propagates with faster speed. Surface waves are also examined on an interface formed with composite plasma (suprathermal and thermal gases) on one side and the other is a non-magnetized plasma. In this case, the modes obtained are two or three depending on whether the sound velocity in thermal gas is equal to or greater than the sound velocity in suprathermal gas. The results lead to the conclusion that the interaction of thermal and suprathermal components may lead to the occurrence of an additional mode called suprathermal mode whose phase velocity is higher than all the other modes.

Geodynamic constraints on the steady and time-dependent inner core axial rotation

In this work, constraints on the steady and time-dependent rates of axial inner core rotation are established based on the angular momentum balance between the inner core, fluid core and mantle. It is shown that the rate of a steadily rotating inner core is limited by the torque on the mantle from surface forces at the core-mantle boundary (CMB). The rate of rotation of an oscillating inner core is constrained by the changes in mantle rotation induced by gravitational coupling, which must not exceed the observed changes in length of day. Assuming that the largest torque at the CMB is from electromagnetic forces, our results suggest that the maximum amplitude of an inner core oscillating at a period of 60 yr is ∼0.03° yr−1, while the maximum amplitude of a steadily rotating inner core is ∼0.3° yr−1. This implies that the largest inner core rotation rate compatible with the ensemble of seismic studies, 0.2° yr−1, may be explained by a steady rotation but cannot be explained by a decadal oscillation. Though a steady rotation of 0.2° yr−1 is possible, it constrains the conductance of the lower mantle to be in the range of 1.6 –2.5 × 109 S and the viscous relaxation timescale of the inner core to be in the range of 5–8 yr (i.e. a bulk inner core viscosity of 2.5 –4 × 1017 Pa s). Larger steady and oscillating rotation rates may be possible if the inner core can deform on a timescale shorter than ∼5 yr or if the conductance of the lower mantle is larger than ∼2.5 × 109 S, though this would then contradict constraints on these two quantities derived from other observations. Finally, we note that a steadily rotating inner core is compatible with the westward motions of magnetic field features at the CMB, as the latter provide the electromagnetic torque on the mantle that balances the gravitational torque from the rotating inner core. In addition, these westward motions must be predominantly due to advection by flow rather than to the propagation of hydromagnetic waves, as the electromagnetic torque at the CMB is otherwise too small to allow an inner core rotation rate as large as 0.2° yr−1.

Hydromagnetic surface waves on a tangential discontinuity

Propagation of hydromagnetic surface waves on an MHD tangential discontinuity, separating two uniform magnetic plasmas, across which the magnetic field changes both its direction and field-strength, is examined. The study is arbitrarily confined to discontinuities one side of which has a plasma-β value larger than unity. A classification scheme to identify the ‘fast’ and the ‘slow’ surface waves is employed thus enabling us to find new features in the modal structure of these waves. In the case of sufficiently small values for the density ratio between the higher and the lower Alfvén speed regions on opposite sides of the interface, this study reveals the presence of a ‘forbidden region’ for propagation of fast surface waves with values of their propagation angle being smaller than a certain critical value. The study also reveals the existence of two distinct slow surface waves with angles of propagation larger than a certain critical value but for two different ranges of values for the angle between magnetic field vectors across the interface. While revealing such new structures of the surface modes for intermediate parameter values, the present investigation also confirms earlier results regarding the asymptotic behaviour of the modes in the incompressible limit. §Present address: Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata, India 700035.

Propagation of hydromagnetic waves in a two-population plasma system consisting of anisotropic relativistic and nonrelativistic polytropic fluids

The paper discusses the propagation of waves and instabilities in a plasma model which consists of the concatenation of two magnetohydrodynamic (MHD) fluids, one of which is relativistic and has anisotropic pressure components given by double adiabatic equations derived by Gedalin [Phys. Rev. E 47, 4354 (1993)] while the other one has pressure components given by generalized polytropic laws. The polytropic laws, though empirical, are useful in that the appropriate values of the polytropic indices enable one to apply the treatment to a variety of situations ranging from an anisotropic ultrarelativistic plasma to an ordinary nonrelativistic isotropic plasma. A linearized analysis is carried out and the dispersion relation is derived using the normal mode technique. The dispersion relation, which gives numerous earlier results in special cases, is discussed both analytically as well as numerically for parameters which simulate cosmic rays and the background interstellar plasma as two MHD components. An additional mode of propagation that arises due to the concatenation of the MHD components is the only mode which transports energy in the direction perpendicular to the ambient magnetic field. Situations where this model supports instabilities are also discussed.

Propagation of thermal and hydromagnetic waves in an ionizing-recombining hydrogen plasma

The propagation of thermal and magnetohydrodynamic (MHD) waves in a heat-conducting, hydrogen plasma, threaded by an external uniform magnetic field (B) and in which photoionization and photorecombination [H++e−⇌H+hν(χ)] processes are progressing, is investigated here using linear analysis. The resulting dispersion equation is solved analytically for varied strength (β≪1 and ∼1) and orientation of the magnetic field, where β denotes the ratio of plasma to magnetic pressures. Application of this model to the interstellar medium shows that heat conduction governs the propagation of thermal waves only at relatively high frequencies regardless of the plasma temperature, strength, and orientation of the magnetic field. When the direction of wave propagation is held perpendicular to B (i.e., k ⊥B), the magnetosonic phase velocity is closely Alfvénic for β≪1, while for β∼1 both the hydrostatic and magnetic pressures determine the wave velocity. As long as k ∥B, the fast (transverse) magnetosonic wave becomes an Alfvén wave for all frequencies independent of the plasma temperature and field strength, while the slow (longitudinal) magnetosonic wave becomes a pure sound wave. Amplification of thermal and MHD waves always occur at low frequencies and preferentially at temperatures for which the plasma is either weakly or partially ionized. Compared to previous analysis for the same hydrogen plasma model with B=0, the presence of the magnetic field makes the functional dependence of the physical quantities span a longer range of frequencies, which becomes progressively longer as the field strength is increased.

Spatial field structure and polarization of geomagnetic pulsations in conjugate areas

The ultra-low-frequency (ULF) geomagnetic pulsations observed at two nearly conjugate mid-latitude sites are examined to study their spatial structure and polarization, and learn about the role of ionospheric conductivity in forming their ground signatures. The data of 1999–2002 from Antarctica and New England ( L of 2.4) are compared with the numerical results obtained in a simple plane model of ULF wave propagation through the ionosphere and atmosphere. The multi-layered model environment includes an anisotropic and parametrically time-dependent ionosphere, a uniform magnetosphere and a conducting Earth, all placed in a tilted geomagnetic field. The measured diurnal and seasonal variations in the orientation angle of the polarization ellipse are interpreted as effects of hydromagnetic wave propagation through the ionosphere and conversion to an electromagnetic field below. Essentially, the phase, amplitude and polarization of ULF waves observed at the ground are controlled by the wave's spatial structure in the magnetosphere and ionospheric transverse conductivities. The differences shown by the characteristics of simultaneous pulsations in conjugate areas arise mainly from different local ionospheric conditions, while the source waves of the pulsations are common to both sites.

Equatorially dominated magnetic field change at the surface of Earth's core.

Slow temporal variations in Earth's magnetic field originate in the liquid outer core. We analyzed the evolution of nonaxisymmetric magnetic flux at the core surface over the past 400 years. We found that the most robust feature is westward motion at 17 kilometers per year, in a belt concentrated around the equator beneath the Atlantic hemisphere. Surprisingly, this motion is dominated by a single wavenumber and persists throughout the observation period. This phenomenon could be produced by an equatorial jet of core fluid, by hydromagnetic wave propagation, or by a combination of both. Discrimination between these mechanisms would provide useful constraints on the dynamics of Earth's core.

Evolution of Hydromagnetic Disturbances in Low Ionized Cosmic Plasmas

We consider the propagation of hydromagnetic waves generated by a compact turbulent source in low ionized plasmas, applying the Lighthill theory. We assume the plasma to be isothermal, and adopt a uniform, stationary medium thread by ordered magnetic fields as an initial condition. Then, the distinct properties of the hydromagnetic waves originating from a source oscillating with a fixed frequency are studied in the linear regime. As is well known, in low ionized plasmas, the generated waves dissipate due to ion-neutral damping. In this paper, the dependence of the dissipation rate on the frequency of the oscillating source is investigated. The larger the frequency becomes, the more substantial is the wave dissipation. Implications of our results on the energy source in molecular clouds are also discussed. Interestingly, since the outflow lobes associated with young stellar objects act as compact turbulent sources, hydromagnetic waves are generated by them. From our order-estimations, about 70% of the energy of the outflow itself propagates as waves or turbulences, while the remaining 30% dissipates and heats the neutrals via ion-neutral damping. Then, we confirm that the outflows are significant energy sources in molecular clouds in the context of the Lighthill theory.

Three‐dimensional numerical simulation of MHD waves observed by the Extreme Ultraviolet Imaging Telescope

We investigate the global large amplitude waves propagating across the solar disk as observed by the SOHO/Extreme Ultraviolet Imaging Telescope (EIT). These waves appear to be similar to those observed in Hα in the chromosphere and which are known as “Moreton waves,” associated with large solar flares [Moreton, 1960, 1964]. Uchida [1968] interpreted these Moreton waves as the propagation of a hydromagnetic disturbance in the corona with its wavefront intersecting the chromosphere to produce the Moreton wave as observed in movie sequences of Hα images. To search for an understanding of the physical characteristics of these newly observed EIT waves, we constructed a three‐dimensional, time‐dependent, numerical magnetohydrodynamic (MHD) model. Measured global magnetic fields, obtained from the Wilcox Solar Observatory (WSO) at Stanford University, are used as the initial magnetic field to investigate hydromagnetic wave propagation in a three‐dimensional spherical geometry. Using magnetohydrodynamic wave theory together with simulation, we are able to identify these observed EIT waves as fast mode MHD waves dominated by the acoustic mode, called magnetosonic waves. The results to be presented include the following: (1) comparison of observed and simulated morphology projected on the disk and the distance‐time curves on the solar disk; (2) three‐dimensional evolution of the disturbed magnetic field lines at various viewing angles; (3) evolution of the plasma density profile at a specific location as a function of latitude; and (4) computed Friedrich's diagrams to identify the MHD wave characteristics.

Ionospheric conductivities according to Doppler radar observations of stimulated turbulence

Results of Doppler radar observations are discussed of HF scattering from heater induced inhomogeneities in an underdense ionospheric plasma. The quasiperiodic variations shown by the Doppler frequency shift are associated with the E× H plasma drift in the electric field of geomagnetic pulsations. Combined with a theoretical model of hydromagnetic wave propagation, with allowance for an arbitrary dip angle of the geomagnetic field and arbitrary angle of incidence, the Doppler shift measurements at several points along the geofield tube permit estimating height-integrated ionospheric conductivities

Evolution of Hydromagnetic Disturbances in Low Ionized Cosmic Plasmas

We consider the propagation of hydromagnetic waves generated by a compact turbulent source in low ionized plasmas, applying the Lighthill theory. We assume the plasma to be isothermal, and adopt a uniform, stationary medium thread by ordered magnetic fields as an initial condition. Then, the distinct properties of the hydromagnetic waves originating from a source oscillating with a fixed frequency are studied in the linear regime. As is well known, in low ionized plasmas, the generated waves dissipate due to ion-neutral damping. In this paper, the dependence of the dissipation rate on the frequency of the oscillating source is investigated. The larger the frequency becomes, the more substantial is the wave dissipation. Implications of our results on the energy source in molecular clouds are also discussed. Interestingly, since the outflow lobes associated with young stellar objects act as compact turbulent sources, hydromagnetic waves are generated by them. From our order-estimations, about 70% of the energy of the outflow itself propagates as waves or turbulences, while the remaining 30% dissipates and heats the neutrals via ion-neutral damping. Then, we confirm that the outflows are significant energy sources in molecular clouds in the context of the Lighthill theory.

Hydromagnetic wave propagation and coupling in a magnetotail waveguide

For some time the magnetotail has been considered as a possible region where hydromagnetic waves can propagate as waveguide modes. Recently, attention has turned to the magnetospheric flanks as waveguides, and much useful insight has been gained into propagation of fast waveguide modes there, and the structure of the field line resonances they can drive. We return to the magnetotail and investigate hydromagnetic wave propagation and coupling in a magnetotail waveguide. This problem is significantly different from the flank waveguide as the ambient magnetic field is directed along the waveguide rather than across. Field line resonances of the flank type are not possible in the lobe waveguide. We describe a numerical simulation of a model waveguide in which the Alfvén speed decreases across the waveguide to the central plasma sheet. The waveguide is stimulated by a short compressional perturbation located in the far tail. The cross‐tail spatial structure is chosen to give relatively weak coupling between fast and Alfvén modes so that phase and group velocities of uncoupled fast modes can be used to interpret the results. We find that the perturbation propagates dispersively down the waveguide in the form of fast waveguide modes. Fourier components with small parallel wavenumber contain most of the energy, and propagate relatively slowly toward the “Earth.” These act as moving sources which launch Alfvén waves continuously earthward. The wave dispersion relations are such that the waveguide modes couple with Alfvén waves only in a limited region of the transverse Alfvén speed gradient. The Alfvén waves travel at the local Alfvén speed along each field line, so that as they travel the wave on a given field line becomes increasingly out of phase with waves on adjacent field lines. The phase mixing in our model is novel in that it includes the effects of transverse gradients in both Alfvén frequency and parallel wavenumber which tend to cancel each other out. Nevertheless, the phase‐mixing process leads to increasingly fine transverse structure as the waves progress down the waveguide. The results are likely to be applicable in regions such as the plasma sheet boundary layer and the plasma mantle.

Anomalous sudden commencement on March 24, 1991

An anomalous geomagnetic sudden commencement (SC) occurred on March 24, 1991. It is characterized by an exceptionally large and sharp impulse observed in its initial part along the noon meridian in middle and low latitudes. The analysis of the SC was made by using high time resolution digital data from the 210° Meridian Magnetometer Chain in the west Pacific, Sub‐Auroral Magnetometer Network (SAMNET) in the United Kingdom and southern Scandinavia, the EISCAT Magnetometer Cross in northern Scandinavia and Svalbard, and Canopus in Canada together with other ground and satellite (GOES 6, GOES 7, CRRES, and GMS) data. The results of the analysis suggest that the pulse observed at lower‐latitude ground stations was caused by the propagation of a strong magnetospheric compression of short duration (less than l min) which has never been observed before this event. The HF Doppler observation in Kyoto near local noon seems to be consistent with existence of the bipolar electric field associated with the propagating compressional magnetic pulse. The SAMNET stations and CRRES in the early morning also detected positive pulses which delays 30–50 s from the pulses in noon sector. Although the delay in the peak time of the pulse observed on the ground is consistent with ionospheric hydromagnetic wave propagation from the dayside to the nightside with finite speed, the initial onset time of the pulse on the ground was almost simultaneous everywhere suggesting the existence of an “almost instantaneous” propagation mode below the ionosphere.

Hydromagnetic waves in rapidly rotating spherical shells generated by poloidal decay modes

Abstract This paper presents the first attempt to examine the stability of a poloidal magnetic field in a rapidly rotating spherical shell of electrically conducting fluid. We find that a steady axisymmetric poloidal magnetic field loses its stability to a non-axisymmetric perturbation when the Elsasser number A based on the maximum strength of the field exceeds a value about 20. Comparing this with observed fields, we find that, for any reasonable estimates of the appropriate parameters in planetary interiors, our theory predicts that all planetary poloidal fields are stable, with the possible exception of Jupiter. The present study therefore provides strong support for the physical relevance of magnetic stability analysis to planetary dynamos. We find that the fluid motions driven by magnetic instabilities are characterized by a nearly two-dimensional columnar structure attempting to satisfy the Proudman-Taylor theorm. This suggests that the most rapidly growing perturbation arranges itself in such a way that the geostrophic condition is satisfied to leading order. A particularly interesting feature is that, for the most unstable mode, contours of the non-axisymmetric azimuthal flow are closely aligned with the basic axisymmetric poloidal magnetic field lines. As a result, the amplitude of the azimuthal component of the instability is smaller than or comparable with that of the poloidal component, in contrast with the instabilities generated by toroidal decay modes (Zhang and Fearn, 1994). It is shown, by examining the same system with and without fluid inertia, that fluid inertia plays a secondary role when the magnetic Taylor number Tm ≳ 105. We find that the direction of propagation of hydromagnetic waves driven by the instability is influenced strongly by the size of the inner core.