Hydromagnetic Waves Research Articles

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.

The Role of Pressure Anisotropy in Cosmic-Ray Hydrodynamics

Abstract The mean free path of cosmic rays in diffuse interstellar and intracluster gas is determined primarily by pitch angle scattering from hydromagnetic waves with wavelength of order the cosmic-ray gyroradius. In the theory of cosmic-ray self confinement, the waves are generated by instabilities driven by the cosmic rays themselves. The dominant instability is due to bulk motion, or streaming, of the cosmic rays, parallel to the background magnetic field , and transfers cosmic-ray momentum and energy to the thermal gas as well as confining the cosmic rays. Classical arguments and recent numerical simulations show that self confinement due to the streaming instability breaks down unless the cosmic-ray pressure and thermal gas density gradients parallel to are aligned, a condition that is unlikely to always be satisfied We investigate an alternative mechanism for cosmic-ray self confinement and heating of thermal gas based on pressure anisotropy instability. Although pressure anisotropy is demonstrably less effective than streaming instability as a self-confinement and heating mechanism on global scales, it may be important on mesoscales, particularly near sites of cosmic-ray injection.

Periodic mixed convection flow along the surface of a thermally and electrically conducting cone

The main aim of the present work is to highlight the significances of periodic mixed convection flow and heat transfer characteristics along the surface of magnetized cone by exerting magnetic field exact at the surface of the cone. The numerical simulations of coupled non-dimensional equations are computed in terms of velocity field, temperature and magnetic field concentration and then used to examine the periodic components of skin friction, ?w, heat transfer, qw, and current density, jw, for various governing parameters. A nice periodic behavior of heat transfer qw is concluded for each value of mixed convection parameter, ?, but maximum periodicity is sketched at ? = 50. It is also computed that the lower value of magnetic Prandtl number ? = 0.1 gets poor amplitude in current density but highest amplitude is sketched for higher ? = 0.5. The behavior of heat and fluid-flow in the pres?ence of aligned magnetic field is associated with the phase angle and amplitude of oscillation. It is also noted that due to the increase in magnetic force parameter, ?, there are wave like disturbances generate within the fluid layers. These disturbances are basically hydromagnetic waves which becomes more prominent as the strength of magnetic force parameter is increased.

Isothermal Motion of Hydromagnetic Cylindrical Shock Waves in Self Gravitating Rotating Gas

In this paper the Chisnell2 Chester1 Whitham3 (CCW1-3) method has been used to study the isothermal propagation of cylindrical hydromagnetic diverging shock waves in self gravitating rotating gas in presence of constant axial magnetic field. Assuming density decreasing atmosphere and exploring magnetic field as weak and strong, the analytical expressions have been derived for both weak and strong shocks and finally the effects of overtaking disturbances behind the flow on the motion of shock have also been included

Solitary wave solutions in plasma physics and acoustic gravity waves of some nonlinear evolution equations through enhanced MSE method

In this work, we probe the Gardner equation and the modified Benjamin-Bona-Mahony (mBBM) equation associated with plasma physics, acoustic-gravity waves in fluid mechanics, hydro-magnetic waves in cold plasma etc Exact wave solutions to the mentioned equations are studied analytically by the enhanced modified simple equation (EMSE) method. The solitary wave solutions are determined including free parameters. Setting definite values of the unknown parameters yield useful and stable solitary wave solutions. We have depicted some 3D and 2D graphs of the obtained solutions to comprehend the physical structure of the tangible events.

Wave heating from proto-neutron star convection and the core-collapse supernova explosion mechanism

ABSTRACT Our understanding of the core-collapse supernova explosion mechanism is incomplete. While the favoured scenario is delayed revival of the stalled shock by neutrino heating, it is difficult to reliably compute explosion outcomes and energies, which depend sensitively on the complex radiation hydrodynamics of the post-shock region. The dynamics of the (non-)explosion depend sensitively on how energy is transported from inside and near the proto-neutron star (PNS) to material just behind the supernova shock. Although most of the PNS energy is lost in the form of neutrinos, hydrodynamic and hydromagnetic waves can also carry energy from the PNS to the shock. We show that gravity waves excited by core PNS convection can couple with outgoing acoustic waves that present an appreciable source of energy and pressure in the post-shock region. Using one-dimensional simulations, we estimate the gravity wave energy flux excited by PNS convection and the fraction of this energy transmitted upwards to the post-shock region as acoustic waves. We find wave energy fluxes near $10^{51}\, \mathrm{erg}\, \mathrm{s}^{-1}\,$ are likely to persist for $\sim \! 1\, \mathrm{s}$ post-bounce. The wave pressure on the shock may exceed $10{{\ \rm per\ cent}}$ of the thermal pressure, potentially contributing to shock revival and, subsequently, a successful and energetic explosion. We also discuss how future simulations can better capture the effects of waves, and more accurately quantify wave heating rates.

An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma

In this paper, we present a coupling of homotopy perturbation technique and sumudu transform known as homotopy perturbation sumudu transform method (HPSTM). We show applicability of this method by solving fractional equal width (EW) equation, fractional modified equal width (MEW) equation and variant of fractional modified equal width (VMEW) equation. The fractional equal width equations play a key role in describing hydro-magnetic waves in cold plasma. Our aim is to study the nonlinear behavior of plasma system and highlight the important points. We examine the ability of HPSTM to study the fractional nonlinear systems and show its supremacy over other available numerical techniques. The other key point of this investigation is to examine two important fractional equations with different nonlinearity. The HPSTM gives excellent accuracy in analogous with the numerical solution. The numerical solutions indicate that the HPSTM is a powerful technique for studying the nonlinear behavior of plasma system very precisely and accurately.

Geomagnetic jerks and rapid hydromagnetic waves focusing at Earth’s core surface

Geomagnetic jerks are abrupt changes in the second time derivative—the secular acceleration—of Earth’s magnetic field that punctuate ground observatory records. As their dynamical origin has not yet been established, they represent a major obstacle to the prediction of geomagnetic field behaviour for years to decades ahead. Recent jerks have been linked to short-lived, temporally alternating and equatorially localized pulses of secular acceleration observed in satellite data, associated with rapidly alternating flows at Earth’s core surface. Here we show that these signatures can be reproduced in numerical simulations of the geodynamo that realistically account for the interaction between slow core convection and rapid hydromagnetic waves. In these simulations, jerks are caused by the arrival of localized Alfven wave packets radiated from sudden buoyancy releases inside the core. As they reach the core surface, the waves focus their energy towards the equatorial plane and along lines of strong magnetic flux, creating sharp interannual changes in core flow and producing geomagnetic jerks through the induced variations in magnetic field acceleration. The ability to numerically reproduce jerks offers a new way to probe the physical properties of Earth’s deep interior. Geomagnetic jerks in the Earth’s magnetic field are caused by the arrival of hydromagnetic waves and could be generated by sudden releases of buoyancy in the Earth’s core, suggest geodynamic numerical model simulations.

KDV limit of the hydromagnetic waves in cold plasma

In this paper, we study the long wavelength limit for the hydromagnetic waves propagating across a magnetic field in cold plasma. Based on the Gardner–Morikawa transform and the reductive perturbation method, it is demonstrated that as $$\varepsilon \rightarrow 0$$ , the solutions of such hydromagnetic waves converge to the solution of the Korteweg–de Vries equation on an $$O(\varepsilon ^{-3/2})$$ time interval.

Poleward-moving recurrent auroral arcs associated with impulse-excited standing hydromagnetic waves

In Earth's high-latitude ionosphere, the poleward motion of east–west elongated auroral arcs has been attributed to standing hydromagnetic waves, especially when the auroral arcs appear quasi-periodically with a recurrence time of a few minutes. The validation of this scenario requires spacecraft observations of ultra-low-frequency hydromagnetic waves in the magnetosphere and simultaneous observations of poleward-moving auroral arcs near the spacecraft footprints. Here we present the first observational evidence from the multi-spacecraft THEMIS (Time History of Events and Macroscale Interactions during Substorms) mission and the conjugated all-sky imager to support the scenario that standing hydromagnetic waves can generate the quasi-periodic appearance of poleward-moving auroral arcs. In this specific event, the observed waves were toroidal branches of the standing hydromagnetic waves, which were excited by a pulse in the solar wind dynamic pressure. Multi-spacecraft measurements from THEMIS also suggest higher wave frequencies at lower L shells (consistent with the distribution of magnetic field line eigenfrequencies), which indicates that the phase difference across latitudes would increase with time. As time proceeds, the enlarged phase difference corresponds to a lower propagation speed of the auroral arcs, which agrees very well with the ground-based optical data.

A new method for probing magnetic field strengths from striations in the interstellar medium

Recent studies of the diffuse parts of molecular clouds have revealed the presence of parallel, ordered low-density filaments termed striations. Flows along magnetic field lines, Kelvin-Helmholtz instabilities and hydromagnetic waves are amongst the various formation mechanisms proposed. Through a synergy of observational, numerical and theoretical analysis, previous studies singled out the hydromagnetic waves model as the only one that can account for the observed properties of striations. Based on the predictions of that model, we develop here a method for measuring the temporal evolution of striations through a combination of molecular and dust continuum observations. Our method allows us to not only probe temporal variations in molecular clouds but also estimate the strength of both the ordered and fluctuating components of the magnetic field projected on the plane-of-the-sky. We benchmark our new method against chemical and radiative transfer effects through two-dimensional magnetohydrodynamic simulations coupled with non-equilibrium chemical modelling and non-local thermodynamic equilibrium line radiative transfer. We find good agreement between theoretical predictions, simulations and observations of striations in the Taurus molecular cloud. We find a value of $\rm{27 \pm 7} ~\rm{\mu G}$ for the plane-of-sky magnetic field, in agreement with previous estimates via the Davis-Chandrasekhar-Fermi method, and a ratio of fluctuating to ordered component of the magnetic field of $\sim$ 10\%.

Geomagnetic acceleration and rapid hydromagnetic wave dynamics in advanced numerical simulations of the geodynamo

Geomagnetic secular acceleration is a unique window on the dynamics taking place in Earth's core. In this study, the behaviours of the secular acceleration and underlying core dynamics are examined in new numerical simulations of the geodynamo that reside on a theoretical path in parameter space connecting the region where most classical models are found to the natural conditions. The typical time scale for geomagnetic acceleration is found to be invariant along this path, at a value close to 10 years that matches Earth's core estimates. Despite this invariance, the spatio-temporal properties of secular acceleration show significant variability along the path, with an asymptotic regime of rapid rotation reached after 30% of this path (corresponding to a model Ekman number $E=3~10^{-7}$). In this regime, the energy of secular acceleration is entirely found at periods longer than that of planetary rotation, and the underlying flow acceleration patterns acquire a two-dimensional columnar structure representative of the rapid rotation limit. The spatial pattern of the secular acceleration at the core-mantle boundary shows significant localisation of energy within an equatorial belt. Rapid hydromagnetic wave dynamics is absent at the start of the path but can be clearly exhibited in the asymptotic regime. This study reports on ubiquitous axisymmetric geostrophic torsional waves of weak amplitude relatively to convective transport, and also stronger, laterally limited, quasi-geostrophic Alfv\'en waves propagating in the cylindrical radial direction from the tip of convective plumes towards the core-mantle boundary. Quasi-geostrophic Alfv\'en waves are shown to be an important carrier of flow acceleration to the core surface that links with the generation of strong, short-lived and intermittent equatorial pulses in the secular acceleration energy.

Application of extended Fan sub-equation method to $$\mathbf {(1+1)}$$ ( 1 + 1 ) -dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation with fractional evolution

The article studies the application of the extended Fan sub-equation method to \((1+1)\)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation with fractional evolution. This equation describes the hydromagnetic waves in cold plasma, acoustic waves in inharmonic crystals and acoustic gravity waves in compressible fluids. The structure of the extended Fan sub-equation method on the basis of time-fractional derivative is presented. The main idea of the method is to take full advantage of the general elliptic equation involving five parameters. The fractional derivatives are taken as in the sense of Jumarie’s modified Riemann–Liouville derivative. The method is reliable and gives more general exact solutions than the existing methods.

Solitary wave solutions for the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony nonlinear evolution equation

In this paper, we utilize the exp(−φ(ξ))-expansion method to find exact and solitary wave solutions of the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony nonlinear evolution equation. The generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony nonlinear evolution equation describes the model for the propagation of long waves that mingle with nonlinear and dissipative impact. This model is used in the analysis of the surface waves of long wavelength in hydro magnetic waves in cold plasma, liquids, acoustic waves in harmonic crystals and acoustic–gravity waves in compressible fluids. By using this method, seven different kinds of traveling wave solutions are successfully obtained for this model. The considered method and transformation techniques are efficient and consistent for solving nonlinear evolution equations and obtain exact solutions that are applied to the science and engineering fields.

Cosmic ray transport in the Galaxy: A review

The physics of energetic particle propagation in magnetized environments plays a crucial role in both the processes of acceleration and transport of cosmic rays. Recent theoretical developments in the field of cosmic ray research have been mainly in the direction of exploring non-linear aspects of the processes in which these particles are involved, namely the action of cosmic rays on the environment in which the transport and/or acceleration take place. When cosmic rays propagate outside of the acceleration region, such action is mainly in two forms: (1) they generate hydromagnetic waves, through streaming instabilities, leading to a dependence of the scattering properties of the medium on the spectrum and spatial distribution of the energetic particles, and (2) they exert a dynamical action on the plasma, which may cause the launching of cosmic ray driven Galactic winds. In this article we discuss these and other recent developments and how they compare with the bulk of new observations on the spectra of primary nuclei (mainly H and He) and secondary to primary ratios, such as the B/C ratio and the p¯/p ratio, and the positrons ratio e+/(e-+e+). We also comment on some radically new models of the origin of CRs, in which the physical meaning of the secondary to primary ratios is not the same as in the standard model.

The solitary hydromagnetic wave revisited: A demonstration of the j×B force in a collisionless plasma

An early paper on a solitary wave in a collision-free plasma, namely, a hydromagnetic wave propagating at right angles to a magnetic field, is further examined. The trajectories of both ions and electrons have been calculated for different wave velocities, up to the limiting value of twice the Alfvén velocity. The study clearly illustrates the fact that the positive ions move under the action of an electrostatic field, and the magnetic force has a negligible effect on their trajectories. The investigation shows that the macroscopic j×B force, i.e., that acting on the whole plasma, is transmitted to the ions via an electrostatic field.

Kinetic Properties of the Neutral Solar Wind

Abstract Charge-exchange collisions between the solar wind protons and interstellar hydrogen produce a distinctive population of neutral hydrogen streaming radially at nearly the solar-wind speed. This tenuous population, known as the neutral solar wind (NSW) is thought to play a key role in the appearance of the Interplanetary Boundary EXplorer ribbon, a bright circular band in the sky that is the source of neutral hydrogen with energies near 1 keV. According to the leading model of the ribbon, the velocity distribution of NSW hydrogen is imparted on the pickup ions (PUIs) generated via charge exchange with the interstellar protons beyond the heliopause, and in this way controls the stability of the resulting ring distribution of PUIs against hydromagnetic wave generation. In this paper, we examine the velocity distributions of the NSW atoms in the heliosphere and the outer heliosheath regions by following the phase-space trajectories of the Boltzmann equation. It is demonstrated that these distributions are highly anisotropic, with the parallel (radial) temperature greatly exceeding the perpendicular temperature. Ions picked up near 90° from the anisotropic NSW would form a stable ring distribution capable of generating the ribbon flux. We also discuss a second population of neutrals born in charge transfer collisions with interstellar PUIs, the so-called neutralized pickup ion (NPI) component. Their high thermal velocities translate into large parallel velocity spread of the daughter ribbon PUIs, which would adversely affect plasma stability in local interstellar space.

Generation of ELF waves during HF heating of the ionosphere at midlatitudes

AbstractModulated high‐frequency radio frequency heating of the ionospheric F region produces a local modulation of the electron temperature, and the resulting pressure gradient gives rise to a diamagnetic current. The oscillations of the diamagnetic current excite hydromagnetic waves in the ELF range that propagate away from the heated region. The generation of the waves in the 2–10 Hz range by a modulated heating in the midlatitude ionosphere is studied using numerical simulations of a collisional Hall‐magnetohydrodynamic model. To model the plasma processes in the midlatitude ionosphere the Earth's dipole magnetic field and typical ionospheric plasma parameters are used. As the hydromagnetic waves propagate away from the heated region in the F region, the varying plasma conditions lead to changes in their characteristics. Magnetosonic waves generated in the heating region and propagating down to the E region, where the Hall conductivity is dominant, excite oscillating Hall currents that produce shear Alfvén waves propagating along the field lines into the magnetosphere, where they propagate as the electromagnetic ion cyclotron (EMIC) and whistler waves. The EMIC waves propagate to the ion cyclotron resonance layer in the magnetosphere, where they are absorbed.

Hydromagnetic waves in a compressed-dipole field via field-aligned Klein–Gordon equations

Abstract. Hydromagnetic waves, especially those of frequencies in the range of a few millihertz to a few hertz observed in the Earth's magnetosphere, are categorized as ultra low-frequency (ULF) waves or pulsations. They have been extensively studied due to their importance in the interaction with radiation belt particles and in probing the structures of the magnetosphere. We developed an approach to examining the toroidal standing Aflvén waves in a background magnetic field by recasting the wave equation into a Klein–Gordon (KG) form along individual field lines. The eigenvalue solutions to the system are characteristic of a propagation type when the corresponding eigenfrequency is greater than a critical frequency and a decaying type otherwise. We apply the approach to a compressed-dipole magnetic field model of the inner magnetosphere and obtain the spatial profiles of relevant parameters and the spatial wave forms of harmonic oscillations. We further extend the approach to poloidal-mode standing Alfvén waves along field lines. In particular, we present a quantitative comparison with a recent spacecraft observation of a poloidal standing Alfvén wave in the Earth's magnetosphere. Our analysis based on the KG equation yields consistent results which agree with the spacecraft measurements of the wave period and the amplitude ratio between the magnetic field and electric field perturbations.

Imprints of impulse‐excited hydromagnetic waves on electrons in the Van Allen radiation belts

AbstractUltralow frequency electromagnetic oscillations, interpreted as standing hydromagnetic waves in the magnetosphere, are a major energy source that accelerates electrons to relativistic energies in the Van Allen radiation belt. Electrons can rapidly gain energy from the waves when they resonate via a process called drift resonance, which is observationally characterized by energy‐dependent phase differences between electron flux and electromagnetic oscillations. Such dependence has been recently observed and interpreted as spacecraft identifications of drift resonance electron acceleration. Here we show that in the initial wave cycles, the observed phase relationship differs from that characteristic of well‐developed drift resonance. We further examine the differences and find that they are imprints of impulse‐excited, coupled fast‐Alfvén waves before they transform into more typical standing waves. Our identification of such imprints provides a new understanding of how energy couples in the inner magnetosphere, and a new diagnostic for the generation and growth of magnetospheric hydromagnetic pulsations.