scholarly journals Dynamics of Alfvén waves in the night-side ionospheric Alfvén resonator at mid-latitudes

2005 ◽  
Vol 23 (2) ◽  
pp. 499-507 ◽  
Author(s):  
V. V. Alpatov ◽  
M. G. Deminov ◽  
D. S. Faermark ◽  
I. A. Grebnev ◽  
M. J. Kosch
Keyword(s):  
Pulse Duration ◽  
Alfven Waves ◽  
Fundamental Period ◽  
Alfvén Waves ◽  
Shear Mode ◽  
Q Factor ◽  
Trapped Waves ◽  
Alfven Resonator ◽  
Ionospheric Alfven Resonator ◽  
The Waves

Abstract. A numerical solution of the problem on dynamics of shear-mode Alfvén waves in the ionospheric Alfvén resonator (IAR) region at middle latitudes at nighttime is presented for a case when a source emits a single pulse of duration τ into the resonator region. It is obtained that a part of the pulse energy is trapped by the IAR. As a result, there occur Alfvén waves trapped by the resonator which are being damped. It is established that the amplitude of the trapped waves depends essentially on the emitted pulse duration τ and it is maximum at τ=(3/4)T, where T is the IAR fundamental period. The maximum amplitude of these waves does not exceed 30% of the initial pulse even under optimum conditions. Relatively low efficiency of trapping the shear-mode Alfvén waves is caused by a difference between the optimum duration of the pulse and the fundamental period of the resonator. The period of oscillations of the trapped waves is approximately equal to T, irrespective of the pulse duration τ. The characteristic time of damping of the trapped waves τdec is proportional to T, therefore the resonator Q-factor for such waves is independent of T. For a periodic source the amplitude-frequency characteristic of the IAR has a local minimum at the frequency π/ω=(3/4)T, and the waves of such frequency do not accumulate energy in the resonator region. At the fundamental frequency ω=2π/T the amplitude of the waves coming from the periodic source can be amplified in the resonator region by more than 50%. This alone is a basic difference between efficiencies of pulse and periodic sources of Alfvén waves. Explicit dependences of the IAR characteristics (T, τdec, Q-factor and eigenfrequencies) on the altitudinal distribution of Alfvén velocity are presented which are analytical approximations of numerical results.

scholarly journals Morphology and diagnostic potential of the ionospheric Alfvén resonator

2021 ◽  
Vol 7 (3) ◽  
pp. 36-52
Author(s):  
Alexander Potapov ◽  
Tatyana Polyushkina ◽  
B. Tsegmed
Keyword(s):  
Magnetic Field ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Field Frequency ◽  
Emission Frequency ◽  
Ionospheric Alfvén Resonator ◽  
Diagnostic Potential ◽  
Wide Range ◽  
Alfven Resonator ◽  
Ionospheric Alfven Resonator

The layering of the ionosphere leads to the formation of resonators and waveguides of various kinds. One of the most well-known is the ionospheric Alfvén resonator (IAR) whose radiation can be observed both on Earth’s surface and in space in the form of a fan-shaped set of discrete spectral bands (DSB), the frequency of which changes smoothly during the day. The bands are formed by Alfvén waves trapped between the lower part of the ionosphere and the altitude profile bending of Alfvén velocity in the transition region between the ionosphere and the magnetosphere. Thus, IAR is one of the important mechanisms of the ionosphere-magnetosphere interaction. The emission frequency lies in the range from tenths of hertz to about 8 Hz — the frequency of the first harmonic of the Schumann resonance. The review describes in detail the morphology of the phenomenon. It is emphasized that the IAR emission is a permanent phenomenon; the probability of observing it is primarily determined by the sensitivity of the equipment and the absence of interference of natural and artificial origin. The daily duration of the DSB observation almost completely depends on the illumination conditions of the lower ionosphere: the bands are clearly visible only when the D layer is shaded. Numerous theoretical IAR models have been systematized. All of them are based on the analysis of the excitation and propagation of Alfvén waves in inhomogeneous ionospheric plasma and differ mainly in sources of oscillation generation and methods of accounting for various factors such as interaction of wave modes, dipole geometry of the magnetic field, frequency dispersion of waves. Predicted by all models of the cavity and repeatedly confirmed experimentally, the close relationship between DSB frequency variations and critical frequency foF2 variations serves as the basis for searching ways of determining in real time the electron density of the ionosphere from IAR emission frequency measurements. It is also possible to estimate the profile of the ion composition over the ionosphere from the data on the IAR emission frequency structure. The review also focuses on other results from a wide range of IAR studies, specifically on the results that revealed the influence of the interplanetary magnetic field orien tation on oscillations of the resonator, and on the facts of the influence of seismic disturbances on IAR.

scholarly journals Morphology and diagnostic potential of the ionospheric Alfvén resonator

2021 ◽  
Vol 7 (3) ◽  
pp. 39-56
Author(s):  
Alexander Potapov ◽  
Tatyana Polyushkina ◽  
B. Tsegmed
Keyword(s):  
Magnetic Field ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Field Frequency ◽  
Emission Frequency ◽  
Ionospheric Alfvén Resonator ◽  
Diagnostic Potential ◽  
Wide Range ◽  
Alfven Resonator ◽  
Ionospheric Alfven Resonator

The layering of the ionosphere leads to the formation of resonators and waveguides of various kinds. One of the most well-known is the ionospheric Alfvén resonator (IAR) whose radiation can be observed both on Earth’s surface and in space in the form of a fan-shaped set of discrete spectral bands (DSB), the frequency of which changes smoothly during the day. The bands are formed by Alfvén waves trapped between the lower part of the ionosphere and the altitude profile bending of Alfvén velocity in the transition region between the ionosphere and the magnetosphere. Thus, IAR is one of the important mechanisms of the ionosphere-magnetosphere interaction. The emission frequency lies in the range from tenths of hertz to about 8 Hz — the frequency of the first harmonic of the Schumann resonance. The review describes in detail the morphology of the phenomenon. It is emphasized that the IAR emission is a permanent phenomenon; the probability of observing it is primarily determined by the sensitivity of the equipment and the absence of interference of natural and artificial origin. The daily duration of the DSB observation almost completely depends on the illumination conditions of the lower ionosphere: the bands are clearly visible only when the D layer is shaded. Numerous theoretical IAR models have been systematized. All of them are based on the analysis of the excitation and propagation of Alfvén waves in inhomogeneous ionospheric plasma and differ mainly in sources of oscillation generation and methods of accounting for various factors such as interaction of wave modes, dipole geometry of the magnetic field, frequency dispersion of waves. Predicted by all models of the cavity and repeatedly confirmed experimentally, the close relationship between DSB frequency variations and critical frequency foF2 variations serves as the basis for searching ways of determining in real time the electron density of the ionosphere from IAR emission frequency measurements. It is also possible to estimate the profile of the ion composition over the ionosphere from the data on the IAR emission frequency structure. The review also focuses on other results from a wide range of IAR studies, specifically on the results that revealed the influence of the interplanetary magnetic field orien tation on oscillations of the resonator, and on the facts of the influence of seismic disturbances on IAR.

scholarly journals Investigating the damping rate of phase-mixed Alfvén waves

2019 ◽  
Vol 632 ◽  
pp. A93 ◽  
Author(s):  
A. P. K. Prokopyszyn ◽  
A. W. Hood
Keyword(s):  
Wave Energy ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Coronal Loops ◽  
Phase Mixing ◽  
Heating Mechanism ◽  
At Resonance ◽  
Damping Rate ◽  
Field Lines ◽  
The Waves

Context. This paper investigates the effectiveness of phase mixing as a coronal heating mechanism. A key quantity is the wave damping rate, γ, defined as the ratio of the heating rate to the wave energy. Aims. We investigate whether or not laminar phase-mixed Alfvén waves can have a large enough value of γ to heat the corona. We also investigate the degree to which the γ of standing Alfvén waves which have reached steady-state can be approximated with a relatively simple equation. Further foci of this study are the cause of the reduction of γ in response to leakage of waves out of a loop, the quantity of this reduction, and how increasing the number of excited harmonics affects γ. Methods. We calculated an upper bound for γ and compared this with the γ required to heat the corona. Analytic results were verified numerically. Results. We find that at observed frequencies γ is too small to heat the corona by approximately three orders of magnitude. Therefore, we believe that laminar phase mixing is not a viable stand-alone heating mechanism for coronal loops. To arrive at this conclusion, several assumptions were made. The assumptions are discussed in Sect. 2. A key assumption is that we model the waves as strictly laminar. We show that γ is largest at resonance. Equation (37) provides a good estimate for the damping rate (within approximately 10% accuracy) for resonant field lines. However, away from resonance, the equation provides a poor estimate, predicting γ to be orders of magnitude too large. We find that leakage acts to reduce γ but plays a negligible role if γ is of the order required to heat the corona. If the wave energy follows a power spectrum with slope −5/3 then γ grows logarithmically with the number of excited harmonics. If the number of excited harmonics is increased by much more than 100, then the heating is mainly caused by gradients that are parallel to the field rather than perpendicular to it. Therefore, in this case, the system is not heated mainly by phase mixing.

Nonlinear Landau Damping of Alfvén Waves in a High β Plasma

1982 ◽  
Vol 37 (8) ◽  
pp. 809-815 ◽  
Author(s):  
Heinrich J. Völk ◽  
Catherine J. Cesarsky
Keyword(s):  
Wave Length ◽  
Wave Spectrum ◽  
Nonlinear Damping ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Propagating Waves ◽  
Damping Rate ◽  
Nonlinear Landau Damping ◽  
The Waves ◽  
The Magnetic Field

A study is made of the nonlinear damping of parallel propagating Alfvén waves in a high β plasma. Two circularly polarized parallel propagating waves give rise to a beat wave, which in general contains both a longitudinal electric field component and a longitudinal gradient in the magnetic field strength. The wave damping is due to the interactions of thermal particles with these fields. If the amplitudes of the waves are low, a given wave (ω1, k1) is damped by the presence of all longer wavelength waves; thus, if the amplitudes of the waves in the wave spectrum increase with wave length, the effect of the longest waves is dominant.However, when the amplitude of the waves is sufficiently high, the particles are trapped in the wave packets, and the damping rate may be considerably reduced. We calculate the induced electrostatic field, and examine the trapping of thermal particles in a pair of waves. Finally, we give examples of modified damping rates of a wave in the presence of a spectrum of waves, and show that, when the trapping is effective, the waves are mostly damped by their interactions with waves of comparable wavelengths

Secondary flow due to Alfvén waves

1977 ◽  
Vol 80 (1) ◽  
pp. 179-202 ◽  
Author(s):  
J. A. Shercliff
Keyword(s):  
Hyperbolic Equations ◽  
Wave Mode ◽  
Alfven Waves ◽  
Secondary Flows ◽  
Alfvén Waves ◽  
Stored Energy ◽  
Axial Field ◽  
Electromagnetic Characteristics ◽  
The Waves ◽  
Made In

Large (gigajoule) amounts of energy can in principle be stored as kinetic energy in liquid metal circulating round a torus and can be extracted at the gigawatt level by Alfvén waves propagating along an imposed axial field. A major limitation on the energy that may be so stored is the disruption of these primary Alfvén waves by secondary flows in meridional planes, associated with out-of-balance centrifugal forces ahead of and behind the waves and non-uniform magnetic pressures at the wave fronts. Vorticity, created at the wave, itself propagates in secondary Alfvén waves.This paper gives a linearized treatment of these secondary motions and the associated perturbations of the imposed axial field and compares the resulting disruption of the primary wave mode with crude estimates made in an earlier paper. The main case treated is the discharge of the stored energy into a matched resistor by an Alfvén step wave but the secondary consequences of standing primary waves are also explored. The nature of the solutions depends on the electromagnetic characteristics of the walls normal to the imposed field. The problem is mathematically interesting because it involves the joint solving of elliptic and hyperbolic equations that are coupled by the boundary conditions at these walls.

scholarly journals Polarization properties of standing shear Alfvén waves in non-axisymmetric background magnetic fields

2007 ◽  
Vol 25 (3) ◽  
pp. 815-822 ◽  
Author(s):  
K. Kabin ◽  
R. Rankin ◽  
I. R. Mann ◽  
A. W. Degeling ◽  
R. Marchand
Keyword(s):  
Geomagnetic Field ◽  
Radiation Belt ◽  
Low Frequency ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Ulf Waves ◽  
Outer Radiation Belt ◽  
Simple Description ◽  
The Waves ◽  
Shear Alfven Waves

Abstract. In this paper we present results concerning periods and polarizations of cold plasma ultra-low frequency (ULF) guided Alfvén waves in a non-axisymmetric geomagnetic field. The background geomagnetic field is approximated by a compressed dipole for which we propose a simple description in terms of Euler potentials. This study is motivated by the problem of outer-radiation belt electron acceleration by ULF waves, for which the polarization of the wave is of paramount importance. We consider an approximation appropriate to decoupled Alfvénic waves and find that the polarization of the waves can change significantly with local time. Therefore, the ULF wave's contribution to the MeV electron energization process can be localized in space.

scholarly journals On viscous and resistive dissipation of Alfvén waves in an isothermal atmosphere

1997 ◽  
Vol 20 (3) ◽  
pp. 605-610
Author(s):  
Hadi Yahya Alkahby
Keyword(s):  
Transition Layer ◽  
Kinematic Viscosity ◽  
Magnetic Energy ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Lower Region ◽  
Propagating Waves ◽  
The Waves ◽  
Isothermal Atmosphere ◽  
Viscosity Changes

In this article we will investigate reflection and dissipation of Alfvén waves, resulting from a uniform vertical magnetic field, in a viscous, resistive and isothermal atmosphere. It is shown that the atmosphere may be divided into two distinct regions connected by an absorbing and reflecting transition layer. In the transition layer the reflection, dissipation and absorption of the magnetic energy of the waves take place and in it the kinematic viscosity changes from small to large values. In the lower region the effect of the resistive diffusivity and kinematic viscosity changes from small to large values. In the lower region the effect of the resistive diffusivity and kinematic viscosity is negligible and in it the solution can be represented as a linear combination of two, incident and reflected, propagating waves with different wavelengths and different dissipative factors. In the upper region the effect of the resistive diffusivity and kinematic viscosity is large and the solution, which satisfies the prescribed boundary conditions, will behave as a constant. The reflection coefficient, the dissipative factors are determined and the conclusions are discussed in connection with solar heating.

scholarly journals Nonlinear Landau Damping of Alfven Waves and the Production and Propagation of Cosmic Rays

1981 ◽  
Vol 94 ◽  
pp. 255-256
Author(s):  
R. J. Stoneham
Keyword(s):  
Cosmic Rays ◽  
Phase Speed ◽  
Alfven Waves ◽  
Magnetized Plasma ◽  
Landau Damping ◽  
Alfvén Waves ◽  
Fermi Acceleration ◽  
Image Position ◽  
Hydromagnetic Waves ◽  
The Waves

The existence of hydromagnetic waves (waves whose frequency ω is less than the ion gyrofrequency Ωi = eB/mic) in a collisionless magnetized plasma with β, the ratio of plasma pressure to magnetic pressure, much greater than unity is required in theories for Fermi acceleration of cosmic rays by converging scattering centres at a shock front, in theories for the adiabatic cooling of cosmic rays due to trapping by plasma instabilities in an expanding supernova remnant (Kulsrud and Zweibel 1975, Schwartz and Skilling 1978) and in theories for resonant scattering of cosmic rays by hydromagnetic waves in the hot phase of the interstellar medium (Holman et al. 1979). Hydromagnetic waves may be damped by thermal ion cyclotron damping for wavenumbers k≳Ωi/vi, where vi = (Ti/mi)1/2 is the average thermal ion speed, and by linear Landau damping for non-zero angles of propagation with respect to the ambient magnetic field (Foote and Kulsrud 1979). Damping by both these processes is strong in a high-β plasma where there are many particles travelling at the phase speed of the waves. Hydromagnetic waves propagating along may be damped by nonlinear wave-particle interactions, the most important of which is thermal ion Landau damping of the beat wave of two Alfvén waves. This nonlinear process has the effect of transferring energy from the waves to the particles and can therefore be considered as a damping process for the waves.

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