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 On resistive dissipation of Alfvén waves in an isothermal atmosphere

1996 ◽  
Vol 19 (3) ◽  
pp. 587-594
Author(s):  
H. Y. Alkahby
Keyword(s):  
Transition Region ◽  
Magnetic Energy ◽  
Alfven Waves ◽  
Scale Height ◽  
Wave Number ◽  
Alfvén Waves ◽  
Propagating Waves ◽  
The Waves ◽  
Isothermal Atmosphere ◽  
Density Scale

In this paper we will examine the reflection and dissipation of Alfvén waves, resulting from a uniform vertical magnetic field, in an inviscid, resistive and isothermal atmosphere. An equation for the damping length distance that wave can travel at Alfvén speed is derived. This equation shows that the damping length is proportional to the wave number and the density scale height and it is valid not only for Alfvén waves but also for any wave that travels at Alfvén speed. Moreover, it is shown that the atmosphere may be divided into two distinct regions connected by an absorbing and reflecting transition region. In the lower region the solution can be represented as a linear combination of two, incident and reflected, propagating waves with the same wavelengths and the same dissipative factors. In the upper region the effect of the resistive diffusivity and Alfvén speed is large and the solution, which satisfies the prescribed boundary conditions, either decays with altitude or behaves as a constant. In the transition region the reflection, dissipation and absorption of the magnetic energy of the waves take place. The reflection coefficient, the dissipative factors, which are proportional to the damping length, are determined and the conclusions are discussed in connection with heating of the solar atmosphere.

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

scholarly journals Effect of the radiative damping on magnetohydrodynamic waves in an isothermal medium

2002 ◽  
Vol 29 (6) ◽  
pp. 341-348 ◽  
Author(s):  
Hadi Alkahby ◽  
Andrew Talmadge ◽  
Abraham Jalbout
Keyword(s):  
Attenuation Factor ◽  
Heat Radiation ◽  
Heating Process ◽  
Magnetohydrodynamic Waves ◽  
Lower Region ◽  
Radiation Coefficient ◽  
Propagating Waves ◽  
Isothermal Medium ◽  
The Waves ◽  
Isothermal Atmosphere

We investigate the effect of the heat radiation on the reflection and dissipation of upward propagating waves in an isothermal atmosphere. It is shown that the magnetic field produces a totally reflecting layer. Consequently, the atmosphere can be divided into two distinct regions. In the lower region, the solution can be written as a linear combination of an upward and a downward propagating wave, and in the upper region the solution, which satisfies the upper boundary condition, decays exponentially or behaves like a constant. These two regions are connected by a region in which the reflection and transmission of the waves takes place. Moreover, the heat radiation affects only the lower region and changes the sound speed from the adiabatic value to the isothermal one. The reflection coefficient and the attenuation factor of the amplitude of the waves are derived for all values of the heat radiation coefficient. Finally, the conclusions are presented in connection with the heating process of the solar atmosphere.

scholarly journals Nonlinear Alfvén waves, discontinuities, proton perpendicular acceleration, and magnetic holes/decreases in interplanetary space and the magnetosphere: intermediate shocks?

2005 ◽  
Vol 12 (3) ◽  
pp. 321-336 ◽  
Author(s):  
B. T. Tsurutani ◽  
G. S. Lakhina ◽  
J. S. Pickett ◽  
F. L. Guarnieri ◽  
N. Lin ◽  
...  
Keyword(s):  
Interplanetary Space ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Reverse Shock ◽  
Propagating Waves ◽  
Mirror Mode ◽  
Interaction Regions ◽  
Electron Holes ◽  
Proton Cyclotron

Abstract. Alfvén waves, discontinuities, proton perpendicular acceleration and magnetic decreases (MDs) in interplanetary space are shown to be interrelated. Discontinuities are the phase-steepened edges of Alfvén waves. Magnetic decreases are caused by a diamagnetic effect from perpendicularly accelerated (to the magnetic field) protons. The ion acceleration is associated with the dissipation of phase-steepened Alfvén waves, presumably through the Ponderomotive Force. Proton perpendicular heating, through instabilities, lead to the generation of both proton cyclotron waves and mirror mode structures. Electromagnetic and electrostatic electron waves are detected as well. The Alfvén waves are thus found to be both dispersive and dissipative, conditions indicting that they may be intermediate shocks. The resultant "turbulence" created by the Alfvén wave dissipation is quite complex. There are both propagating (waves) and nonpropagating (mirror mode structures and MDs) byproducts. Arguments are presented to indicate that similar processes associated with Alfvén waves are occurring in the magnetosphere. In the magnetosphere, the "turbulence" is even further complicated by the damping of obliquely propagating proton cyclotron waves and the formation of electron holes, a form of solitary waves. Interplanetary Alfvén waves are shown to rapidly phase-steepen at a distance of 1AU from the Sun. A steepening rate of ~35 times per wavelength is indicated by Cluster-ACE measurements. Interplanetary (reverse) shock compression of Alfvén waves is noted to cause the rapid formation of MDs on the sunward side of corotating interaction regions (CIRs). Although much has been learned about the Alfvén wave phase-steepening processfrom space plasma observations, many facets are still not understood. Several of these topics are discussed for the interested researcher. Computer simulations and theoretical developments will be particularly useful in making further progress in this exciting new area.

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 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.

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.

On the effects of viscosity and anisotropic resistivity on the damping of Alfvén waves

2000 ◽  
Vol 63 (3) ◽  
pp. 221-238 ◽  
Author(s):  
L. M. B. C. CAMPOS ◽  
P. M. V. M. MENDES
Keyword(s):  
Wave Equation ◽  
Fourth Order ◽  
Magnetic Energy ◽  
Propagation Speed ◽  
Alfven Waves ◽  
Second Order ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Total Energy Density ◽  
Polarized Waves

The equations of magnetohydrodynamics (MHD) are written for non-uniform viscosity and resistivity – the latter in the cases of Ohmic and anisotropic resistivity. In the case of Ohmic (anisotropic) diffusivity, there is (are) one (two) transverse components of the velocity and magnetic field perturbation(s), leading to a second-order (fourth-order) dissipative Alfvén- wave equation. In the more general case of dissipative Alfvén waves with isotropic viscosity and anisotropic resistivity, the fourth-order wave equation may be replaced by two decoupled second-order equations for right- and left-polarized waves, whose dispersion relations show that the first resistive diffusivity causes dissipation like the viscosity, whereas the second resistive diffusivity causes a change in propagation speed. The second resistive diffusivity invalidates the equipartition of kinetic and magnetic energy, modifies the energy flux through the propagation speed, and also changes the ratio of viscous to resistive dissipation. If the directions of propagation and polarization are equal (i.e. for right-polarized upward-propagating or left-polarized downward-propagating waves), the magnetic energy increases relative to the kinetic energy, the resistive dissipation increases relative to the viscous dissipation, and the total energy density and flux increase relative to the case of isotropic resistivity; the reverse is the case for opposite directions of propagation, i.e. upward-propagating left-polarized waves and downward-propagating right-polarized waves, which can lead to the existence of a critical layer. The role of the viscosity and first and second resistive diffusiveness on the dissipation of Alfvén waves is discussed with reference to the solar atmosphere.

scholarly journals On the coronal heating mechanism by the resonant absorption of Alfven waves

1993 ◽  
Vol 16 (4) ◽  
pp. 811-816 ◽  
Author(s):  
H. Y. Alkahby
Keyword(s):  
Magnetic Field ◽  
Resonant Absorption ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Heating Process ◽  
Oscillatory Process ◽  
Horizontal Magnetic Field ◽  
Resonance Frequencies ◽  
Isothermal Atmosphere ◽  
The Magnetic Field

In this paper, we will investigate the heating of the solar corona by the resonant absorption of Alfven waves in a viscous and isothermal atmosphere permeated by a horizontal magnetic field. It is shown that if the viscosity dominates the motion in a high (low)-βplasma, it creates an absorbing and reflecting layer and the heating process is acoustic (magnetoacoustic). When the magnetic field dominates the oscillatory process it creates a non-absorbing reflecting layer. Consequently, the heating process is magnetohydrodynamic. An equation for resonance is derived. It shows that resonances may occur for many values of the frequency and of the magnetic field if the wavelength is matched with the strength of the magnetic field. At the resonance frequencies, magnetic and kinetic energies will increase to very large values which may account for the heating process. When the motion is dominated by the combined effects of the viscosity and the magnetic field, the nature of the reflecting layer and the magnitude of the reflection coefficient depend on the relative strengths of the magnetic field and the viscosity.

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