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.

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.

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 Reflection and dissipation of oblique Alfvén waves in an isothermal atmosphere

1999 ◽  
Vol 22 (1) ◽  
pp. 161-169 ◽  
Author(s):  
Hadi Yahya Alkahby ◽  
M. A. Mahrous
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Transition Region ◽  
Solar Atmosphere ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Heating Mechanism ◽  
Downward Propagation ◽  
Isothermal Atmosphere ◽  
The Magnetic Field

In this article, we investigate the combined effects of viscosity and Ohmic electrical conductivity on upward and downward propagation oblique Alfvén waves in an isothermal atmosphere. It is shown that the presence and direction of the magnetic field play an important role in the structure and the heating mechanism of solar atmosphere. In addition, the atmosphere can be divided into two distinct regions connected by a transition region. In the lower region, the solution can be written as a linear combination of an upward and a downward propagation wave with unequal wavelengths. In the upper region, the solution decays exponentially with the altitude. Moreover, the magnetic field creates a reflecting and a non-absorbing transition region. On the contrary, the viscosity and Ohmic electrical conductivity produce a reflecting and an absorbing transition region. The nature of the transition region depends on the relative strength of the viscous diffusivity with respect to the resistive diffusivity and on the direction of the magnetic field. A unique solution is determined. The reflection coefficient and damping factors are derived and the conclusions are discussed in connection with the nature of the heating mechanism of the solar atmosphere.

scholarly journals Spatial localization and azimuthal wave numbers of Alfvén waves generated by drift-bounce resonance in the magnetosphere

2005 ◽  
Vol 23 (12) ◽  
pp. 3775-3784 ◽  
Author(s):  
P. N. Mager ◽  
D. Yu. Klimushkin
Keyword(s):  
Spatial Localization ◽  
Energetic Particles ◽  
Alfven Waves ◽  
Wave Number ◽  
Alfvén Waves ◽  
Azimuthal Wave ◽  
Wave Numbers ◽  
Azimuthal Wave Number ◽  
Two Factors ◽  
The Waves

Abstract. Spatial localization and azimuthal wave numbers m of poloidal Alfvén waves generated by energetic particles in the magnetosphere are studied in the paper. There are two factors that cause the wave localization across magnetic shells. First, the instability growth rate is proportional to the distribution function of the energetic particles, hence waves must be predominantly generated on magnetic shells where the particles are located. Second, the frequency of the generated poloidal wave must coincide with the poloidal eigenfrequency, which is a function of the radial coordinate. The combined impact of these two factors also determines the azimuthal wave number of the generated oscillations. The beams with energies about 10 keV and 150 keV are considered. As a result, the waves are shown to be strongly localized across magnetic shells; for the most often observed second longitudinal harmonic of poloidal Alfvén wave (N=2), the localization region is about one Earth radius across the magnetic shells. It is shown that the drift-bounce resonance condition does not select the m value for this harmonic. For 10 keV particles (most often involved in the explanation of poloidal pulsations), the azimuthal wave number was shown to be determined with a rather low accuracy, -100<m<0. The 150 keV particles provide a little better but still a poor determination of this value, -90<m<-70. For the fundamental harmonic (N=1), the azimuthal wave number is determined with a better accuracy, but both of these numbers are too small (if the waves are generated by 150 keV particles), or the waves are generated on magnetic shells (in 10 keV case) which are too far away. The calculated values of γ/ω are not large enough to overcome the damping on the ionosphere. All these have cast some suspicion on the possibility of the drift-bounce instability to generate poloidal pulsations in the magnetosphere.

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.

Concerning the Dynamics of Energetic Protons in Coronal Magnetic Loops: Dispersion Effects of Alfven Waves

1985 ◽  
Vol 107 ◽  
pp. 559-559
Author(s):  
V. A. Mazur ◽  
A. V. Stepanov
Keyword(s):  
Magnetic Field ◽  
Wave Dispersion ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Wave Number ◽  
Alfvén Waves ◽  
Coronal Loops ◽  
Coronal Magnetic Loops ◽  
The Magnetic Field ◽  
Solar Coronal

It is shown that the existence of plasma density inhomogeneities (ducts) elongated along the magnetic field in coronal loops, and of Alfven wave dispersion, associated with the taking into account of gyrotropy U ≡ ω/ωi ≪ 1 (Leonovich et al., 1983), leads to the possibility of a quasi-longitudinal k⊥ < √U k‖ propagation (wave guiding) of Alfven waves. Here ω is the frequency of Alfven waves, ωi is the proton gyrofrequency, and k is the wave number. It is found that with the parameter ξ = ω2 R/ωi A > 1, where R is the inhomogeneity scale of a loop across the magnetic field, and A is the Alfven wave velocity, refraction of Alfven waves does not lead, as contrasted to Wentzel's inference (1976), to the waves going out of the regime of quasi-longitudinal propagation. As the result, the amplification of Alfven waves in solar coronal loops can be important. A study is made of the cyclotron instability of Alfven waves under solar coronal conditions.

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 Concerning the Dynamics of Energetic Protons in Coronal Magnetic Loops: Dispersion Effects of Alfven Waves

1985 ◽  
Vol 107 ◽  
pp. 559-559
Author(s):  
V. A. Mazur ◽  
A. V. Stepanov
Keyword(s):  
Magnetic Field ◽  
Wave Dispersion ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Wave Number ◽  
Alfvén Waves ◽  
Coronal Loops ◽  
Coronal Magnetic Loops ◽  
The Magnetic Field ◽  
Solar Coronal

It is shown that the existence of plasma density inhomogeneities (ducts) elongated along the magnetic field in coronal loops, and of Alfven wave dispersion, associated with the taking into account of gyrotropy U ≡ ω/ωi ≪ 1 (Leonovich et al., 1983), leads to the possibility of a quasi-longitudinal k⊥ < √U k‖ propagation (wave guiding) of Alfven waves. Here ω is the frequency of Alfven waves, ωi is the proton gyrofrequency, and k is the wave number. It is found that with the parameter ξ = ω2 R/ωi A > 1, where R is the inhomogeneity scale of a loop across the magnetic field, and A is the Alfven wave velocity, refraction of Alfven waves does not lead, as contrasted to Wentzel's inference (1976), to the waves going out of the regime of quasi-longitudinal propagation. As the result, the amplification of Alfven waves in solar coronal loops can be important. A study is made of the cyclotron instability of Alfven waves under solar coronal conditions.

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.

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