On the Hall effect on vertical Alfvén waves in an isothermal atmosphere

1992 ◽  
Vol 4 (9) ◽  
pp. 2975-2982 ◽  
Author(s):  
L. M. B. C. Campos
Keyword(s):  
Hall Effect ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Isothermal 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.

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 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.

On vertical spinning Alfvén waves in a magnetic flux tube

1992 ◽  
Vol 48 (3) ◽  
pp. 415-434 ◽  
Author(s):  
L. M. B. C. Campos ◽  
N. L. Isaeva
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Magnetic Flux ◽  
Hall Effect ◽  
Flux Tube ◽  
Critical Level ◽  
Alfven Waves ◽  
Second Order ◽  
Magnetic Flux Tube ◽  
Alfvén Waves

We derive the Alfvén-wave equation for an atmosphere in the presence of a non-uniform vertical magnetic field and the Hall effect, allowing for Alfvén speed and ion gyrofrequency that may vary with altitude; the pair of coupled second-order differential equations for the horizontal wave variables, namely magnetic field or velocity perturbations, is reduced to a single complex, second-order differential equation. The latter is applied to spinning Alfvén waves in a magnetic flux tube, in magnetohydrostatic equilibrium, in an isothermal atmosphere. The exact solution is found in terms of hypergeometric functions, from which it is shown that at ‘high altitude’the magnetic field perturbation tends to grow to a non-small fraction of the background magnetic field. By ‘high-altitude’ is meant far above the critical level, which acts as a reflecting layer for left-polarized waves incident from below, i.e. from the ‘low-altitude’ range. We also obtain the exact solution near the critical level, where the left-polarized wave has a logarithmic singularity, and the right-polarized wave is finite. The latter is plotted in this region of wave frequency comparable to ion gyrofrequency, and it is shown that the Hall effect can cause oscillations of wave amplitude and non-monotonic phases with slope of alternating sign. The latter corresponds to ‘tunnelling’, i.e. waves propagating in opposite directions or trapped in adjoining atmospheric layers; this could explain the appearance of inward- and outward-propagating waves, with almost random phases, in the solar wind beyond the earth, for which the Hall effect on Alfvén waves should be significant.

scholarly journals Joint action of Hall and ambipolar effects in 3D magneto-convection simulations of the quiet Sun

2020 ◽  
Vol 642 ◽  
pp. A220
Author(s):  
P. A. González-Morales ◽  
E. Khomenko ◽  
N. Vitas ◽  
M. Collados
Keyword(s):  
Hall Effect ◽  
Three Dimensional ◽  
Stationary Regime ◽  
Alfven Waves ◽  
Ambipolar Diffusion ◽  
Alfvén Waves ◽  
Poynting Flux ◽  
Mhd Dynamo ◽  
Biermann Battery ◽  
High Frequency Waves

The partial ionization of the solar plasma causes several nonideal effects such as the ambipolar diffusion, the Hall effect, and the Biermann battery effect. Here we report on the first three-dimensional realistic simulations of solar local dynamo where all three effects were taken into account. The simulations started with a snapshot of already saturated battery-seeded dynamo, where two new series were developed: one with solely ambipolar diffusion and another one also taking into account the Hall term in the generalized Ohm’s law. The simulations were then run for about 4 h of solar time to reach the stationary regime and improve the statistics. In parallel, a purely MHD dynamo simulation was also run for the same amount of time. The simulations are compared in a statistical way. We consider the average properties of simulation dynamics, the generation and dissipation of compressible and incompressible waves, and the magnetic Poynting flux. The results show that, with the inclusion of the ambipolar diffusion, the amplitudes of the incompressible perturbations related to Alfvén waves are reduced, and the Poynting flux is absorbed, with a frequency dependence. The Hall effect causes the opposite action: significant excess of incompressible perturbations is generated and an excess of the Poynting flux is observed in the chromospheric layers. The model with ambipolar diffusion shows, on average, sharper current sheets and slightly more abundant fast magneto-acoustic shocks in the chromosphere. The model with the Hall effect has higher temperatures at the lower chromosphere and stronger and more vertical magnetic field concentrations all over the chromosphere. The study of high-frequency waves reveals that significant power of incompressible perturbations is associated with areas with intense and more vertical magnetic fields and larger temperatures. This behavior explains the large Poynting fluxes in the simulations with the Hall effect and provides confirmation as to the role of Alfvén waves in chromospheric heating in internetwork regions, under the action of both Hall and ambipolar effects. We find a positive correlation between the magnitude of the ambipolar heating and the temperature increase at the same location after a characteristic time of 102 s.

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.

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