Finite-amplitude solitary Alfvén waves in a low-beta plasma

1986 ◽  
Vol 35 (2) ◽  
pp. 267-272 ◽  
Author(s):  
M. K. Kalita ◽  
B. C. Kalita
Keyword(s):  
Magnetic Field ◽  
Finite Amplitude ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Propagation Vector ◽  
The Magnetic Field

An exact nonlinear Alfvén wave in a low-β plasma is investigated. Both super-and sub-Alfvénic rarefactive solitons are found to exist depending upon the angle of inclination of the propagation vector to the magnetic field.

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 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.

On Alfvén wave propagation along a circle on dipolar coordinates

2019 ◽  
Vol 85 (6) ◽  
Author(s):  
L. M. B. C. Campos ◽  
M. J. S. Silva ◽  
F. Moleiro
Keyword(s):  
Magnetic Field ◽  
Wave Equation ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Far Field ◽  
Perturbation Spectrum ◽  
The Magnetic Field ◽  
Zero Frequency ◽  
Conformal Coordinates

The multipolar representation of the magnetic field has, for the lowest-order term, a magnetic dipole that dominates the far field. Thus the far-field representation of the magnetic field of the Earth, Sun and other celestial bodies is a dipole. Since these bodies consist of or are surrounded by plasma, which can support Alfvén waves, their propagation along dipole magnetic field lines is considered using a new coordinate system: dipolar coordinates. The present paper introduces multipolar coordinates, which are an example of conformal coordinates; conformal coordinates are orthogonal with equal scale factors, and can be extended from the plane to space, for instance as cylindrical or spherical dipolar coordinates. The application considered is to Alfvén waves propagating along a circle, that is a magnetic field line of a dipole, with transverse velocity and magnetic field perturbations; the various forms of the wave equation are linear second-order differential equations, with variable coefficients, specified by a background magnetic field, which is force free. The absence of a background magnetic force leads to a mean state of hydrostatic equilibrium, specified by the balance of gravity against the pressure gradient, for a perfect gas or incompressible liquid. The wave equation is simplified to a Gaussian hypergeometric type in the case of zero frequency, otherwise, for non-zero frequency, an extended Gaussian hypergeometric equation is obtained. The solution of the latter specifies the magnetic field perturbation spectrum, and also, via a polarisation relation, the velocity perturbation spectrum; both are plotted, over half a circle, for three values of the dimensionless frequency.

TRANSVERSE WAVES PROPAGATING ALONG AN APPLIED MAGNETIC FIELD IN A PLASMA

1964 ◽  
Vol 42 (5) ◽  
pp. 906-917
Author(s):  
R. E. Burgess ◽  
J. G. Cook
Keyword(s):  
Magnetic Field ◽  
Dispersion Equation ◽  
Applied Magnetic Field ◽  
Equation Of Motion ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Transverse Waves ◽  
The Magnetic Field

Transverse waves propagating along an applied magnetic field are studied, with special attention to the role of the magnetic field in determining the behavior of the wave. No restrictions are placed on the hole (or ion) mass, and the electron and hole densities may differ. The behavior of the magnetic-field-dominated waves is studied, and it is shown that it is profitable to extend the concept of an Alfvén wave to include those waves for which essentially B0 instead of B02 appears in the dispersion equation. Both intrinsic and extrinsic cases are studied.The dispersion equation approach is compared with the equation of motion and Ohm's law approach used by Watanabe for a study of Alfvén waves, and Watanabe's starting equations are generalized to make a study of Alfvén waves in solid-state plasmas with Watanabe's approach possible.

Double Alfvén waves

2011 ◽  
Vol 78 (1) ◽  
pp. 71-85 ◽  
Author(s):  
G. M. WEBB ◽  
Q. HU ◽  
B. DASGUPTA ◽  
G. P. ZANK
Keyword(s):  
Magnetic Field ◽  
Differential Geometry ◽  
Fluid Velocity ◽  
Alfven Waves ◽  
Gas Pressure ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Field Lines ◽  
Wave Normal ◽  
The Magnetic Field

AbstractDouble Alfvén wave solutions of the magnetohydrodynamic equations in which the physical variables (the gas density ρ, fluid velocity u, gas pressure p, and magnetic field induction B) depend only on two independent wave phases ϕ1(x,t) and ϕ2(x,t) are obtained. The integrals for the double Alfvén wave are the same as for simple waves, namely, the gas pressure, magnetic pressure, and group velocity of the wave are constant. Compatibility conditions on the evolution of the magnetic field B due to changes in ϕ1 and ϕ2, as well as constraints due to Gauss's law ∇ · B = 0 are discussed. The magnetic field lines and hodographs of B in which the tip of the magnetic field B moves on the sphere |B| = B = const. are used to delineate the physical characteristics of the wave. Hamilton's equations for the simple Alfvén wave with wave normal n(ϕ), and with magnetic induction B(ϕ) in which ϕ is the wave phase, are obtained by using the Frenet–Serret equations for curves x=X(ϕ) in differential geometry. The use of differential geometry of 2D surfaces in a 3D Euclidean space to describe double Alfvén waves is briefly discussed.

Analysis of The Phase Velocities of (Pure, Slow And Fast ) Alfvèn Waves In The E Region of The Ionosphere For Low Latitudes

2022 ◽  
Author(s):  
kadri kurt
Keyword(s):  
Magnetic Field ◽  
Field Vector ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Phase Velocities ◽  
Propagation Vector ◽  
Low Latitudes ◽  
E Region ◽  
Dip Angle ◽  
The Magnetic Field

Abstract In this paper, (pure, slow, and fast) Alfvèn waves for the accepted conditions in Northern-hemisphere at E-region of ionospheric plasma were calculated with low latitudes by using Eq. (20,25-26) and the real geometry of Earth’s magnetic field, at hours 12.00 LT for the 1990 year which sunspot is maximum. One of the most important results of this study is to show analytically that the “MHD modes= (pure, slow and fast) Alfvèn waves” depend not only on the angle between the wave propagation vector (k) and the magnetic field (B) but also on the declination (D=It is the angle value between the direction of the sun's rays and the equatorial plane) and magnetic dip angle (I=It is the angle between real north and magnetic north). From the results obtained, the behavior of the magnitudes of the squares of the phase velocities of all MHD modes is consistent with the behavior of the distribution of electron density with low geographic latitude, even if the magnetic field vector is both perpendicular and parallel to the propagation vector of the wave. In parallel, the phase velocities of the waves are greater in summer than in winter. It has been determined that the propagation velocities of the fast and slow MHD mode in the magnetic equatorial trough region at (q = I) are very small, the energy is almost non-existent, but if q = 90 + I, the energy increases with latitude and is approximately maximum at the low latitude limit. It can be said that the minimum points are between 0-10 oN latitudes where the wave energies are the smallest, and the maximum points are between 20-30 oN latitudes the wave energies are the biggest.

scholarly journals Alfvén Waves in Dusty Interstellar Clouds

1997 ◽  
Vol 14 (2) ◽  
pp. 170-178 ◽  
Author(s):  
N. F. Cramer ◽  
S. V. Vladimirov
Keyword(s):  
Magnetic Field ◽  
Negative Charge ◽  
Alfven Waves ◽  
Dust Particles ◽  
Alfvén Waves ◽  
Interstellar Clouds ◽  
General Dispersion ◽  
The Right ◽  
The Magnetic Field ◽  
Field Wave

AbstractDust particles in a plasma can be higWy charged, and can carry a proportion of the negative charge of the plasma. Even if this proportion is quite small, as in interstellar dusty clouds, it can have a large effect on hydromagnetic Alfvén waves propagating at frequencies well below the ion–cyclotron frequency. In particular, the right-hand circularly polarised mode experiences a cutoff due to the presence of the dust. We generalise previous work on Alfvén waves in dusty interstellar plasmas by considering the general dispersion relation for waves propagating at an arbitrary angle with respect to the magnetic field. Wave energy propagating at oblique angles to the magnetic field in an increasing density gradient can be very efficiently damped by the Alfvén resonance absorption process in a dusty plasma, and we consider this damping mechanism for waves in interstellar clouds.

Effect of the magnetic field curvature on the generation of zonal flows by drift-Alfvén waves

2007 ◽  
Vol 33 (5) ◽  
pp. 407-419 ◽  
Author(s):  
A. B. Mikhailovskii ◽  
E. A. Kovalishen ◽  
M. S. Shirokov ◽  
V. S. Tsypin ◽  
R. M. O. Galvão
Keyword(s):  
Magnetic Field ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Zonal Flows ◽  
Field Curvature ◽  
The Magnetic Field

A note on the modulational instability of long Alfvén waves parallel to the magnetic field

1978 ◽  
Vol 19 (3) ◽  
pp. 437-447 ◽  
Author(s):  
Einar Mjølhus
Keyword(s):  
Magnetic Field ◽  
Inverse Scattering ◽  
Modulational Instability ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Stable Case ◽  
Unstable Case ◽  
Modulational Stability ◽  
Limiting Case ◽  
The Magnetic Field

An amplitude dependent criterion for modulational stability of long Alfvén waves parallel to the magnetic field is interpreted in terms of a recently obtained inverse scattering solution to the modified nonlinear Schrödinger equation. It is found that the solitons formed are of two types. In the strongly unstable case, normal solitons are formed. In the transition region of weakly unstable and stable cases, the anomalous type, which in a limiting case becomes the algebraic soliton, dominates. In the strongly stable case, no solitons are formed.

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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