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.

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.

scholarly journals Generation and propagation of Alfvén waves in solar atmosphere

2008 ◽  
Vol 4 (S257) ◽  
pp. 555-561 ◽  
Author(s):  
Yuri T. Tsap ◽  
Alexander V. Stepanov ◽  
Yulia. G. Kopylova
Keyword(s):  
Magnetic Field ◽  
Cutoff Frequency ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Flux Tubes ◽  
Convective Motions ◽  
Magnetic Flux Tubes ◽  
The Magnetic Field ◽  
Lower Chromosphere

AbstractThe propagation of Alfvén waves from the photosphere into the corona with regard to the fine structure of the magnetic field is considered. The energy flux of Alfvén–type waves generated in the photosphere by convective motions does not depend on the ionization ratio. The reflection coefficient continuously decreases with a decrease of wave period. Influence of the external magnetic field on the Spruit cutoff frequency for transverse (kink) modes excited in the thin magnetic flux tubes is analyzed. Torsional modes can penetrate into the upper atmosphere most effectively since their amplitudes does not increase with height in the photosphere while kink ones can be transformed into shock waves in the lower chromosphere because of a significant increase of amplitudes. In spite of stratification the linearity of Alfvén–type modes in the chromosphere is conserved due to violation of the WKB approximation. The important role of the magnetic canopy is discussed. Alfvén waves generated by convective motions in the photosphere can contribute significantly to the heating of the coronal plasma in quite regions of the Sun.

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.

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.

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.

The role of slow magnetostrophic waves in dipole formation in rapidly rotating dynamos

2021 ◽  
Author(s):  
Aditya Varma ◽  
Binod Sreenivasan
Keyword(s):  
Magnetic Field ◽  
Threshold Value ◽  
Dipole Field ◽  
Wave Frequency ◽  
Alfven Wave ◽  
Inertial Waves ◽  
Axial Dipole ◽  
Wide Range ◽  
The Magnetic Field

&lt;p&gt;It is known that the columnar structures in rapidly rotating convection are affected by the magnetic field in ways that enhance their helicity. This may explain the dominance of the axial dipole in rotating dynamos. Dynamo simulations starting from a small seed magnetic field have shown that the growth of the field is accompanied by the excitation of convection in the energy-containing length scales. Here, this process is studied by examining axial wave motions in the growth phase of the dynamo for a wide range of thermal forcing. In the early stages of evolution where the field is weak, fast inertial waves weakly modified by the magnetic field are abundantly present. As the field strength(measured by the ratio of the Alfven wave to the inertial wave frequency) exceeds a threshold value, slow magnetostrophic waves are spontaneously generated. The excitation of the slow waves coincides with the generation of helicity through columnar motion, and is followed by the formation of the axial dipole from a chaotic, multipolar state. In strongly driven convection, the slow wave frequency is attenuated, causing weakening of the axial dipole intensity. Kinematic dynamo simulations at the same parameters, where only fast inertial waves are present, fail to produce the axial dipole field. The dipole field in planetary dynamos may thus be supported by the helicity from slow magnetostrophic waves.&lt;/p&gt;

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.

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