A note on the westward drift of the earth's magnetic field

1977 ◽  
Vol 82 (2) ◽  
pp. 389-400 ◽  
Author(s):  
W. W. Wood
Keyword(s):  
Magnetic Field ◽  
Liquid Core ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Stratified Medium ◽  
Alfvén Waves ◽  
Axially Symmetric ◽  
Basic States ◽  
The Waves ◽  
Westward Drift

A model of the earth's liquid core is assumed in which the underlying magnetic field and velocity are zonal and axially symmetric. Alfvén waves that vary as ei(kϕ−σt) are considered, where ϕ is the angle of longitude. Buoyancy and Coriolis forces Ω × U are included.For a wide class of basic states and regions of flow, it is shown that roughly as many of the waves with a given k [ges ] 2 propagate eastwards as propagate westwards. All these waves are neutrally stable. The class of basic states is restricted by certain inequalities involving their velocity, magnetic field and entropy gradient.it is observed that the known equivalence (Malkus 1967) between Alfvén waves with frequencies σ [Lt ] Ω and inertial waves with frequencies σp which are O(Ω) still holds when buoyancy forces are present. The equivalence requires σp2 to be real. If σp is pure imaginary, as is possible (though perhaps uncommon) in an unstably stratified medium, then the corresponding Alfvén wave is not neutrally stable and travels westwards.

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 Phase mixing of Alfvén waves in two-dimensional magnetic plasma configurations with exponentially decreasing density

2018 ◽  
Vol 620 ◽  
pp. A44
Author(s):  
Michael S. Ruderman ◽  
Nikolai S. Petrukhin
Keyword(s):  
Magnetic Field ◽  
Shear Viscosity ◽  
Alfven Waves ◽  
Mhd Equations ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Field Variation ◽  
Characteristic Scale ◽  
Wave Damping ◽  
Magnetic Plasma

We study damping of phase-mixed Alfvén waves propagating in axisymmetric magnetic plasma configurations. We use the linear magnetohydrodynamic (MHD) equations in the cold plasma approximation. The only dissipative process that we take into account is shear viscosity. We reduce the MHD equations describing the Alfvén wave damping to a Klein–Gordon-type equation. We assume that the two terms in this equation, one describing the effect of inhomogeneity and the other the effect of viscosity, are small. Then we use the WKB method to derive the expression describing the wave energy flux attenuation with the height. We apply the general theory to particular equilibria with the exponentially divergent magnetic field lines with the characteristic scale H. The plasma density exponentially decreases with the height with the characteristic scale Hρ. We study the wave damping for typical parameters of coronal plumes and various values of the wave period, the characteristic scale of the magnetic field variation H, and kinematic shear viscosity ν. We show that to have an appreciable wave damping at the height 6H we need to increase shear viscosity by at least six orders of magnitude in comparison with the value given by the classical plasma theory. Another important result is that the efficiency of wave damping strongly depends on the ratio H/Hρ. It increases fast when H/Hρ decreases. We present a physical explanation of this phenomenon.

scholarly journals FRB coherent emission from decay of Alfvén waves

2020 ◽  
Vol 494 (2) ◽  
pp. 2385-2395 ◽  
Author(s):  
Pawan Kumar ◽  
Željka Bošnjak
Keyword(s):  
Magnetic Field ◽  
Wave Packet ◽  
Electric Field ◽  
Static Magnetic Field ◽  
Strong Electric Field ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Radio Waves ◽  
Electron Positron

ABSTRACT We present a model for fast radio bursts (FRBs) where a large-amplitude Alfvén wave packet is launched by a disturbance near the surface of a magnetar, and a substantial fraction of the wave energy is converted to coherent radio waves at a distance of a few tens of neutron star radii. The wave amplitude at the magnetar surface should be about 1011 G in order to produce an FRB of isotropic luminosity 1044 erg s−1. An electric current along the static magnetic field is required by Alfvén waves with non-zero component of transverse wave vector. The current is supplied by counter-streaming electron–positron pairs, which have to move at nearly the speed of light at larger radii as the plasma density decreases with distance from the magnetar surface. The counter-streaming pairs are subject to two-stream instability, which leads to formation of particle bunches of size of the order of c/ωp, where ωp is the plasma frequency. A strong electric field develops along the static magnetic field when the wave packet arrives at a radius where electron–positron density is insufficient to supply the current required by the wave. The electric field accelerates particle bunches along the curved magnetic field lines, and that produces the coherent FRB radiation. We provide a number of predictions of this model.

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.

On Alfvén waves in a radial flow and magnetic field

1999 ◽  
Vol 62 (1) ◽  
pp. 1-33 ◽  
Author(s):  
L. M. B. C. CAMPOS ◽  
N. L. ISAEVA
Keyword(s):  
Magnetic Field ◽  
Wave Equation ◽  
Flow Velocity ◽  
Mass Density ◽  
Alfven Waves ◽  
Uniform Flow ◽  
Critical Layer ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Mean Flow

This paper considers Alfvén waves in a radially stratified medium where all background quantities, namely mass density, magnetic field strength and mean flow velocity, depend only on the distance from the centre, the latter two being assumed to lie in the radial direction. It is shown that the radial dependence of Alfvén waves is the same for two cases: (i) when the velocity and magnetic field perturbations are along parallels, in the one-dimensional case of only radial and time dependence; (ii) in the three-dimensional case with dependence on all three spherical coordinates and time, for velocity and magnetic field perturbations with components along parallels and meridians, represented by the radial components of the vorticity and electric current respectively. Elimination between these equations leads to the convected Alfvén-wave equation in the case of uniform flow, and an equation with an additional term in the case of non-uniform flow with mean flow velocity a linear function of distance. The latter case, namely that of non-uniform flow with flow velocity increasing linearly with distance, is analysed in detail; conservation of mass flux requires the mass density to decay as the inverse cube of the distance. The Alfvén-wave equation has a critical layer where the flow velocity equals the Alfvén speed, leading to three sets of two solutions, namely below, above and across the critical layer. The latter is used to specify the wave behaviour in the vicinity of the critical layer, where local partial transmission occurs. The problem has two dimensionless parameters: the frequency and the initial Alfvén number. It is shown, by plotting the wave fields relative to the critical layer, that these two dimensionless parameters appear in a single combination. This simplifies the plotting of the wave fields for several combinations of physical conditions. It is shown in the Appendix that the formulation of the equations of MHD in the original Elsässer (1956) form, often used in the recent literature, does not apply if the background mass density is non-uniform on the scale of a wavelength. The present theory, based on exact solutions of the Alfvén-wave equation for a inhomogeneous moving medium, is unrestricted as to the relative magnitude of the local wavelength and scale of change of properties of the background medium. The present theory shows that the rate-of-decay of wave amplitude is strongly dependent on wave frequency beyond the critical layer, i.e. the process of change with distance of the spectrum of Alfvén waves in the solar wind starts at the critical layer.

scholarly journals Second-order perturbations in Alfvén waves in cold plasma approximatio

2019 ◽  
Vol 5 (2) ◽  
pp. 81-87
Author(s):  
Ирина Дмитриенко ◽  
Irina Dmitrienko
Keyword(s):  
Cold Plasma ◽  
Alfven Waves ◽  
Magnetic Pressure ◽  
Second Order ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Plasma Flows ◽  
Plasma Displacement ◽  
Environment Model ◽  
The Waves

The second-order amplitude perturbations driven by Alfvén waves are studied. Equations for such second-order perturbations are derived and their solutions are found. The second-order perturbations are shown to be generated by the magnetic pressure of the waves. They represent plasma flows and magnetic field perturbations in a plane perpendicular to the direction of the field perturbation and plasma displacement in the Alfvén wave. In connection with the interpretation of fast plasma flows observed in the magnetotail, of particular interest is the description of second-order flows, which relates their properties to properties of Alfvén waves and the disturbance that generates them. The results suggest that at least some of the fast plasma flows observed in the magnetotail can be one of the manifestations of propagating Alfvén waves. The environment model and cold plasma approximation in use are quite applicable for the plasma sheet boundary layers, where an essential part of the fast plasma flows occurs.

scholarly journals Ionospheric cusp flows pulsed by solar wind Alfvén waves

2002 ◽  
Vol 20 (2) ◽  
pp. 161-174 ◽  
Author(s):  
P. Prikryl ◽  
G. Provan ◽  
K. A. McWilliams ◽  
T. K. Yeoman
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Surface Waves ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Mhd Waves ◽  
Alfvén Waves ◽  
Propagation Time ◽  
Short Period ◽  
The Imf

Abstract. Pulsed ionospheric flows (PIFs) in the cusp foot-print have been observed by the SuperDARN radars with periods between a few minutes and several tens of minutes. PIFs are believed to be a consequence of the interplanetary magnetic field (IMF) reconnection with the magnetospheric magnetic field on the dayside magnetopause, ionospheric signatures of flux transfer events (FTEs). The quasiperiodic PIFs are correlated with Alfvénic fluctuations observed in the upstream solar wind. It is concluded that on these occasions, the FTEs were driven by Alfvén waves coupling to the day-side magnetosphere. Case studies are presented in which the dawn-dusk component of the Alfvén wave electric field modulates the reconnection rate as evidenced by the radar observations of the ionospheric cusp flows. The arrival of the IMF southward turning at the magnetopause is determined from multipoint solar wind magnetic field and/or plasma measurements, assuming plane phase fronts in solar wind. The cross-correlation lag between the solar wind data and ground magnetograms that were obtained near the cusp footprint exceeded the estimated spacecraft-to-magnetopause propagation time by up to several minutes. The difference can account for and/or exceeds the Alfvén propagation time between the magnetopause and ionosphere. For the case of short period ( < 13 min) PIFs, the onset times of the flow transients appear to be further delayed by at most a few more minutes after the IMF southward turning arrived at the magnetopause. For the case of long period (30 – 40 min) PIFs, the observed additional delays were 10–20 min. We interpret the excess delay in terms of an intrinsic time scale for reconnection (Russell et al., 1997) which can be explained by the surface-wave induced magnetic reconnection mechanism (Uberoi et al., 1999). Here, surface waves with wavelengths larger than the thickness of the neutral layer induce a tearing-mode instability whose rise time explains the observed delay of the reconnection onset. The compressional fluctuations in solar wind and those generated in the magnetosheath through the interaction between the solar wind Alfvén waves and the bow shock were the source of magnetopause surface waves inducing reconnection.Key words. Interplanetary physics (MHD waves and turbulence) – Magnetospheric physics (magnetosphere-ionosphere interactions; solar wind-magnetosphere interactions)

Non-inductive current drive via helicity injection by Alfvén waves in low-aspect-ratio tokamaks

1996 ◽  
Vol 56 (1) ◽  
pp. 149-174 ◽  
Author(s):  
S. Cuperman ◽  
C. Bruma ◽  
K. Komoshvili
Keyword(s):  
Magnetic Field ◽  
Aspect Ratio ◽  
Alfven Waves ◽  
Current Drive ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Drive Power ◽  
Helicity Injection ◽  
Low Aspect Ratio ◽  
Optimal Current

A theoretical investigation of radio-frequency (RF) current drive via helicity injection in low aspect ratio tokamaks is carried out. A current-carrying cylindrical plasma surrounded by a helical sheet-current antenna and situated inside a perfectly conducting shell is considered. Toroidal features of low-aspect-ratio tokamaks are simulated by incorporating the following effects: (i) arbitrarily small aspect ratio, Ro/a ≡1/∈; (ii) strongly sheared equilibrium magnetic field; and (iii) relatively large poloidal component of the equilibrium magnetic field. This study concentrates on the Alfvén continuum, i.e. the case in which the wave frequency satisfies the condition , where is an eigenfrequency of the shear Alfven wave (SAW). Thus, using low-β magneto- hydrodynamics, the wave equation with correct boundary (matching) conditions is solved, the RF field components are found, and subsequently current drive, power deposition and efficiency are computed. The results of our investigation clearly demonstrate the possibility of generation of RF-driven currents via helicity injection by Alfvén waves in low-aspect-ratio tokamaks, in the SAW mode. A special algorithm is developed that enables one to select the antenna parameters providing optimal current drive efficiency.

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.

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