PERTURBATION THEORY FOR THE ALFVÉN WAVE

1995 ◽  
Vol 09 (22) ◽  
pp. 2857-2898 ◽  
Author(s):  
Z. YOSHIDA ◽  
S.M. MAHAJAN
Keyword(s):  
Magnetic Field ◽  
Perturbation Theory ◽  
Electron Beam ◽  
Continuous Spectrum ◽  
Point Spectrum ◽  
Alfven Wave ◽  
Wave Number ◽  
Ambient Magnetic Field ◽  
Field Lines ◽  
The Magnetic Field

The Alfvén wave is the dominant low frequency transverse mode of a magnetized plasma. The Alfvén wave propagates along the magnetic field, and displays a continuous spectrum even in a bounded plasma. This is essentially due to the degeneracy of the wave characteristics, i.e. the frequency (ω) is primarily determined by the wave number in the direction parallel to the ambient magnetic field (k||) and is independent of the perpendicular wavenumbers. The characteristics, that are the direction along which the wave energy propagates, are identical to the ambient magnetic field lines. Therefore, the spectral structure of the Alfvén wave has a close relationship with the geometric structure of the magnetic field lines. In an inhomogeneous plasma, the Alfvén resonance (ω−cAk||=0; cA is the phase velocity of the Alfvén wave) constitutes a singularity for the defining wave equation; this results in a singular eigenfunction corresponding to the continuous spectrum. The aim of this review is to present an overview of the perturbation theory for the Alfvén wave. Emphasis is placed on those perturbations of the continuous spectrum which lead to the creation of point spectra. Such qualitative changes in the spectrum are relevant to many plasma phenomena. The first category of perturbations consists of nonideal effects such as the finite conductivity, kinetic effects arising from the finite electron inertia, and finite gyroradius. These effects add singular perturbations to the mode equation, and modify the spectrum dramatically. These modification, viz. the conversion of the continuous to the point spectrum, can lead to interesting physical phenomenon. A case in point is that of an electron beam propagating in a plasma which Cherenkov emits a left-hand circularly polarized Alfvén wave. The helicity of the ambient magnetic field imparts a frequency shift to the eigenmodes changing the critical velocity for Cherenkov emission. It, then, becomes possible for a sub-Alfvénic electron beam to excite a nonsingular Alfvén wave corresponding to a point spectrum. The second category comprises of geometric perturbations associated with higher dimensional inhomogeneity of the ambient field. Forbidden bands occur when a periodic modulation is applied. In a chaotic magnetic field, the weak localization of the wave occurs, resulting in a point spectrum.

scholarly journals The development of magnetic field line wander by plasma turbulence

2017 ◽  
Vol 83 (4) ◽  
Author(s):  
Gregory G. Howes ◽  
Sofiane Bourouaine
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Large Scale ◽  
Magnetic Energy ◽  
Plasma Turbulence ◽  
Alfven Wave ◽  
Astrophysical Plasmas ◽  
Field Lines ◽  
The Magnetic Field

Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices and the fundamental processes of turbulence, magnetic reconnection and particle acceleration. The various potential impacts of magnetic field line wander are reviewed in detail, and a number of important theoretical considerations are identified that may influence the development and saturation of magnetic field line wander in astrophysical plasma turbulence. The results of nonlinear gyrokinetic simulations of kinetic Alfvén wave turbulence of sub-ion length scales are evaluated to understand the development and saturation of the turbulent magnetic energy spectrum and of the magnetic field line wander. It is found that turbulent space and astrophysical plasmas are generally expected to contain a stochastic magnetic field due to the tangling of the field by strong plasma turbulence. Future work will explore how the saturated magnetic field line wander varies as a function of the amplitude of the plasma turbulence and the ratio of the thermal to magnetic pressure, known as the plasma beta.

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 Guided Propagation of the Alfvén Wave in a Tokamak

1996 ◽  
Vol 49 (5) ◽  
pp. 953
Author(s):  
GG Borg
Keyword(s):  
Magnetic Field ◽  
Cyclotron Frequency ◽  
Alfven Wave ◽  
Tokamak Plasma ◽  
Azimuthal Magnetic Field ◽  
Tem Mode ◽  
Field Lines ◽  
Guided Propagation ◽  
High Degree ◽  
The Magnetic Field

Experimental observations are presented of the magnetically guided Alfvén wave excited directly by a small dipole loop antenna located in the scrape-off layer of a tokamak plasma. This wave is excited most efficiently by antenna current elements aligned along the magnetic field and measurements indicate that, at all frequencies below the ion cyclotron frequency, the wave propagates for several transits around the machine with a high degree of localization about magnetic field lines intersecting the antenna. Along the field, the wave has both a slowly varying amplitude and phase with predominantly radial electric and azimuthal magnetic field components. These experiments demonstrate that the Alfvén wave can propagate as a magnetically guided TEM mode in plasmas which are highly inhomogeneous. We also present a simplified mathematical description of the wave.

Role of interchange instability in flux transfer event origin

1994 ◽  
Vol 12 (2/3) ◽  
pp. 183-187 ◽  
Author(s):  
B. V. Rezhenov ◽  
Y. P. Maltsev
Keyword(s):  
Magnetic Field ◽  
Wave Number ◽  
Curvature Radius ◽  
Transfer Event ◽  
Flux Transfer Events ◽  
Interchange Instability ◽  
Flux Transfer ◽  
Field Lines ◽  
The Magnetic Field

Abstract. It is shown that the interaction of the interplanetary magnetic field (IMF), when it has southward component, with the geomagnetic field leads to the formation of an enhanced pressure layer (EPL) near the magnetopause. Currents flowing on the boundary between the EPL and the magnetosheath prevent the IMF from penetrating the magnetosphere. However, the outward boundary of the EPL is unstable. The interchange instability permanently destroys the EPL. Separate filaments of the EPL move away from the Earth. New colder plasma of the magnetosheath with a frozen magnetic field replaces the hotter EPL plasma, and the process of EPL formation and destruction repeats itself. The instability increment is calculated for various magnitudes of the azimuthal wave number, ky, and curvature radius of the magnetic field lines, Rc. The disturbances with R-1e≤ky≤4R-1e (where Re is the Earth's radius) and Rc≅Re are the most unstable. A possible result of the interchange instability of the EPL may be patchy reconnection, displayed as flux transfer events (FTEs) near the magnetopause.

Numerical simulation of propagation of the MHD waves in sunspots

2009 ◽  
Vol 5 (H15) ◽  
pp. 354-354
Author(s):  
K. Parchevsky ◽  
A. Kosovichev ◽  
E. Khomenko ◽  
V. Olshevsky ◽  
M. Collados
Keyword(s):  
Magnetic Field ◽  
Sound Speed ◽  
Amplitude Distribution ◽  
Alfven Wave ◽  
Mhd Waves ◽  
Convex Shape ◽  
Wave Source ◽  
Deep Model ◽  
Field Lines ◽  
The Magnetic Field

AbstractWe present results of numerical 3D simulation of propagation of MHD waves in sunspots. We used two self consistent magnetohydrostatic background models of sunspots. There are two main differences between these models: (i) the topology of the magnetic field and (ii) dependence of the horizontal profile of the sound speed on depth. The model with convex shape of the magnetic field lines near the photosphere has non-zero horizorntal perturbations of the sound speed up to the depth of 7.5 Mm (deep model). In the model with concave shape of the magnetic field lines near the photosphere Δ c/c is close to zero everywhere below 2 Mm (shallow model). Strong Alfven wave is generated at the wave source location in the deep model. This wave is almost unnoticeable in the shallow model. Using filtering technique we separated magnetoacoustic and magnetogravity waves. It is shown, that inside the sunspot magnetoacoustic and magnetogravity waves are not spatially separated unlike the case of the horizontally uniform background model. The sunspot causes anisotropy of the amplitude distribution along the wavefront and changes the shape of the wavefront. The amplitude of the waves is reduced inside the sunspot. This effect is stronger for the magnetogravity waves than for magnetoacoustic waves. The shape of the wavefront of the magnetogravity waves is distorted stronger as well. The deep model causes bigger anisotropy for both mgnetoacoustic and magneto gravity waves than the shallow model.

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.

scholarly journals SIMULATION OF THE COMPENSATION OF A HIGH-CURRENT ION BEAM BY AN ELECTRON BEAM IN A CUSP MAGNETIC SYSTEM

2021 ◽  
pp. 122-127
Author(s):  
I.N. Onishchenko ◽  
O.V. Fedorovskaya
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Space Charge ◽  
Longitudinal Magnetic Field ◽  
Ion Beam ◽  
Zero Magnetic Field ◽  
High Current ◽  
Field Lines ◽  
Dynamics Of Particles ◽  
The Magnetic Field

The results of 2.5D-simulation of the dynamics of particles of a high-current ion beam moving in a magnetic field of acute-angled geometry (cusp), compensated in charge and current by an electron beam injected along the radius onto the axis from the periphery, uniformly in azimuth, are presented. The influence of own space charge fields and polarization fields on the dynamics of ions is clarified. It is shown that at high densities of the electron and ion beams, the electron beam injected into the cusp together with the ion beam, moving along the magnetic field lines, drags the ion beam away from the axis to the periphery into the region of zero magnetic field. At the exit from the cusp, the electron beam injected along the radius onto the axis drifts along the axis in a uniform magnetic field, while the ion beam performs oscillatory motion by radius in the crossed the electric field of the electron beam space charge and the longitudinal magnetic field.

scholarly journals Interaction of an electron beam with whistler waves in magnetoplasmas

2015 ◽  
Vol 33 (3) ◽  
pp. 455-461 ◽  
Author(s):  
Ruby Gupta ◽  
Ved Prakash ◽  
Suresh C. Sharma ◽  
Vijayshri
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Electron Beam ◽  
Whistler Wave ◽  
Wave Number ◽  
Whistler Waves ◽  
Parallel Beam ◽  
Whistler Mode ◽  
Beam Velocity ◽  
The Magnetic Field

AbstractThe present paper studies the whistler wave interaction with an electron beam propagating through magnetized plasma. A dispersion relation of whistler waves has been derived, and first-order perturbation theory has been employed to obtain the growth rate of whistlers in the presence of parallel as well as oblique electron beam. For whistler waves propagating parallel to the magnetic field, that is, parallel whistlers, only the cyclotron resonance appears with a parallel beam, while for whistler waves propagating at an angle to the magnetic field, that is, oblique whistlers interaction with parallel beam or parallel whistlers interaction with oblique beam, the Cerenkov and the cyclotron resonances both appear. The growth rate is found to increase with an increase in the transverse component of beam velocity and with an increase in the strength of magnetic field. The whistler wave frequency decreases with an increase in the beam velocity. The obliqueness of the whistler mode modifies its dispersion characteristics as well as growth rate of the instability. For purely parallel-propagating beams, it is essential for the growth of whistler mode that the wave number perpendicular to the magnetic field should not be zero. The results presented may be applied to explain the mechanisms of the whistler wave excitation in space plasma.

Materials for Electron Beam Information Storage

1969 ◽  
Vol 27 ◽  
pp. 152-153 ◽  
Author(s):  
D. E. Speliotis
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Recent Literature ◽  
Electron Beams ◽  
Information Storage ◽  
The Subject ◽  
The Magnetic Field

The interaction of electron beams with a large variety of materials for information storage has been the subject of numerous proposals and studies in the recent literature. The materials range from photographic to thermoplastic and magnetic, and the interactions with the electron beam for writing and reading the information utilize the energy, or the current, or even the magnetic field associated with the electron beam.

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