scholarly journals Excitation of nonlinear Alfvén waves by an ion beam in a plasma: 1. Right-hand polarized waves

1997 ◽  
Vol 102 (A10) ◽  
pp. 22365-22376 ◽  
Author(s):  
V. L. Galinsky ◽  
V. I. Shevchenko ◽  
S. K. Ride ◽  
M. Baine
Keyword(s):  
Ion Beam ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Right Hand ◽  
Polarized Waves

On the effects of viscosity and anisotropic resistivity on the damping of Alfvén waves

2000 ◽  
Vol 63 (3) ◽  
pp. 221-238 ◽  
Author(s):  
L. M. B. C. CAMPOS ◽  
P. M. V. M. MENDES
Keyword(s):  
Wave Equation ◽  
Fourth Order ◽  
Magnetic Energy ◽  
Propagation Speed ◽  
Alfven Waves ◽  
Second Order ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Total Energy Density ◽  
Polarized Waves

The equations of magnetohydrodynamics (MHD) are written for non-uniform viscosity and resistivity – the latter in the cases of Ohmic and anisotropic resistivity. In the case of Ohmic (anisotropic) diffusivity, there is (are) one (two) transverse components of the velocity and magnetic field perturbation(s), leading to a second-order (fourth-order) dissipative Alfvén- wave equation. In the more general case of dissipative Alfvén waves with isotropic viscosity and anisotropic resistivity, the fourth-order wave equation may be replaced by two decoupled second-order equations for right- and left-polarized waves, whose dispersion relations show that the first resistive diffusivity causes dissipation like the viscosity, whereas the second resistive diffusivity causes a change in propagation speed. The second resistive diffusivity invalidates the equipartition of kinetic and magnetic energy, modifies the energy flux through the propagation speed, and also changes the ratio of viscous to resistive dissipation. If the directions of propagation and polarization are equal (i.e. for right-polarized upward-propagating or left-polarized downward-propagating waves), the magnetic energy increases relative to the kinetic energy, the resistive dissipation increases relative to the viscous dissipation, and the total energy density and flux increase relative to the case of isotropic resistivity; the reverse is the case for opposite directions of propagation, i.e. upward-propagating left-polarized waves and downward-propagating right-polarized waves, which can lead to the existence of a critical layer. The role of the viscosity and first and second resistive diffusiveness on the dissipation of Alfvén waves is discussed with reference to the solar atmosphere.

scholarly journals Excitation of shear Alfvén waves by a spiraling ion beam in a large magnetoplasma

2015 ◽  
Vol 91 (1) ◽  
Author(s):  
S. K. P. Tripathi ◽  
B. Van Compernolle ◽  
W. Gekelman ◽  
P. Pribyl ◽  
W. Heidbrink
Keyword(s):  
Ion Beam ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Shear Alfven Waves

Electromagnetic ion-beam instabilities in a cold plasma

1996 ◽  
Vol 55 (1) ◽  
pp. 77-86 ◽  
Author(s):  
G. Gnavi ◽  
L. Gomberoff ◽  
F. T. Gratton ◽  
R. M. O. Galvão
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
External Magnetic Field ◽  
Cold Plasma ◽  
Ion Beam ◽  
Negative Energy ◽  
Left Hand ◽  
Right Hand ◽  
Polarized Waves ◽  
The Stability

We study the stability of the cold-plasma dispersion relation for circularly polarized waves in a plasma composed of an ion background and an ion beam. The presence of the beam introduces a resonant branch into the dispersion relation for right-hand-polarized waves propagating in the direction of the external magnetic field, which, for V>Vφ, has negative energy (here V is the beam velocityVφ is the wave phase velocity). Therefore this branch may give rise to explosive instabilities when the waves experience parametric decays. It is shown graphically that resonant right-hand-polarized and non-resonant left-hand-polarized waves, propagating parallel to the external magnetic field, can be unstable. It is also shown that the instability region can extend to large frequencies and wavenumnbers, and that the instability regions have a band structure. The parametric dependence of instability thresholds and marginal modes is also studied.

scholarly journals Toroidal and poloidal Alfvén waves with arbitrary azimuthal wavenumbers in a finite pressure plasma in the Earth's magnetosphere

2004 ◽  
Vol 22 (1) ◽  
pp. 267-287 ◽  
Author(s):  
D. Yu. Klimushkin ◽  
P. N. Mager ◽  
K.-H. Glassmeier
Keyword(s):  
Extreme Values ◽  
Second Harmonic ◽  
Alfven Waves ◽  
Wave Number ◽  
Mhd Waves ◽  
Alfvén Waves ◽  
Left Hand ◽  
Azimuthal Wave ◽  
Polarized Waves ◽  
Radially Polarized

Abstract. In this paper, in terms of an axisymmetric model of the magnetosphere, we formulate the criteria for which the Alfvén waves in the magnetosphere can be toroidally and poloidally polarized (the disturbed magnetic field vector oscillates azimuthally and radially, respectively). The obvious condition of equality of the wave frequency ω to the toroidal (poloidal) eigenfrequency ΩTN (ΩPN) is a necessary and sufficient one for the toroidal polarization of the mode and only a necessary one for the poloidal mode. In the latter case we must also add to it a significantly stronger condition ∣ΩTN–ΩPN∣/ΩTN ≫ m–1 where m is the azimuthal wave number, and N is the longitudinal wave number. In cold plasma (the plasma to magnetic pressure ratio β = 0) the left-hand side of this inequality is too small for the routinely recorded (in the magnetosphere) second harmonic of radially polarized waves, therefore these waves must have nonrealistically large values of m. By studying several models of the magnetosphere differing by the level of disturbance, we found that the left-hand part of the poloidality criterion can be satisfied by taking into account finite plasma pressure for the observed values of m ∼ 50 – 100 (and in some cases, for even smaller values of the azimuthal wave numbers). When the poloidality condition is satisfied, the existence of two types of radially polarized Alfvén waves is possible. In magnetospheric regions, where the function ΩPN is a monotonic one, the mode is poloidally polarized in a part of its region of localization. It propagates slowly across magnetic shells and changes its polarization from poloidal to toroidal. The other type of radially polarized waves can exist in those regions where this function reaches its extreme values (ring current, plasmapause). These waves are standing waves across magnetic shells, having a poloidal polarization throughout the region of its existence. Waves of this type are likely to be exemplified by giant pulsations. If the poloidality condition is not satisfied, then the mode is toroidally polarized throughout the region of its existence. Furthermore, it has a resonance peak near the magnetic shell, the toroidal eigenfrequency of which equals the frequency of the wave. Key words. Magnetospheric physics (plasmasphere; MHD waves and instabilities) – Space plasma physics (kinetic and MHD theory)

scholarly journals Parametric instabilities of circularly polarized small-amplitude Alfvén waves in Hall plasmas

2008 ◽  
Vol 74 (1) ◽  
pp. 119-138 ◽  
Author(s):  
MICHAEL S. RUDERMAN ◽  
PHILIPPE CAILLOL
Keyword(s):  
Alfvén Waves ◽  
Circularly Polarized ◽  
Instability Increment ◽  
Decay Instability ◽  
Right Hand ◽  
Polarized Waves ◽  
Wave Numbers ◽  
The Stability ◽  
Pump Waves ◽  
Limiting Value

AbstractWe study the stability of circularly polarized Alfvén waves (pump waves) in Hall plasmas. First we re-derive the dispersion equation governing the pump wave stability without making anad hocassumption about the dependences of perturbations on time and the spatial variable. Then we study the stability of pump waves with small non-dimensional amplitudea(a≪ 1) analytically, restricting our analysis tob< 1, wherebis the ratio of the sound and Alfvén speed. Our main results are the following. The stability properties of right-hand polarized waves are qualitatively the same as in ideal MHD. For any values ofband the dispersion parameter τ they are subject to decay instability that occurs for wave numbers from a band with width of ordera. The instability increment is also of ordera. The left-hand polarized waves can be subject, in general, to three different types of instabilities. The first type is the modulational instability. It only occurs whenbis smaller than a limiting value that depends on τ. Only perturbations with wave numbers smaller than a limiting value of orderaare unstable. The instability increment is proportional toa2. The second type is the decay instability. It has the same properties as in the case of right-hand polarized waves; however, it occurs only whenb< 1 τ. The third type is the beat instability. It occurs for any values ofband τ, and only perturbations with the wave numbers from a narrow band with the width of ordera2are unstable. The increment of this instability is proportional toa2, except for τ close to τcwhen it is proportional toa, where τcis a function ofb.

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