Stability of relativistic anisotropic plasmas to perpendicular magnetosonic waves

1970 ◽  
Vol 4 (3) ◽  
pp. 495-510 ◽  
Author(s):  
R. W. Landau ◽  
S. Cuperman
Keyword(s):  
Dispersion Relation ◽  
Cyclotron Frequency ◽  
Plasma Frequency ◽  
Interplanetary Medium ◽  
Alfven Wave ◽  
Larmor Radius ◽  
First Order ◽  
Ion Plasma ◽  
The Stability ◽  
The Magnetic Field

The stability of relativistic anisotropic plasmas to the magnetosonic (or righthand compressional Alfvén) wave, near the ion cyclotron frequency, propagating perpendicular to the magnetic field, is investigated. For this case, and for wavelengths larger than the ion Larmor radius and large ion plasma frequency () the dispersion relation is obtained in a simple form and solved. It is shown that for T‖ ╪ T⊥ (even T‖ ≥ T⊥) no instability occurs. This conclusion applies also to the case of the anisotropic interplanetary medium.We note a peculiarity of the dispersion relation. Zero-order and first-order terms cancel so that the relation is of second order in our expansion parameter. The non-relativistic numerical results of Fredricks and Kennel are recovered.

Stability of anisotropic plasmas to almost-perpendicular magnetosonic waves

1971 ◽  
Vol 6 (3) ◽  
pp. 495-512 ◽  
Author(s):  
R. W. Landau† ◽  
S. Cuperman
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Simple Form ◽  
Cyclotron Frequency ◽  
Plasma Frequency ◽  
Alfven Wave ◽  
Larmor Radius ◽  
Ion Plasma ◽  
The Stability ◽  
The Magnetic Field

The stability of anisotropic plasmas to the magnetosonic (or right-hand compressional Alfvén) wave, near the ion cyclotron frequency, propagating almost perpendicular to the magnetic field, is investigated. For this case, and for wavelengths larger than the ion Larmor radius and for large ion plasma frequency (w2p+ ≫ Ωp+) the dispersion relation is obtained in a simple form. It is shown that for T # T' (even T ≫ T) no instabifity occurs. The resonant ters are also included, and it is shown that there is no resonant instabifity, only damping.

scholarly journals On Minimum-B Stabilization of Electrostatic Drift Instabilities

1966 ◽  
Vol 21 (11) ◽  
pp. 1953-1959 ◽  
Author(s):  
R. Saison ◽  
H. K. Wimmel
Keyword(s):  
Dispersion Relation ◽  
Particle Distribution ◽  
Inhomogeneous Plasma ◽  
Distribution Functions ◽  
Loss Cone ◽  
First Order ◽  
Stabilization Theorem ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Limiting Case

A check is made of a stabilization theorem of ROSENBLUTH and KRALL (Phys. Fluids 8, 1004 [1965]) according to which an inhomogeneous plasma in a minimum-B field (β ≪ 1) should be stable with respect to electrostatic drift instabilities when the particle distribution functions satisfy a condition given by TAYLOR, i. e. when f0 = f(W, μ) and ∂f/∂W < 0 Although the dispersion relation of ROSENBLUTH and KRALL is confirmed to first order in the gyroradii and in ε ≡ d ln B/dx z the stabilization theorem is refuted, as also is the validity of the stability criterion used by ROSEN-BLUTH and KRALL, ⟨j·E⟩ ≧ 0 for all real ω. In the case ωpi ≫ | Ωi | equilibria are given which satisfy the condition of TAYLOR and are nevertheless unstable. For instability it is necessary to have a non-monotonic ν ⊥ distribution; the instabilities involved are thus loss-cone unstable drift waves. In the spatially homogeneous limiting case the instability persists as a pure loss cone instability with Re[ω] =0. A necessary and sufficient condition for stability is D (ω =∞, k,…) ≦ k2 for all k, the dispersion relation being written in the form D (ω, k, K,...) = k2+K2. In the case ωpi ≪ | Ωi | adherence to the condition given by TAYLOR guarantees stability.

Ion-cyclotron modes in weakly relativistic plasmas

1994 ◽  
Vol 51 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Chandu Venugopal ◽  
P. J. Kurian ◽  
G. Renuka
Keyword(s):  
Dispersion Relation ◽  
High Frequency ◽  
Low Frequency ◽  
Dispersion Relations ◽  
The Other ◽  
Larmor Radius ◽  
Relativistic Plasmas ◽  
Ion Plasma ◽  
Maxwellian Plasma ◽  
Relativistic Dispersion

We derive a dispersion relation for the perpendicular propagation of ioncyclotron waves around the ion gyrofrequency ω+ in a weaklu relaticistic anisotropic Maxwellian plasma. These waves, with wavelength greater than the ion Larmor radius rL+ (k⊥ rL+ < 1), propagate in a plasma characterized by large ion plasma frequencies (). Using an ordering parameter ε, we separated out two dispersion relations, one of which is independent of the relativistic terms, while the other depends sensitively on them. The solutions of the former dispersion relation yield two modes: a low-frequency (LF) mode with a frequency ω < ω+ and a high-frequency (HF) mode with ω > ω+. The plasma is stable to the propagation of these modes. The latter dispersion relation yields a new LF mode in addition to the modes supported by the non-relativistic dispersion relation. The two LF modes can coalesce to make the plasma unstable. These results are also verified numerically using a standard root solver.

Kinetic Alfvén waves in an inhomogeneous anisotropic magnetoplasma in the presence of an inhomogeneous electric field: particle aspect analysis

2000 ◽  
Vol 63 (4) ◽  
pp. 311-328 ◽  
Author(s):  
A. BARONIA ◽  
M. S. TIWARI
Keyword(s):  
Growth Rate ◽  
Dispersion Relation ◽  
Electric Field ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Larmor Radius ◽  
Alfvén Waves ◽  
Temperature Anisotropy ◽  
Inhomogeneous Electric Field ◽  
Kinetic Alfvén Waves

Kinetic Alfvén waves in the presence of an inhomogeneous electric field applied perpendicular to the ambient magnetic field in an anisotropic, inhomogeneous magnetoplasma are investigated. The particle aspect approach is adopted to investigate the trajectories of charged particles in the electromagnetic field of a kinetic Alfvén wave. Expressions are found for the field-aligned current, the perpendicular current, the dispersion relation and the particle energies. The growth rate of the wave is obtained by an energy- conservation method. It is predicted that plasma density inhomogeneity is the main source of instability, and an enhancement of the growth rate by electric field inhomogeneity and temperature anisotropy is found. The dispersion relation and growth rate involve the finite-Larmor-radius effect, electron inertia and the temperature anisotropy of the magnetoplasma. The applicability of the investigation to the auroral acceleration region is discussed.

Magnetic stabilization of transverse plasma instabilitiest

1971 ◽  
Vol 5 (3) ◽  
pp. 467-474 ◽  
Author(s):  
B. Buti ◽  
G. S. Lakhina
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Cyclotron Frequency ◽  
Plasma Frequency ◽  
Electron Plasma ◽  
Wave Number ◽  
Uniform External Magnetic Field ◽  
Magnetic Stabilization ◽  
Streaming Velocity ◽  
The Magnetic Field

Waves, propagating transverse to the direction of the streaming of a plasma in the presence of a uniform external magnetic field, are unstable if the streaming exceeds a certain minimum value. The magnetic field reduces the growth rate of this instability, and also increases the value of the minimum streaming velocity, above which the system is unstable. The thermal motions in the plasma, however, tend to stabilize the system if the magnetic field is weak (i.e. , Ω being the electron cyclotron frequency, k the characteristic wave-number, and Vt the thermal velocity); but, in case of strong magnetic field (i.e. ), they increase the growth rate, provided (ωp being the electron plasma frequency).

Finite-frequency surface waves on current sheets

1991 ◽  
Vol 45 (3) ◽  
pp. 389-406 ◽  
Author(s):  
K. P. Wessen ◽  
N. F. Cramer
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Surface Waves ◽  
Cyclotron Frequency ◽  
Low Frequency ◽  
Dielectric Tensor ◽  
Magnetic Field Direction ◽  
Field Reversal ◽  
Ion Cyclotron ◽  
The Magnetic Field

The dispersion relation for low-frequency surface waves at a current sheet between two magnetized plasmas is derived using the cold-plasma dielectric tensor with finite ion-cyclotron frequency. The magnetic field direction is allowed to change discontinuously across the sheet, but the plasma density remains constant. The cyclotron frequency causes a splitting of the dispersion relation into a number of mode branches with frequencies both less than and greater than the ion-cyclotron frequency. The existence of these modes depends in particular upon the degree of magnetic field discontinuity and the direction of wave propagation in the sheet relative to the magnetic field directions. Sometimes two modes can exist for the same direction of propagation. The existence of modes undamped by Alfvén resonance absorption is predicted. Analytical solutions are obtained in the low-frequency and magnetic-field-reversal limits. The solutions are obtained numerically in the general case.

Hydromagnetic stability of a compressible jet

1975 ◽  
Vol 14 (3) ◽  
pp. 443-448 ◽  
Author(s):  
B. B. Chakraborty ◽  
H. K. S. Iyengar
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Magnetic Fields ◽  
Axial Direction ◽  
Vortex Sheet ◽  
Fluid Velocities ◽  
The Stability ◽  
Axisymmetric Disturbances ◽  
Jet Velocities ◽  
The Magnetic Field

This paper studies the hydromagnetic stability of a cylindrical jet of a perfectly-conducting, inviscid and compressible fluid. The fluid velocities and magnetic fields, inside and outside the jet, are uniform and in the axial direction, with possible discontinuities in their values across the jet surface. For large wavelength disturbances, the jet behaves as though it were incompressible. Numerical evaluation of the roots of the dispersion relation for a number of different magnetic-field strengths and jet velocities, but for disturbances of finite ranges of wavenumbers, indicates that the jet is stable against axisymmetric disturbances, but instability is present for asymmetric disturbances when the magnetic fields are sufficiently small. The magnetic field is found to have a stabilizinginfluence when compressibility is not very large; for high compressibility, it may have even a destabilizing effect. The paper explains physically the roles of compressibility and the magnetic field in bringing about the stability of the jet. When the wavelengths of disturbances are small, the dispersion relation reduces to that for a two-dimensional jet and a vortex sheet; and the results for these cases are known from earlier studies.

Wave propagation in a moving plasma. Part 1. Wave propagation normal to the magnetic field and motion of the plasma along the magnetic field

1974 ◽  
Vol 11 (3) ◽  
pp. 389-395 ◽  
Author(s):  
D. N. Srivastava
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Dispersion Relation ◽  
Magnetic Fields ◽  
Plasma Frequency ◽  
Electron Plasma ◽  
Ordinary Wave ◽  
Moving Plasma ◽  
The Magnetic Field

The dispersion relation for a collisionless moving electron plasma, when the direction of motion is along the magnetic field, and that of the wave propagation normal to the magnetic field, is analysed. It is shown that in small magnetic fields the ordinary wave develops a new band of backward waves below the plasma frequency. When the frequency of the wave is higher than the plasma frequency, the effect of the motion of the plasma is identical to a deviation of the direction of propagation.

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.

scholarly journals Alfvén wave interaction with inhomogeneous plasmas: acceleration and energy cascade towards small-scales

2004 ◽  
Vol 22 (6) ◽  
pp. 2081-2096 ◽  
Author(s):  
V. Génot ◽  
P. Louarn ◽  
F. Mottez
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Waves ◽  
Wave Interaction ◽  
Skin Depth ◽  
Alfven Wave ◽  
Double Layers ◽  
Larmor Radius ◽  
Density Gradients ◽  
Particle In Cell ◽  
The Magnetic Field

Abstract. Investigating the process of electron acceleration in auroral regions, we present a study of the temporal evolution of the interaction of Alfvén waves (AW) with a plasma inhomogeneous in a direction transverse to the static magnetic field. This type of inhomogeneity is typical of the density cavities extended along the magnetic field in auroral acceleration regions. We use self-consistent Particle In Cell (PIC) simulations which are able to reproduce the full nonlinear evolution of the electromagnetic waves, as well as the trajectories of ions and electrons in phase space. Physical processes are studied down to the ion Larmor radius and electron skin depth scales. We show that the AW propagation on sharp density gradients leads to the formation of a significant parallel (to the magnetic field) electric field (E-field). It results from an electric charge separation generated on the density gradients by the polarization drift associated with the time varying AW E-field. Its amplitude may reach a few percents of the AW E-field. This parallel component accelerates electrons up to keV energies over a distance of a few hundred Debye lengths, and induces the formation of electron beams. These beams trigger electrostatic plasma instabilities which evolve toward the formation of nonlinear electrostatic structures (identified as electron holes and double layers). When the electrostatic turbulence is fully developed we show that it reduces the further wave/particle exchange. This sequence of mechanisms is analyzed with the program WHAMP, to identify the instabilities at work and wavelet analysis techniques are used to characterize the regime of energy conversions (from electromagnetic to electrostatic structures, from large to small length scales). This study elucidates a possible scenario to account for the particle acceleration and the wave dissipation in inhomogeneous plasmas. It would consist of successive phases of acceleration along the magnetic field, the development of an electrostatic turbulence, the thermalization and the heating of the plasma. Space plasma physics (charged particle motion and acceleration; numerical studies).

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