A numerical investigation of current-driven instabilities near the ion-ion hybrid frequency

1984 ◽  
Vol 32 (3) ◽  
pp. 387-398 ◽  
Author(s):  
Diane J. Grayson ◽  
M. A. Hellberg
Keyword(s):  
Dispersion Relation ◽  
Numerical Investigation ◽  
Electrostatic Waves ◽  
Ion Plasma ◽  
Hybrid Frequency ◽  
Parameter Values ◽  
A Current

A dispersion relation for electrostatic waves in a current-carrying, resistive, magnetized, two-ion plasma has been solved numerically for a range of parameter values. The behaviour of the resistive ion-ion hybrid instability is described and in addition a two-stream ion-ion hybrid instability is identified.

Low-frequency drift-induced instabilities in a magnetized two-ion plasma

1986 ◽  
Vol 35 (3) ◽  
pp. 393-412 ◽  
Author(s):  
R. Bharuthram ◽  
M. A. Hellberg
Keyword(s):  
Dispersion Relation ◽  
Numerical Solutions ◽  
Cyclotron Frequency ◽  
Low Frequency ◽  
Frequency Drift ◽  
Transition Diagram ◽  
Electrostatic Waves ◽  
Ion Plasma ◽  
Parameter Values ◽  
A Current

Numerical solutions of a dispersion relation for low-frequency electrostatic waves in a current-carrying, cold, weakly collisional, magnetized two-ion plasma are used to discuss the two-stream and resistive natures of the ion-ion hybrid instability. An instability with analogous behaviour is found to be associated with the light ion cyclotron frequency. Analytical results explain the behaviour. A numerically derived transition diagram summarizes the parameter values for which transitions between different modes take place.

Instability of tangential discontinuities in pinching plasmas

1999 ◽  
Vol 62 (1) ◽  
pp. 117-123 ◽  
Author(s):  
S. P. TSYBENKO
Keyword(s):  
Dispersion Relation ◽  
Simple Model ◽  
Current Pulse ◽  
Current Density ◽  
Strong Dependence ◽  
Plasma Instability ◽  
Tangential Discontinuity ◽  
Instability Increment ◽  
Tangential Discontinuities ◽  
A Current

A new mechanism for the formation of pinching plasma instability related to a tangential discontinuity is discussed. With this in mind we use a simple model of the Davydov–Zakharov class. It appears that there is a strong dependence of the instability increment on current density, resulting from the corresponding dispersion relation. Modulation of a current pulse is shown to be a possible way of stabilizing powerful discharges.

On Drift Instabilities in a Collisionless Electron-Proton Plasma from the point of view of Energy Absorption of Resonant Particles

1963 ◽  
Vol 18 (4) ◽  
pp. 446-453 ◽  
Author(s):  
Asbjørn Kildal
Keyword(s):  
Energy Absorption ◽  
Constant Electric Field ◽  
Wave Length ◽  
Collisionless Plasma ◽  
Phase Region ◽  
Point Of View ◽  
Electrostatic Waves ◽  
Transverse Current ◽  
Special Cases ◽  
A Current

The present paper is essentially devoted to the study of instabilities of electrostatic waves in a current-carrying collisionless plasma. As the underlying physical cause of the instabilities is the same as that of the LANDAU damping in an electron plasma, a detailed analysis of the latter is first given. It is shown that the damping may be considered as being due to the fact that there are more electrons in the phase-region where energy is absorbed by the particles from the field than in the phase-region where energy is given up to the field.We then proceed to the evaluation of the energy absorption A of the resonant particles, first in the absence of an external magnet field, B0 , next when the wave is propagated under an arbitrary angle with respect to B0 . When A > 0, the wave is damped, and vice-versa. Without appeal to a dispersion equation, stability criteria can thus be found, dependent on the wave frequency and wave-vector. Next some special cases are investigated and compared with the results of other authors where such results exist.As a consequence of the fact that some ions and electrons, the resonant particles, experience a constant electric field, these particles also experience a constant drift transverse to both E and B0. This drift gives rise to a transverse current which is closely related to the damping or growing of the wave. An expression for this current, averaged over one wave-length is found.

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.

Electromagnetic instability supported by a rippled, magnetically focused relativistic electron beam

1984 ◽  
Vol 31 (2) ◽  
pp. 239-251 ◽  
Author(s):  
S. Cuperman ◽  
F. Petran ◽  
A. Gover
Keyword(s):  
Electron Beam ◽  
Dispersion Relation ◽  
Growth Rates ◽  
Relativistic Electron Beam ◽  
Electron Beams ◽  
Wave Instability ◽  
Electrostatic Waves ◽  
Long Wavelength ◽  
Ripple Amplitude ◽  
Electromagnetic Instability

The coupling of volume, long-wavelength TM electromagnetic and longitudinal space charge (electrostatic) waves by the rippling of magnetically focused electron beams is examined analytically. The dispersion relation is obtained and then solved for these types of wave. Instability, with growth rates proportional to the relative ripple amplitude of the beam, is found and discussed.

Linear electrostatic waves in a three-component electron-positron-ion plasma

2014 ◽  
Vol 21 (12) ◽  
pp. 122119 ◽  
Author(s):  
A. Mugemana ◽  
I. J. Lazarus ◽  
S. Moolla
Keyword(s):  
Electrostatic Waves ◽  
Ion Plasma ◽  
Electron Positron

Interaction of electrostatic waves in collisionless plasmast

1971 ◽  
Vol 5 (1) ◽  
pp. 51-63 ◽  
Author(s):  
G. J. Lewak
Keyword(s):  
Energy Conservation ◽  
Fourth Order ◽  
Time Reversal ◽  
Phase Plane ◽  
Collisionless Plasma ◽  
Particle Interaction ◽  
Coupling Constants ◽  
Electrostatic Waves ◽  
Hybrid Frequency ◽  
The Difference

The interaction of three electrostatic waves in a collisionless plasma is treated to fourth order neglecting the wave—particle interaction (damping). Using the principles of energy conservation, and invariance under time reversal, conditions on the coupling constants are derived, enabling the solution to be expressed as a function of only two coupling constants. Phase plane diagrams of the solutions are sketched showing that the only singular points are stable equili bria. It is suggested how the theory may be applied to the explanation of the ‘floating spike’ resonance observable when one-half the hybrid frequency is the difference between the plasma and gyro frequencies (Hagg & Muldrew 1968).

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