Instability of ion–ion hybrid waves in current-carrying collisional plasmas with two ion species

1979 ◽  
Vol 22 (1) ◽  
pp. 59-70 ◽  
Author(s):  
Kai Fong Lee
Keyword(s):  
Magnetic Field ◽  
Electrostatic Waves ◽  
Hybrid Frequency ◽  
Background Magnetic Field ◽  
Field Aligned Current ◽  
The Stability ◽  
Hybrid Waves ◽  
Simple Equations ◽  
Ion Species

The stability of electrostatic waves propagating at large angles with respect to the background magnetic field is studied in collisional, fully ionized plasmas with two types of ion species and carrying a field-aligned current. By considering plasmas with ma/mb ≪ Nb/Na ≪ mb/ma where m and N denote mass and density respectively and subscripts a and b refer to the two ion species, a complicated dispersion relation is reduced to two simple equations for the determination of the real and imaginary parts of the frequency. It is found that, under appropriate conditions, an instability occurs at frequencies slightly above but very close to the ion–ion hybrid frequency. The growth rate scales directly as the electron–ion collisional frequency.

Instability of lower-hybrid waves in collisional plasmas with a field-aligned current

1980 ◽  
Vol 23 (2) ◽  
pp. 249-257 ◽  
Author(s):  
Kai Fong Lee
Keyword(s):  
Drift Velocity ◽  
Electron Drift Velocity ◽  
Necessary Condition ◽  
Lower Hybrid ◽  
Electron Drift ◽  
Electrostatic Waves ◽  
Hybrid Frequency ◽  
Background Magnetic Field ◽  
Field Aligned Current ◽  
Hybrid Waves

A study is presented for electrostatic waves propagating at large angles with respect to the background magnetic field in collisional, fully ionized plasmas carrying a field-aligned current. In addition to a mode at the usual lower-hybrid frequency, it is found that the presence of electron drift velocity introduces two more modes of oscillation at several times the lower-hybrid frequency. Under appropriate conditions, a resistive instabifity, with frequency very close to the lower-hybrid frequency and growth rate proportional to the electron–ion collisional frequency, can occur. A necessary condition is that the parallel phase velocity of the wave be smaller than the electron drift velocity. A numerical example is given to illustrate the essential features of the instability.

Stimulated backscattering of electromagnetic waves from ion–ion hybrid waves in a magnetized plasma

1975 ◽  
Vol 14 (2) ◽  
pp. 245-253 ◽  
Author(s):  
Kai Fong Lee
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Waves ◽  
Magnetized Plasma ◽  
Threshold Power ◽  
Lower Hybrid ◽  
Stimulated Scattering ◽  
Electrostatic Waves ◽  
Hybrid Frequency ◽  
Hybrid Waves ◽  
The Magnetic Field

In a high-density magnetized plasma composed of two ion species of different charge-to-mass ratios, electrostatic waves propagating across the magnetic field exhibit a resonance at the Buchsbaum or ion-ion hybrid frequency, in addition to the resonances at the upper and lower hybrid frequencies. In this paper, the possibility of stimulated scattering of electromagnetic waves incident normal to the magnetic field from electrostatic waves at the ion-ion hybrid frequency is investigated. Based on the cold-plasma equations, it is found that such a process is theoretically possible. Formulas for the threshold power and growth rate are obtained, which show that the threshold power is much greater, and the growth rate much less, than those of stimulated scattering from upper and lower hybrid waves.

Magnetic Field

2013 ◽  
Author(s):  
Gary A. Glatzmaier
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Background Field ◽  
Magnetohydrodynamic Equations ◽  
Electrically Conducting ◽  
Background Magnetic Field ◽  
Nonlinear Simulations ◽  
Uniform Background ◽  
The Stability ◽  
2D Model

This chapter focuses on magnetoconvection, which refers to thermal convection of an electrically conducting fluid within a background magnetic field maintained by some external mechanism. It first provides a brief overview of magnetohydrodynamics and the magnetohydrodynamic equations before explaining how to make a 2D model of magnetic field. In this approach, the case of a uniform vertical background field and the case of a uniform horizontal background field are both considered. The chapter then describes how one could simulate a case of a uniform background field that is tilted relative to both the vertical and horizontal axes. It also considers what can be learned about the stability and structure of magnetoconvection and the dispersion relation for magneto-gravity waves from analytical analyses without the nonlinear terms. Finally, it discusses nonlinear simulations of magnetoconvection in a box with impermeable side boundaries, along with magnetoconvection with a horizontal background field and an arbitrary background field.

Stability of interfacial waves in aluminium reduction cells

1998 ◽  
Vol 362 ◽  
pp. 273-295 ◽  
Author(s):  
P. A. DAVIDSON ◽  
R. I. LINDSAY
Keyword(s):  
Magnetic Field ◽  
Wave Equation ◽  
Fourier Analysis ◽  
Lorentz Force ◽  
Travelling Waves ◽  
Fluid Motion ◽  
Standing Waves ◽  
Background Magnetic Field ◽  
The Stability ◽  
Aluminium Reduction

We investigate the stability of interfacial waves in conducting fluids under the influence of a vertical current density, paying particular attention to aluminium reduction cells in which such instabilities are commonly observed. We develop a wave equation for the interface in which the Lorentz force is expressed explicitly in terms of the fluid motion. Our wave equation differs from previous models, most notably that developed by Urata (1985), in that earlier formulations rested on a more complex, implicit coupling between the fluid motion and the Lorentz force. Our formulation furnishes a number of quite general stability results without the need to resort to Fourier analysis. (The need for Fourier analysis typifies previous studies.) Moreover, our equation supports both travelling and standing waves. We investigate each in turn.We obtain three new results. First, we show that travelling waves may become unstable in the presence of a uniform, vertical magnetic field. (Our travelling waves are quite different to those discovered by previous investigators (Sneyd 1985 and Moreau & Ziegler 1986) which require more complex magnetic fields to become unstable.) Second, in line with previous studies we confirm that standing waves may also become unstable. In this context we derive a simple energy criterion which shows which types of motion may extract energy from the background magnetic field. This indicates that a rotating, tilted interface is particularly prone to instability, and indeed such a motion is often seen in practice. Finally, we use Gershgorin's theorem to produce a sufficient condition for the stability of standing waves in a finite domain. This allows us to place a lower bound on the critical value of the background magnetic field at which an instability first appears, without solving the governing equations of motion.

Electromagnetic and electrostatic wavesin a multi-component plasma near the lower hybrid frequency

1976 ◽  
Vol 15 (1) ◽  
pp. 115-131 ◽  
Author(s):  
M. Hamelin ◽  
C. Beghin
Keyword(s):  
Microscopic Theory ◽  
Dispersion Curves ◽  
Lower Hybrid ◽  
Electrostatic Waves ◽  
Hybrid Frequency ◽  
Hot Plasma ◽  
Component Plasma ◽  
Ion Species ◽  
The Magnetic Field ◽  
Theoretical Results

In propagation perpendicular to the magnetic field, the lower hybrid frequency is the transition between long electromagnetic and short electrostatic waves. Cold, warm and hot plasma theories are applied to the case of a plasma composed of different ion species. For cold and warm (adiabatic) theories, the dispersion curves are not qualitatively different from the single-ion case. In the hot microscopic theory, the dispersion curves, the so-called ‘Bernstein modes’, have a structure mainly related to the lightest ion gyroharmonics, even in concentration as low as 1 %. The theoretical results can explain the ray structure observed in the ISIS II and Electron Echo 1 experiments.

scholarly journals Stability and dynamics of magnetocapillary interactions

Soft Matter ◽  
2015 ◽  
Vol 11 (9) ◽  
pp. 1828-1838 ◽  
Author(s):  
Rujeko Chinomona ◽  
Janelle Lajeunesse ◽  
William H. Mitchell ◽  
Yao Yao ◽  
Saverio E. Spagnolie
Keyword(s):  
Magnetic Field ◽  
Self Assembly ◽  
Micro Particles ◽  
Background Magnetic Field ◽  
The Stability ◽  
Insight Into

We investigate the stability and dynamics of floating ferromagnetic beads under the influence of an oscillating background magnetic field. Striking behaviors are observed in fast transitions to and from locomotory states, offering insight into the behavior and self-assembly of interface-bound micro-particles.

scholarly journals Stability of the 3D incompressible MHD equations with horizontal dissipation in periodic domain

2021 ◽  
Vol 6 (11) ◽  
pp. 11837-11849
Author(s):  
Ruihong Ji ◽  
◽  
Ling Tian ◽  
Keyword(s):  
Magnetic Field ◽  
Stability Problem ◽  
Stability Result ◽  
Mhd Equations ◽  
Periodic Domain ◽  
Magnetic Diffusion ◽  
Partial Dissipation ◽  
Background Magnetic Field ◽  
The Stability ◽  
Incompressible Mhd

<abstract><p>The stability problem on the magnetohydrodynamics (MHD) equations with partial or no dissipation is not well-understood. This paper focuses on the 3D incompressible MHD equations with mixed partial dissipation and magnetic diffusion. Our main result assesses the stability of perturbations near the steady solution given by a background magnetic field in periodic domain. The new stability result presented here is among few stability conclusions currently available for ideal or partially dissipated MHD equations.</p></abstract>

Determining the Norton’s Equivalent Model of Distribution System with Distributed Generation (DG) for Stability Analysis

2019 ◽  
Vol 12 (2) ◽  
pp. 190-198
Author(s):  
Sunny Katyara ◽  
Lukasz Staszewski ◽  
Faheem Akhtar Chachar
Keyword(s):  
Distributed Generation ◽  
Normal Condition ◽  
Distribution System ◽  
Distribution Networks ◽  
Equivalent Model ◽  
Stability Factor ◽  
Matlab Simulation ◽  
The Stability ◽  
Stability Issues

Background: Since the distribution networks are passive until Distributed Generation (DG) is not being installed into them, the stability issues occur in the distribution system after the integration of DG. Methods: In order to assure the simplicity during the calculations, many approximations have been proposed for finding the system’s parameters i.e. Voltage, active and reactive powers and load angle, more efficiently and accurately. This research presents an algorithm for finding the Norton’s equivalent model of distribution system with DG, considering from receiving end. Norton’s model of distribution system can be determined either from its complete configuration or through an algorithm using system’s voltage and current profiles. The algorithm involves the determination of derivative of apparent power against the current (dS/dIL) of the system. Results: This work also verifies the accuracy of proposed algorithm according to the relative variations in the phase angle of system’s impedance. This research also considers the varying states of distribution system due to switching in and out of DG and therefore Norton’s model needs to be updated accordingly. Conclusion: The efficacy of the proposed algorithm is verified through MATLAB simulation results under two scenarios, (i) normal condition and (ii) faulty condition. During normal condition, the stability factor near to 1 and change in dS/dIL was near to 0 while during fault condition, the stability factor was higher than 1 and the value of dS/dIL was away from 0.

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