Pressure driven long wavelength MHD instabilities in an axisymmetric toroidal resistive plasma

2021 ◽  
Vol 64 (1) ◽  
pp. 014001
Author(s):  
J P Graves ◽  
M Coste-Sarguet ◽  
C Wahlberg
Keyword(s):  
Acoustic Waves ◽  
Rational Surface ◽  
Ion Acoustic Waves ◽  
Equilibrium Conditions ◽  
Rational Surfaces ◽  
Long Wavelength ◽  
Mhd Instabilities ◽  
Axisymmetric Equilibrium ◽  
First Time ◽  
Pressure Driven

Abstract A general set of equations that govern global resistive interchange, resistive internal kink and resistive infernal modes in a toroidal axisymmetric equilibrium are systematically derived in detail. Tractable equations are developed such that resistive effects on the fundamental rational surface can be treated together with resistive effects on the rational surfaces of the sidebands. Resistivity introduces coupling of pressure driven toroidal instabilities with ion acoustic waves, while compression introduces flute-like flows and damping of instabilities, enhanced by toroidal effects. It is shown under which equilibrium conditions global interchange, internal kink modes or infernal modes occur. The m = 1 internal kink is derived for the first time from higher order infernal mode equations, and new resistive infernal modes resonant at the q = 1 surface are reduced analytically. Of particular interest are the competing effects of resistive corrections on the rational surfaces of the fundamental harmonic and on the sidebands, which in this paper is investigated for standard profiles developed for the m = 1 internal kink problem.

Stability of ion-acoustic solitons in a multispecies plasma consisting of non-isothermal electrons

1998 ◽  
Vol 60 (1) ◽  
pp. 151-158 ◽  
Author(s):  
DEBALINA CHAKRABORTY ◽  
K. P. DAS
Keyword(s):  
Acoustic Waves ◽  
Perturbation Expansion ◽  
Expansion Method ◽  
Ion Acoustic Waves ◽  
Long Wavelength ◽  
Petviashvili Equation ◽  
Ion Acoustic ◽  
Ion Acoustic Solitons ◽  
The Stability ◽  
Perturbation Expansion Method

A modified Kadomtsev–Petviashvili equation is derived for ion-acoustic waves in a multispecies plasma consisting of non-isothermal electrons. This equation is used to investigate the stability of modified KdV solitons against long-wavelength plane-wave perturbation using the small-k perturbation expansion method of Rowlands and Infeld. It is found that modified KdV solitons are stable.

Landau damping of long wavelength ion acoustic waves in a collision-free plasma with a gravity field

1969 ◽  
Vol 3 (1) ◽  
pp. 13-20 ◽  
Author(s):  
D. Parkinson ◽  
K. Schindler
Keyword(s):  
Gravity Field ◽  
Acoustic Waves ◽  
Fluid Dynamic ◽  
Scale Height ◽  
Landau Damping ◽  
Ion Acoustic Waves ◽  
Equilibrium Plasma ◽  
Long Wavelength ◽  
Ion Acoustic ◽  
Free Plasma

Ion acoustic waves propagating in a collision-free gravity-supported one-dimeiisional plasma are studied, including conditions where the wavelength is of the order of the scale height of the equilibrium plasma. It turns out that the fluid dynamic steepening tendency of waves propagating in the direction of decreasing density is overcome by Landau damping up to wavelengths of the order of the scale height or even larger, depending on the ratio of the electron and the ion temperatures.

Long wavelength ion-acoustic waves in a magneto-plasma in a gravitational field

1970 ◽  
Vol 4 (3) ◽  
pp. 617-627 ◽  
Author(s):  
C. H. Liu
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Static Magnetic Field ◽  
Acoustic Waves ◽  
Fluid Dynamic ◽  
Debye Length ◽  
Ion Acoustic Waves ◽  
Long Wavelength ◽  
Special Cases ◽  
Ion Acoustic

Ion-acoustic waves propagating in a collision-free, gravity-supported plasma in a static magnetic field are studied with a linearized Vlasov equation. The dispersion relation is derived in the limit of vanishing electron to ion mass ratio and wavelength much larger than the Debye length. From this dispersion relation it is shown that the well-known fluid dynamic steepening tendency of waves propagating in the direction of decreasing density is competing with the effect of Landau damping. Depending on the ratio of electron and ion temperatures, the direction of propagation and the strength of the static magnetic field, waves of wavelengths of the order of the scale height or even greater are shown to be damped. Several special cases are discussed.

scholarly journals Modulational instability in the beat-wave generation

1988 ◽  
Vol 6 (2) ◽  
pp. 199-210 ◽  
Author(s):  
D. Pesme ◽  
S. J. Karttunen ◽  
R. R. E. Salomaa ◽  
G. Laval ◽  
N. Silvestre
Keyword(s):  
Dispersion Relation ◽  
Acoustic Waves ◽  
Wave Process ◽  
Short Pulse ◽  
Modulational Instability ◽  
Ion Acoustic Waves ◽  
Long Wavelength ◽  
Ion Acoustic ◽  
Large Growth ◽  
General Dispersion

The coupling of a large amplitude plasmon, generated by the beat-wave process, to ion acoustic waves may lead to modulational or decay instabilities, which are investigated here. A general dispersion relation obtainable from Zakharov equations predicts large growth rates (∼ωpi) for short wavelength modulations. To avoid these, extremely short pulse lengths are required in the beat-wave experiments. Due to the very long wavelength of the beat-plasmon, the decay instability is not likely below the ke V-temperatures.

Long-Wavelength Ion-Acoustic Waves

1972 ◽  
Vol 29 (22) ◽  
pp. 1499-1501 ◽  
Author(s):  
Glenn Bateman
Keyword(s):  
Acoustic Waves ◽  
Ion Acoustic Waves ◽  
Long Wavelength ◽  
Ion Acoustic

scholarly journals New extended generalized Kudryashov method for solving three nonlinear partial differential equations

2020 ◽  
Vol 25 (4) ◽  
Author(s):  
Elsayed M.E. Zayed ◽  
Reham M.A. Shohib ◽  
Mohamed E.M. Alngar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Nonlinear Partial Differential Equations ◽  
Magnetized Plasma ◽  
Ion Acoustic Waves ◽  
Partial Differential ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
First Time

New extended generalized Kudryashov method is proposed in this paper for the first time. Many solitons and other solutions of three nonlinear partial differential equations (PDEs), namely, the (1+1)-dimensional improved perturbed nonlinear Schrödinger equation with anti-cubic nonlinearity, the (2+1)-dimensional Davey–Sterwatson (DS) equation and the (3+1)-dimensional modified Zakharov–Kuznetsov (mZK) equation of ion-acoustic waves in a magnetized plasma have been presented. Comparing our new results with the well-known results are given. Our results in this article emphasize that the used method gives a vast applicability for handling other nonlinear partial differential equations in mathematical physics.

On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

2018 ◽  
Vol 5 (1) ◽  
pp. 31-36
Author(s):  
Md Monirul Islam ◽  
Muztuba Ahbab ◽  
Md Robiul Islam ◽  
Md Humayun Kabir
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Rectangular Channel ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Ion Acoustic Waves ◽  
Analytical System

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

scholarly journals High time resolution PFISR and optical observations of naturally enhanced ion acoustic lines

2009 ◽  
Vol 27 (4) ◽  
pp. 1457-1467 ◽  
Author(s):  
R. G. Michell ◽  
K. A. Lynch ◽  
C. J. Heinselman ◽  
H. C. Stenbaek-Nielsen
Keyword(s):  
High Resolution ◽  
Time Resolution ◽  
Acoustic Waves ◽  
Fast Moving ◽  
High Time ◽  
High Time Resolution ◽  
Ion Acoustic Waves ◽  
Raw Data ◽  
Ion Acoustic ◽  
Auroral Imaging

Abstract. Observations of naturally enhanced ion acoustic lines (NEIALs) taken with the Poker Flat Incoherent Scatter Radar (PFISR) using a mode with very high time resolution are presented. The auroral event took place over Poker Flat, Alaska on 8 February 2007 at 09:35 UT (~22:00 MLT), and the radar data are complemented by common-volume high-resolution auroral imaging. The NEIALs occurred during only one of the standard 15-s integration periods. The raw data of this time show very intermittent NEIALs which occur only during a few very short time intervals (≤1 s) within the 15-s period. The time sampling of the raw data, ~19 ms on average, allows study of the time development of the NEIALs, though there are indications that even finer time resolution would be of interest. The analysis is based on the assumption that the NEIAL returns are the result of Bragg scattering from ion-acoustic waves that have been enhanced significantly above thermal levels. The spectra of the raw data indicate that although the up- and down-shifted shoulders can both become enhanced at the same time, (within 19 ms), they are most often enhanced individually. The overall power in the up-and down-shifted shoulders is approximately equal throughout the event, with the exception of one time, when very large up-shifted power was observed with no corresponding down-shifted power. This indicates that during the 480 μs pulse, the strongly enhanced ion-acoustic waves were only traveling downward and not upward. The exact time that the NEIALs occurred was when the radar beam was on the boundary of a fast-moving (~10 km/s), bright auroral structure, as seen in the high resolution auroral imaging of the magnetic zenith. When viewed with high time resolution, the occurrence of NEIALs is associated with rapid changes in auroral luminosity within the radar field of view due to fast-moving auroral fine structures.

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