Evolution of nonlinear magnetosonic waves propagating obliquely to an external magnetic field in a collisionless plasma

2000 ◽  
Vol 64 (3) ◽  
pp. 211-226 ◽  
Author(s):  
DEBALINA CHAKRABORTY ◽  
K. P. DAS
Keyword(s):  
Magnetic Field ◽  
Hall Current ◽  
Collisionless Plasma ◽  
Momentum Equation ◽  
Finite Amplitude ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Petviashvili Equation ◽  
Flr Effects ◽  
External Uniform Magnetic Field

It is shown that the asymptotic evolution of finite-amplitude magnetosonic waves propagating obliquely to an external uniform magnetic field in a warm homogeneous plasma is governed by a Kadomtsev–Petviashvili equation having an extra dispersive term. The dispersion is provided by finite-Larmor-radius (FLR) effects in the momentum equation and by the Hall-current and electron-pressure corrections in the generalized Ohm's law. A double-layer-type solution of the equation is obtained, and the equation is shown to reduce to a KdV–Burgers equation under certain assumptions.

Evolution of nonlinear Alfvén waves propagating along the magnetic field in a collisionless plasma

1982 ◽  
Vol 28 (3) ◽  
pp. 459-468 ◽  
Author(s):  
M. Khanna ◽  
R. Rajaram
Keyword(s):  
Magnetic Field ◽  
Collisionless Plasma ◽  
Momentum Equation ◽  
Finite Amplitude ◽  
Alfven Wave ◽  
Mhd Waves ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Flr Effects ◽  
The Magnetic Field

It is shown that the asymptotic evolution of a finite-amplitude Alfvén wave propagating parallel to the uniform magnetic field in a warm homogeneous collisionless plasma is governed by the modified nonlinear Schrödinger equation. The dispersion is provided by the ion finite Larmor radius (FLR) effects in the momentum equation and the Hall current and electron pressure corrections to the generalized Ohm's law. In the cold plasma limit the equations reduce to those available in the literature. It is suggested that these calculations can have a bearing on the investigation of the structure of MHD waves in the solar wind.

Derivation of CGL theory with finite Larmor radius corrections

1980 ◽  
Vol 23 (2) ◽  
pp. 205-208 ◽  
Author(s):  
R. K. Chhajlani ◽  
S. C. Bhand
Keyword(s):  
Magnetic Field ◽  
Strong Magnetic Field ◽  
Collisionless Plasma ◽  
Larmor Frequency ◽  
Higher Order ◽  
Larmor Radius ◽  
Pressure Tensor ◽  
Zeroth Order ◽  
Tensor Equation ◽  
Finite Larmor Radius

A method has been developed for the derivation of Chew–Goldberger–Low (CGL) theory for a collisionless plasma in the presence of a strong magnetic field. The pressure tensor in the pressure tensor equation is expanded in the inverse power of Larmor frequency. In the zeroth order, CGL equations are obtained and, the higher order, finite Larmor radius corrections to CGL equations are derived.

Thermal instability of a compressible finite-Larmor-radius Hall plasma in a porous medium

1996 ◽  
Vol 55 (1) ◽  
pp. 35-45 ◽  
Author(s):  
R. C. Sharma ◽  
Sunil
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Instability ◽  
Hall Current ◽  
Larmor Radius ◽  
Vertical Magnetic Field ◽  
Finite Larmor Radius ◽  
Medium Permeability ◽  
Hall Plasma

The thermal instability of a compressible plasma in a porous medium is considered in the presence of a uniform vertical magnetic field to include the Hall-current and finite-Larmor-radius effects. The system is found to be stable for (cp/g) β < 1, where cp, β and g are the specific heat at constant-pressure, the uniform adverse temperature gradient and the acceleration due to gravity respectively. The uniform vertical magnetic field, Hall-current and finite. Laimor-radius effects introduce oscillatory modes in the system for (cp/g) β ≤ 1, which were non-existent in their absence. The Hall current and finite Larmor radius (FLR) individually have destabilizing and stabilizing effects respectively on the system. In their simultaneous presence there is competition between the destabilizing role of the Hall current and the stabilizing role of the FLR, and each succeeds in stabilizing a certain wavenumber range. In the absence of a magnetic field (and hence the absence of an FLR and Hall current), the destabilizing effect of medium permeability is seen, but in the presence of a magnetic field (and hence the presence of an FLR and Hall current), the medium permeability may have a stabilizing or a destabilizing effect on the thermal instability of the plasma. The effect of compressibility is found to postpone the onset of thermal instability in plasma.

Assessments of Magnetic Reconnection and Kelvin-Helmholtz Instability at Ganymede's Upstream Magnetopause

2020 ◽  
Author(s):  
Nawapat Kaweeyanun ◽  
Adam Masters ◽  
Xianzhe Jia
Keyword(s):  
Magnetic Field ◽  
Magnetic Reconnection ◽  
Larmor Radius ◽  
Helmholtz Instability ◽  
Reconnection Rate ◽  
Permanent Magnetic Field ◽  
Field Orientation ◽  
Finite Larmor Radius ◽  
Energy Flows ◽  
Flr Effects

&lt;p&gt;Ganymede is the largest moon of Jupiter and the only Solar System moon known to generate a permanent magnetic field. Motions of Jupiter&amp;#8217;s magnetospheric plasma around Ganymede create an upstream magnetopause, where energy flows are thought to be driven by magnetic reconnection and/or Kelvin-Helmholtz Instability (KHI). Previous numerical simulations of Ganymede indicate evidence for transient reconnection events and KHI wave structures, but the natures of both processes remain poorly understood. Here we present an analytical model of steady-state conditions at Ganymede&amp;#8217;s magnetopause, from which we conduct first assessments of reconnection and KHI onset criteria at the boundary. We find that reconnection may occur wherever Ganymede&amp;#8217;s closed magnetic field encounters Jupiter&amp;#8217;s ambient magnetic field, regardless of variations in magnetopause conditions. Unrestricted reconnection onset highlights possibilities for multiple X-lines or widespread transient reconnection at Ganymede. The reconnection rate is controlled by the ambient Jovian field orientation and hence driven by Jupiter&amp;#8217;s rotation. We also determine Ganymede&amp;#8217;s magnetopause conditions to be favorable for KHI wave growths in two confined regions each along a magnetopause flank, both of which grow in area whenever Ganymede moves toward Jupiter&amp;#8217;s magnetospheric current sheet. KHI growth rates are calculated with the Finite Larmor Radius (FLR) effects incorporated and found to be asymmetric favoring the magnetopause flank closest to Jupiter. The significance of KHI wave growth on energy flows at Ganymede&amp;#8217;s magnetopause remains to be investigated. Future progress on both topics is highly relevant for the upcoming JUpiter ICy moon Explorer (JUICE) mission.&lt;/p&gt;

scholarly journals Diffusion at the Earth magnetopause: enhancement by Kelvin-Helmholtz instability

2007 ◽  
Vol 25 (1) ◽  
pp. 271-282 ◽  
Author(s):  
R. Smets ◽  
G. Belmont ◽  
D. Delcourt ◽  
L. Rezeau
Keyword(s):  
Magnetic Field ◽  
Distribution Functions ◽  
Larmor Radius ◽  
Simple Analytical Model ◽  
Helmholtz Instability ◽  
Field Reversal ◽  
Finite Larmor Radius ◽  
The Earth ◽  
Specific Distribution ◽  
The Magnetic Field

Abstract. Using hybrid simulations, we examine how particles can diffuse across the Earth's magnetopause because of finite Larmor radius effects. We focus on tangential discontinuities and consider a reversal of the magnetic field that closely models the magnetopause under southward interplanetary magnetic field. When the Larmor radius is on the order of the field reversal thickness, we show that particles can cross the discontinuity. We also show that with a realistic initial shear flow, a Kelvin-Helmholtz instability develops that increases the efficiency of the crossing process. We investigate the distribution functions of the transmitted ions and demonstrate that they are structured according to a D-shape. It accordingly appears that magnetic reconnection at the magnetopause is not the only process that leads to such specific distribution functions. A simple analytical model that describes the built-up of these functions is proposed.

scholarly journals Reduced models accounting for parallel magnetic perturbations: gyrofluid and finite Larmor radius–Landau fluid approaches

2016 ◽  
Vol 82 (6) ◽  
Author(s):  
E. Tassi ◽  
P. L. Sulem ◽  
T. Passot
Keyword(s):  
Fluid Model ◽  
Collisionless Plasma ◽  
Low Frequency ◽  
Wave Model ◽  
Plasma Phys ◽  
Alfven Wave ◽  
Larmor Radius ◽  
Closure Relation ◽  
Reduced Models ◽  
Finite Larmor Radius

Reduced models are derived for a strongly magnetized collisionless plasma at scales which are large relative to the electron thermal gyroradius and in two asymptotic regimes. One corresponds to cold ions and the other to far sub-ion scales. By including the electron pressure dynamics, these models improve the Hall reduced magnetohydrodynamics (MHD) and the kinetic Alfvén wave model of Boldyrev et al. (2013 Astrophys. J., vol. 777, 2013, p. 41), respectively. We show that the two models can be obtained either within the gyrofluid formalism of Brizard (Phys. Fluids, vol. 4, 1992, pp. 1213–1228) or as suitable weakly nonlinear limits of the finite Larmor radius (FLR)–Landau fluid model of Sulem and Passot (J. Plasma Phys., vol 81, 2015, 325810103) which extends anisotropic Hall MHD by retaining low-frequency kinetic effects. It is noticeable that, at the far sub-ion scales, the simplifications originating from the gyroaveraging operators in the gyrofluid formalism and leading to subdominant ion velocity and temperature fluctuations, correspond, at the level of the FLR–Landau fluid, to cancellation between hydrodynamic contributions and ion finite Larmor radius corrections. Energy conservation properties of the models are discussed and an explicit example of a closure relation leading to a model with a Hamiltonian structure is provided.

Rayleigh-Taylor Instability of a Stratified Plasma

1974 ◽  
Vol 29 (3) ◽  
pp. 518-523 ◽  
Author(s):  
K. M. Srivastava
Keyword(s):  
Magnetic Field ◽  
Boussinesq Approximation ◽  
Short Wave ◽  
Taylor Instability ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Wave Disturbances ◽  
Magnetic Field Gradients ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field

We have investigated the effect of finite Larmor radius on the Rayleigh-Taylor instability of a semi-infinite, compressible, stratified and infinitely conducting plasma. The plasma is assumed to have a one dimensional density and magnetic field gradients. The eigenvalue problem has been solved under Boussinesq approximation for disturbances parallel to the magnetic field. It has been established that for perturbation parallel to the magnetic field, the system is stable for both stable and unstable stratification. For perturbation perpendicular to the magnetic field, the problem has been solved without Boussinesq approximation. The dispersion relation has been discussed in the two limiting cases, the short and long wave disturbances. It has been observed that the gyroviscosity has a destabilizing influence from k = 0 to k = 4.5 for ß* = 0.1 and for ß* = 0.1 up to k* = 2.85 and then onwards it acts as a stabilizing agent. It has a damping effect on the short wave disturbances. For some parameters, the largets imaginary part has been shown in Figs. 1 and 2

Effect of Finite Larmor Radius on the Rayleigh-Taylor Instability of Two Component Magnetized Rotating Plasma

1998 ◽  
Vol 53 (12) ◽  
pp. 937-944 ◽  
Author(s):  
P. K. Sharma ◽  
R. K. Chhajlani
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Larmor Radius ◽  
Horizontal Magnetic Field ◽  
Finite Larmor Radius ◽  
Neutral Particles ◽  
Rayleigh Taylor Instability ◽  
Superposed Fluids

Abstract The Rayleigh-Taylor (R-T) instability of two superposed plasmas, consisting of interacting ions and neutrals, in a horizontal magnetic field is investigated. The usual magnetohydrodynamic equations, including the permeability of the medium, are modified for finite Larmor radius (FLR) corrections. From the relevant linearized perturbation equations, using normal mode analysis, the dispersion relation for the two superposed fluids of different densities is derived. This relation shows that the growth rate unstability is reduced due to FLR corrections, rotation and the presence of neutrals. The horizontal magnetic field plays no role in the R-T instability. The R-T instability is discussed for various simplified configurations. It remains unaffected by the permeability of the porous medium, presence of neutral particles and rotation. The effect of different factors on the growth rate of R-T instability is investigated using numerical analysis. Corresponding graphs are plotted for showing the effect of these factors on the growth of the R-T instability.

On the structure of collisionless waves

1969 ◽  
Vol 3 (4) ◽  
pp. 673-689 ◽  
Author(s):  
James B. Fedele
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Small Amplitude ◽  
Single Mode ◽  
Larmor Radius ◽  
Collisionless Shock ◽  
Finite Larmor Radius ◽  
First Order ◽  
Pulse Solution ◽  
Solitary Pulse

Small amplitude waves and collisionless shock waves are investigated within the framework of the first-order Chew—Goldberger—Low equations. For linearized oscillations, two modes are present for propagation along an applied magnetic field. One is an acoustic type which contains no finite Larmor radius effects. The other which contains the ‘fire hose’ instability in its lowest order terms, does possess finite Larmor radius corrections. These corrections, however, do not produce instabilities or dissipation. There are no finite Larmor radius corrections to the single mode present for propagation normal to the applied magnetic field. Normal shock structure is investigated, but it is shown that jump solutions do not exist. An analytic solitary pulse solution is found and is compared with the Adlam—Allen pulse solution.

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