Properties of Alfvén solitons in a finite-beta plasma

1982 ◽  
Vol 27 (2) ◽  
pp. 193-198 ◽  
Author(s):  
Steven R. Spangler ◽  
James P. Sheerin
Keyword(s):  
Functional Form ◽  
Magnetic Energy ◽  
Potential Method ◽  
Reductive Perturbation Method ◽  
Magnetized Plasma ◽  
Envelope Soliton ◽  
Magnetic Energy Density ◽  
Pseudo Potential ◽  
The Magnetic Field ◽  
Two Fluid

The properties of Alfvén solitons are examined (solitons propagating parallel to the magnetic field in a magnetized plasma) in the case when the plasma possesses a finite pressure. Starting from a two-fluid system of equations, the reductive perturbation method is used to derive a derivative nonlinear Schr ödinger equation, which is solved by a pseudo-potential method. An envelope soliton is found which possesses a width –amplitude relationship. The same functional form for the envelope of the magnetic energy density is obtained regardless of the value of the plasma &bgr;.

scholarly journals Structure of nonlinear whistlers moving through plasma at an angle to the magnetic field

2018 ◽  
Vol 4 (1) ◽  
pp. 25-28
Author(s):  
Геннадий Кичигин ◽  
Gennadiy Kichigin
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Numerical Solutions ◽  
Field Vector ◽  
Magnetized Plasma ◽  
Small Scale ◽  
Motion Direction ◽  
Magnetic Field Change ◽  
The Magnetic Field ◽  
Two Fluid

The paper presents solutions of two-fluid magnetic hydrodynamics equations describing small-scale fast magnetosonic stable waves — nonlinear whist-lers moving in a cold magnetized plasma at an angle α to the external magnetic field. At the fixed angle α, the Alfvén Mach number of the whistlers has a narrow range of allowed values. It has been found that when passing from extremely small Mach numbers to ex-tremely large ones, amplitudes and spatial structure of wave velocity components and whistler magnetic field change significantly. The range of angles of the motion direction of whistlers with respect to direction of the the external magnetic field vector is determined. Within this range, the obtained approximate analytical and numerical solutions are in satisfactory agreement.

Nonlinear waves and shocks in relativistic two-fluid hydrodynamics

2012 ◽  
Vol 78 (3) ◽  
pp. 295-302 ◽  
Author(s):  
L. HAIM ◽  
M. GEDALIN ◽  
A. SPITKOVSKY ◽  
V. KRASNOSELSKIKH ◽  
M. BALIKHIN
Keyword(s):  
Energy Density ◽  
Shock Front ◽  
Magnetic Energy ◽  
Ambient Medium ◽  
Nonlinear Effects ◽  
Magnetic Energy Density ◽  
Fluid Analysis ◽  
Relativistic Shocks ◽  
Wide Range ◽  
Two Fluid

AbstractRelativistic shocks are present in a number of objects where violent processes are accompanied by relativistic outflows of plasma. The magnetization parameter σ = B2/4πnmc2 of the ambient medium varies in wide range. Shocks with low σ are expected to substantially enhance the magnetic fields in the shock front. In non-relativistic shocks the magnetic compression is limited by nonlinear effects related to the deceleration of flow. Two-fluid analysis of perpendicular relativistic shocks shows that the nonlinearities are suppressed for σ≪1 and the magnetic field reaches nearly equipartition values when the magnetic energy density is of the order of the ion energy density, Beq2 ~ 4πnmic2γ. A large cross-shock potential eφ/mic2γ0 ~ B2/Beq2 develops across the electron–ion shock front. This potential is responsible for electron energization.

scholarly journals The Origin of Interplanetary Sectors

1980 ◽  
Vol 91 ◽  
pp. 67-72
Author(s):  
Kenneth H. Schatten
Keyword(s):  
Magnetic Field ◽  
Energy Density ◽  
Magnetic Energy ◽  
Coronal Magnetic Field ◽  
Restrictive Assumption ◽  
Plasma Energy ◽  
Magnetic Energy Density ◽  
Physical Phenomena ◽  
The Magnetic Field ◽  
Shed Light

The coronal magnetic models of Altschuler and Newkirk (1969), Schatten, Wilcox and Ness (1969), and Schatten (1971) that allowed calculations of the coronal magnetic field from the observed photospheric magnetic field shed light on the origin of sectors. Figure 1 from Schatten's (1971) “Current Sheet Model” is a schematic representation of these similar models. There are three distinct regions in these models where different physical phenomena occur. The photosphere, where the magnetic fields are governed by the detailed motions and currents in the plasma is considered a boundary condition for the model. Above the photosphere, the plasma density diminishes very rapidly with only moderate decreases in the magnetic energy density. This results in the middle region where the magnetic energy density is greater than plasma energy density and hence controls the configuration. One may then utilize the force-free condition, j × B = 0, and in fact make the more restrictive assumption that this region is current free. The magnetic field in this region can be derived from a solution to the Laplace equation.

Electron acoustic double layers in a magnetized plasma in the presence of superthermal particles

2019 ◽  
Vol 85 (3) ◽  
Author(s):  
D. Dutta ◽  
K. S. Goswami
Keyword(s):  
Acoustic Waves ◽  
Small Amplitude ◽  
Analytical Study ◽  
Potential Method ◽  
Magnetized Plasma ◽  
Double Layers ◽  
Electrons And Ions ◽  
Mach Numbers ◽  
Electron Acoustic ◽  
Pseudo Potential

An analytical study of the small amplitude electron acoustic double layers in a magnetized plasma consisting of superthermal electrons and ions along with cold fluid electrons is discussed. The dispersion relation allows electron acoustic waves with the frequency within electron and ion gyro-frequency in the modelled plasma. In the process of study of the nonlinear structures, the Sagdeev pseudo-potential method for small amplitude regions is employed. The existence domains for the double layers are investigated in terms of the Mach numbers of the structures and the temperature ratios of the species for different ratios of their concentration. The effects of the compositional parameters on the nature and size of the double layers are also explored and it is observed that the plasma can support both compressive and rarefactive double layers depending on the values of those parameters and the Mach numbers.

Kinematic dynamos and the Earth’s magnetic field

1973 ◽  
Vol 275 (1251) ◽  
pp. 425-461 ◽  
Keyword(s):  
Magnetic Field ◽  
Inner Core ◽  
Magnetic Energy ◽  
Liquid Core ◽  
Outer Part ◽  
Ohmic Dissipation ◽  
Tidal Dissipation ◽  
Magnetic Dipoles ◽  
Magnetic Energy Density ◽  
The Magnetic Field

The Bullard—Gellman formalism is applied to investigate the existence of convergent solutions for steady kinematic dynamos. It is found that the solutions for the Bullard—Gellman dynamo, as well as for Lilley’s modification of it, do not converge. Convergent solutions have been found for a class of spherical convective cells which would be stationary in a perfect fluid in the absence of rotation and of the magnetic field. By calibrating the theoretical magnetic dipole so as to fit the observed value at the Earth’s surface, one can find a dynamo in the above class which also matches the observed equatorial magnetic dipoles. There is a dynamo which has a rate of total ohmic dissipation of only 1.8 x 1016 erg s-1 for an assumed electrical conductivity of 3 x 10~6 e.m.u.'f This is one thousandth the rate of tidal dissipation, and one hundred thousandth the rate of heat outflow from the surface of the Earth. The required velocities are of the order of 10~3 cm s_1, and the average magnetic energy density is 4 erg cm-3. The internal structure of the magnetic field in this model shows a dynamo mechanism situated in the outer part of the liquid core and is thus insensitive to possible rigidity of the material in the * inner core.

scholarly journals Structure of nonlinear whistlers moving through plasma at an angle to the magnetic field

2018 ◽  
Vol 4 (1) ◽  
pp. 28-32 ◽  
Author(s):  
Геннадий Кичигин ◽  
Gennadiy Kichigin
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Numerical Solutions ◽  
Field Vector ◽  
Magnetized Plasma ◽  
Small Scale ◽  
Motion Direction ◽  
Magnetic Field Change ◽  
The Magnetic Field ◽  
Two Fluid

The paper presents solutions of two-fluid magnetic hydrodynamics equations describing small-scale fast magnetosonic stable waves — nonlinear whist-lers moving in a cold magnetized plasma at an angle α to the external magnetic field. At the fixed angle α, the Alfvén Mach number of the whistlers has a narrow range of allowed values. It has been found that when passing from extremely small Mach numbers to ex-tremely large ones, amplitudes and spatial structure of wave velocity components and whistler magnetic field change significantly. The range of angles of the motion direction of whistlers with respect to direction of the the external magnetic field vector is determined. Within this range, the obtained approximate analytical and numerical solutions are in satisfactory agreement.

scholarly journals Avalanches of Magnetic Reconnection

1993 ◽  
Vol 141 ◽  
pp. 112-114
Author(s):  
Edward T. Lu
Keyword(s):  
Magnetic Field ◽  
Magnetic Reconnection ◽  
Energy Release ◽  
Power Law ◽  
Magnetic Energy ◽  
Magnetized Plasma ◽  
Release Process ◽  
3 Dimensional ◽  
Convective Motions ◽  
The Magnetic Field

AbstractActive region coronal magnetic fields are expected to be in a twisted tangled state due to photospheric convective motions. These motions can drive the magnetic field to a statistically steady state where energy is released impulsively (Lu and Hamilton 1991). These relaxation events in the magnetic field can be interpreted as avalanches of many small reconnection events. We argue that the frequency distribution of these magnetic reconnection avalanches must be a power law. Furthermore, we calculate the expected distributions in a simple model of magnetic energy release events in a 3-dimensional complex magnetized plasma, and compare these to the distributions of solar flares. These distributions are found to match the observed power law distributions of solar flare energies, peak fluxes, and durations. This model implies that the energy-release process is fundamentally the same for flares of all sizes. Observational predictions of this model are discussed.

scholarly journals The Magnetic Field Configuration in Solar and Stellar Chromospheres

1983 ◽  
Vol 102 ◽  
pp. 339-344
Author(s):  
U. Anzer ◽  
D.J. Galloway
Keyword(s):  
Magnetic Field ◽  
Energy Density ◽  
Magnetic Energy ◽  
Active Regions ◽  
Model Atmosphere ◽  
Inhomogeneous Magnetic Field ◽  
Field Configuration ◽  
Magnetic Energy Density ◽  
Stellar Photosphere ◽  
The Magnetic Field

Calculations are presented for the inhomogeneous magnetic field structure above a stellar photosphere which has magnetic flux tubes located at the downdraughts of its supergranulation pattern. Regions can be delineated where the ambient magnetic energy density is large or small compared with the thermal energy density derived from a model atmosphere. This enables the relative importance of magnetic versus non-magnetic heating mechanisms to be assessed. For the quiet Sun, over half the chromospheric emission must be supplied non-magnetically, whilst the network and active regions require a magnetic supply. For other late-type stars, a simple working rule suggests that when the magnetic field is strong enough to be directly observable, the chromosphere will be magnetically dominated.

scholarly journals MHD turbulence in the intracluster medium

2012 ◽  
Vol 10 (H16) ◽  
pp. 406-406
Author(s):  
Diego Falceta-Gonçalves ◽  
G. Kowal ◽  
E. de Gouveia Dal Pino ◽  
R. Santos-Lima ◽  
S. Nakwacki ◽  
...  
Keyword(s):  
Magnetic Energy ◽  
Collisionless Plasma ◽  
Distribution Functions ◽  
Intracluster Medium ◽  
Mhd Turbulence ◽  
Magnetic Energy Density ◽  
Fluid Approximations ◽  
Small Scales ◽  
High Beta ◽  
Two Fluid

AbstractIn this work we discuss the turbulent evolution of structures in the intracluster medium based on the two fluid approximations: MHD and collisionless plasma under Chew Goldberger Low (CGL) closure. Turbulence excited by galactic motions and gas inflow in intracluster medium will develop in very different ways considering the two fluid approaches. Statistics of density distributions, and velocity and magnetic fields are provided. Compared to the standard MHD case, the instabilities that arise from CGL-MHD models strongly modify the probability distribution functions of the plasma velocity and density, basically increasing their dispersion. Moreover, the spectra of both density and velocity show increased power at small scales, due to the instabilities growth rate that are larger as smaller scales. Finally, in high beta plasmas, i.e. B2 << P, a fast increase of the magnetic energy density is observed in the CGL-MHD models, faster than the standard MHD turbulent dynamo that operates at timescales τ ~ L/vL. The signatures of the increased power at small scales and the increase of magnetic field intensity from CGL-MHD models could be observed at radio wavelengths. A comparison of the structure function of the synchrotron emission, as well as the statistics of Faraday rotation effects on the synchrotron polarization, for both the MHD and CGL-MHD models is provided.

Extensions of the Pseudo-Potential Method

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Potential Method ◽  
Original Model ◽  
Original Formulation ◽  
The Face ◽  
Pseudo Potential

This chapter provides an account of subsequent extensions of the Shan-Chen pseudo-potential method, including more elaborated potentials which extend beyond the first Brillouin cell. These extensions permit us to lift a number of limitations of the original model and considerably expand its scope and range of applications. In Chapter 27, a variety of LB techniques for nonideal fluids have been discussed. As usual, each method comes with its ups and downs, but actual evidence shows that the Shan–Chen (SC) model has enjoyed increasing popularity over the years. Interestingly, such popularity stands in the face of a fair amount of substantial criticism. In this chapter, first the Shan–Chen model is revisited in some more detail along with a discussion of ways out of the above criticism. Subsequently, the extension of the SC technique to the case of multi-range potentials extending beyond the first Brillouin cell is discussed. This extension proves pretty effective in softening many of the weaknesses of the original formulation, thereby considerably expanding its scope and range of applications.

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