Nonlinear, superluminous, periodic waves in a plasma with magnetic field

1977 ◽  
Vol 17 (2) ◽  
pp. 301-316 ◽  
Author(s):  
P. C. Clemmow
Keyword(s):  
Magnetic Field ◽  
Periodic Solutions ◽  
Average Rate ◽  
Plane Waves ◽  
First Integral ◽  
Laboratory Frame ◽  
Static Field ◽  
Particle Velocities ◽  
Space Dependence ◽  
The Magnetic Field

The exact theory of plane waves of fixed profile travelling with constant velocity cZ/n (0 ≤ n ≤ 1) through a uniform, cold, electron-ion plasma in a magneto-static field is examined in terms of the governing equations referred to the frame of reference in which there is no space dependence. Canonical periodic solutions are defined as those with zero average rate of flow of electrons (and a fortiori of ions) in the laboratory frame. It is shown that the equations lead to a second- order, nonlinear, ordinary vector differential equation for the reduced velocity u of the electrons. A scalar first integral is obtained, from which it is deduced that the path in u-space of any solution lies within a bounded domain. It is shown that, for propagation across the magnetic field, a polarization is possible in which the particle velocities and the electric field are orthogonal to the magnetic field. The simpler model of an electron Plasma is considered. Explicit canonical periodic solutions, with the stated polarization, are obtained for propagation across the magnetic field in the case n = 0 and the case n ≃ 1. These support the conjecture that, for any fixed value of n in [0, 1], there are two ‘modes’ of arbitrary amplitude which reduce to the familiar monochromatic waves of linear magneto-ionic theory in the small amplitude limit.

Further analysis of nonlinear, periodic, highly superluminous waves in a magnetized plasma

1982 ◽  
Vol 27 (1) ◽  
pp. 177-187 ◽  
Author(s):  
P. C. Clemmow
Keyword(s):  
Magnetic Field ◽  
Power Series ◽  
Periodic Solutions ◽  
Wave Speed ◽  
Nonlinear Differential Equations ◽  
Plane Waves ◽  
Electron Plasma ◽  
Finite Amplitude ◽  
Magnetized Plasma ◽  
Cold Electron

A perturbation method is applied to the pair of second-order, coupled, nonlinear differential equations that describe the propagation, through a cold electron plasma, of plane waves of fixed profile, with direction of propagation and electric vector perpendicular to the ambient magnetic field. The equations are expressed in terms of polar variables π, φ, and solutions are sought as power series in the small parameter n, where c/n is the wave speed. When n = 0 periodic solutions are represented in the (π,φ) plane by circles π = constant, and when n is small it is found that there are corresponding periodic solutions represented to order n2 by ellipses. It is noted that further investigation is required to relate these finite-amplitude solutions to the conventional solutions of linear theory, and to determine their behaviour in the vicinity of certain resonances that arise in the perturbation treatment.

scholarly journals Multiplicity of periodic solutions in bistable equations

2006 ◽  
Vol 462 (2067) ◽  
pp. 1001-1019 ◽  
Author(s):  
Gregory Berkolaiko ◽  
Michael Grinfeld
Keyword(s):  
Magnetic Field ◽  
Periodic Solutions ◽  
Time Varying ◽  
Discontinuous Change ◽  
First Order ◽  
Stable Periodic ◽  
The Mean ◽  
Autonomous Differential Equations ◽  
Ising Magnet ◽  
The Magnetic Field

We study the number of periodic solutions in two first-order non-autonomous differential equations, both of which have been used to describe, among other things, the mean magnetization of an Ising magnet in a time-varying external magnetic field. When the amplitude of the external field is increased, the set of periodic solutions undergoes a bifurcation in both equations. We prove that despite superficial similarities between the equations, the character of the bifurcation can be very different. This results in a different number of coexisting stable periodic solutions in the vicinity of the bifurcation. As a consequence, in one of the models, the Suzuki–Kubo equation, one can effect a discontinuous change in magnetization by adiabatically varying the amplitude of the magnetic field.

On the stability of nonlinear magneto-sonic waves in a collisionless plasma

1975 ◽  
Vol 13 (1) ◽  
pp. 189-191 ◽  
Author(s):  
E. Infeld ◽  
G. Rowlands
Keyword(s):  
Magnetic Field ◽  
Collisionless Plasma ◽  
Nonlinear Function ◽  
Sonic Waves ◽  
The Stability ◽  
Space Dependence ◽  
The Magnetic Field

Demehenko & Hussein (1973) discussed some properties of nonlinear magneto-sonic waves in a collisionless plasma. The relevant equation describing the space dependence x of the magnetic field may be written in the form d2y/dx2+f(y) = 0, (1) where f(y) is a nonlinear function of y only.

Magneto-thermo-elastic plane waves

1965 ◽  
Vol 61 (4) ◽  
pp. 939-944 ◽  
Author(s):  
C. M. Purushothama
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Shear Wave ◽  
Wave Velocity ◽  
Compression Wave ◽  
Thermal Field ◽  
Plane Waves ◽  
Elastic Plane ◽  
Magnetic Diffusivity ◽  
The Magnetic Field

AbstractThe combined effects of uniform thermal and magnetic fields on the propagation of plane waves in a homogeneous, initially unstressed, electrically conducting elastic medium have been investigated.When the magnetic field is parallel to the direction of wave propagation, the compression wave is purely thermo-elastic and the shear wave is purely magneto-elastic in nature. For a transverse magnetic field, the shear waves remain elastic whereas the compression wave assumes magneto-thermo-elastic character due to the coupling of all the three fields—mechanical, magnetic and thermal. In the general case, the waves polarized in the plane of the direction of wave propagation and the magnetic field are not only coupled but are also influenced by the thermal field, once again exhibiting the coupling of the three fields. The shear wave polarized transverse to the plane retains its magneto-elastic character.Notation.Hi = primary magnetic field components,ht = induced magnetic field components,To = initial thermal field,θ = induced thermal field,C = compression wave velocity.S = shear wave velocity,ui = displacement components,cv = specific heat at constant volume,k = thermal conductivity,η = magnetic diffusivity,μe = magnetic permeability,λ, μ = Lamé's constants,β = ratio of coefficient of volume expansion to isothermal compressibility.

scholarly journals Identification of linear slow sausage waves in magnetic pores

2007 ◽  
Vol 3 (S247) ◽  
pp. 351-354 ◽  
Author(s):  
I. Dorotovič ◽  
R. Erdélyi ◽  
V. Karlovský
Keyword(s):  
Magnetic Field ◽  
Gravity Waves ◽  
Morphological Changes ◽  
Average Rate ◽  
Linear Trend ◽  
Solar Interior ◽  
Small Scale ◽  
Temporal Area ◽  
Acoustic Gravity Waves ◽  
The Magnetic Field

AbstractThe analysis of an 11-hour series of high resolution white light observations of a large pore in the sunspot group NOAA 7519, observed on 5 June 1993 with the Swedish Vacuum Solar Telescope at La Palma on Canary Islands, has been recently described by Dorotovičet al. (2002). Special attention was paid to the evolution of a filamentary region attached to the pore, to horizontal motions around the pore, and to small-scale morphological changes. One of the results, relevant to out work here, was the determination of temporal area evolution of the studied pore where the area itself showed a linear trend of decrease with time at an average rate of −0.23 Mm2h−1during the entire observing period. Analysing the time series of the are of the pore, there is strong evidence that coupling between the solar interior and magnetic atmosphere can occur at various scales and that the referred decrease of the area may be connected with a decrease of the magnetic field strength according to the magnetic field-to-size relation. Periods of global acoustic, e.g.p-mode, driven waves are usually in the range of 5–10 minutes, and are favourite candidates for the coupling of interior oscillations with atmospheric dynamics. However, by assuming that magneto-acoustic gravity waves may be there too, and may act as drivers, the observed periodicities (frequencies) are expected to be much longer (smaller), falling well within the mMHz domain. In this work we determine typical periods of such range in the area evolution of the pore using wavelet analysis. The resulted periods are in the range of 20–70 minutes, suggesting that periodic elements of the temporal evolution of the area of this studied pore could be linked to, and considered as, observational evidence of linear low-frequency slow sausage (magneto-acoustic gravity) waves in magnetic pores. This would give us further evidence on the coupling of global solar oscillations to the overlaying magnetic atmosphere.

Memory features of water cyclically treated with magnetic field

2016 ◽  
Vol 13 (2) ◽  
pp. 120-123 ◽  
Author(s):  
Jacob Azoulay
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Pure Water ◽  
Static Field ◽  
Permanent Magnetic Field ◽  
Content Type ◽  
Cyclical Time ◽  
Untreated Water ◽  
The Impact ◽  
The Magnetic Field

Purpose This paper aims to study the properties of cyclically treated pure water in magnetic fields and its comparison with pure untreated water. Design/methodology/approach The magnetic treatment was carried out using a static permanent magnetic field and alternating electromagnetic field. We have measured the magnetic effect on the rising level of the water in capillary tubes and the relaxation time for restoration after removing the magnetic field. The dependence on the magnetic field intensity and on the cyclical time treatments was investigated and discussed. The results of magnetization by static field and electromagnetic field were compared and discussed. It is well known that the clustering structure of hydrogen-bonded chains and polarization effects of water molecules are enhanced after magnetization. Therefore, each experimental series was followed by a “memory” test, the results of which enabled us to have some insights into the molecular and hydrogen bonds of water. Findings It was found that water remembers and keeps the impact of its passing through a magnetic field for several hours and also that many mechanical features were changed under cyclical treatment of a magnetic field.

scholarly journals Reflection of Plane Waves in Generalized Thermoelastic Half Space under the Action of Uniform Magnetic Field

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Narottam Maity ◽  
S. P. Barik ◽  
P. K. Chaudhuri
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Uniform Magnetic Field ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Longitudinal Displacement ◽  
Amplitude Ratios ◽  
Wave Velocities ◽  
Generalized Thermoelastic ◽  
The Magnetic Field

Reflection of longitudinal displacement waves in a generalized thermoelastic half space under the action of uniform magnetic field has been investigated. The magnetic field is applied in such a direction that the problem can be considered as a two-dimensional one. The discussion is based on the three theories of generalized thermoelasticity: Lord-Shulman (L-S), Green-Lindsay (G-L), and Green-Naghdi (G-N) with energy dissipation. We compute the possible wave velocities for different models. Amplitude ratios have been presented. The effects of magnetic field on various subjects of interest are discussed and shown graphically.

THE MAGNETIC FIELD AT THE SURFACE OF A STRATIFIED FLAT CONDUCTOR IN THE FIELD OF PLANE WAVES WITH APPLICATION TO GEOPHYSICS

1962 ◽  
Vol 40 (11) ◽  
pp. 1583-1592 ◽  
Author(s):  
H. W. Dosso
Keyword(s):  
Magnetic Field ◽  
Surface Layer ◽  
Electromagnetic Waves ◽  
Plane Waves ◽  
Geomagnetic Variations ◽  
Wide Range ◽  
The Magnetic Field

The problem of plane electromagnetic waves incident on a stratified flat conductor is considered. Expressions for the amplitude and phase of the components of the resultant magnetic field at the surface of the conductor are obtained and evaluated for a wide range of frequencies, conductivities, surface layer depths, and angles of incidence. The frequencies f = 10−3 to 103 cycles/sec and the conductivities σ = 10−11 to 10−16 emu considered are of interest in studying geomagnetic variations.

Electromagneto-Thermoelastic Plane Waves in Solids With Thermal Relaxation

1972 ◽  
Vol 39 (1) ◽  
pp. 108-113 ◽  
Author(s):  
A. H. Nayfeh ◽  
S. Nemat-Nasser
Keyword(s):  
Magnetic Field ◽  
Relaxation Time ◽  
Thermal Field ◽  
Plane Waves ◽  
Electric Displacement ◽  
Thermal Relaxation ◽  
Displacement Current ◽  
Perturbation Techniques ◽  
Thermoelastic Waves ◽  
The Magnetic Field

Perturbation techniques are used to study the influence of small thermoelastic and magnetoelastic couplings on the propagation of plane electromagneto-thermoelastic waves in an unbounded isotropic medium. The thermal relaxation time of heat conduction, and the electric displacement current are included in the analysis. It is found that the thermal field may affect transverse motions, and that the magnetic field may affect motions that occur parallel to its line of action.

scholarly journals Three-dimensional simulation of the electromagnetic ion/ion beam instability: cross field diffusion

2000 ◽  
Vol 7 (3/4) ◽  
pp. 167-172 ◽  
Author(s):  
H. Kucharek ◽  
M. Scholder ◽  
A. P. Matthews
Keyword(s):  
Magnetic Field ◽  
Diffusion Coefficient ◽  
Ion Beam ◽  
Three Dimensional ◽  
Spatial Dimension ◽  
Static Field ◽  
Beam Instability ◽  
Field Diffusion ◽  
The Cross ◽  
The Magnetic Field

Abstract. In a system with at least one ignorable spatial dimension charged particles moving in fluctuating fields are tied to the magnetic field lines. Thus, in one-and two-dimensional simulations cross-field diffusion is inhibited and important physics may be lost. We have investigated cross-field diffusion in self-consistent 3-D magnetic turbulence by fully 3-dimensional hybrid simulation (macro-particle ions, massless electron fluid). The turbulence is generated by the electromagnetic ion/ion beam instability. A cold, low density, ion beam with a high velocity stream relative to the background plasma excites the right-hand resonant instability. Such ion beams may be important in the region of the Earth's foreshock. The field turbulence scatters the beam ions parallel as well as perpendicular to the magnetic field. We have determined the parallel and perpendicular diffusion coefficient for the beam ions in the turbulent wave field. The result compares favourably well (within a factor 2) with hard-sphere scattering theory for the cross-field diffusion coefficient. The cross-field diffusion coefficient is larger than that obtained in a static field with a Kolmogorov type spectrum and similar total fluctuation power. This is attributed to the resonant behaviour of the particles in the fluctuating field.

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