scholarly journals Klein-Gordon equations for toroidal hydromagnetic waves in an axi-symmetric field

2010 ◽  
Vol 28 (3) ◽  
pp. 737-742 ◽  
Author(s):  
J. F. McKenzie ◽  
Q. Hu
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Wave Equations ◽  
Magnetic Field Direction ◽  
Geomagnetic Pulsations ◽  
Eigenvalues And Eigenfunctions ◽  
Hydromagnetic Wave ◽  
Dipole Magnetic Field ◽  
Klein Gordon ◽  
Hydromagnetic Waves

Abstract. In this paper we develop the hydromagnetic wave equations for toroidal Alfvén waves in a background axi-symmetric magnetic field. In the case where spatial variations are directed along the ambient magnetic field direction, the equations can be cast in a Klein-Gordon form in which the adiabatic-geometric amplitude factor of the perturbations varies as √ρL5sin5θ along a magnetic field line (where θ is colatitude and L the L-shell number) and the cut-off frequency, associated with the Klein-Gordon form, displays an astonishing variation with distance along a field line (see Eqs. 35 and 37 of the text), in the case of a dipole magnetic field. We compute the eigenvalues and eigenfunctions for the Earth's dipole field which are relevant to geomagnetic pulsations.

SEASONAL FEATURES OF THE CORRELATION OF THE TOTAL ELECTRON CONTENT AT MAGNETICALLY CONJUGATE POINTS

2021 ◽  
Vol 44 ◽  
pp. 130-132
Author(s):  
A.V. Timchenko ◽  
◽  
F.S. Bessarab ◽  
A.V. Radievsky ◽  
◽  
...  
Keyword(s):  
Magnetic Field ◽  
Solar Activity ◽  
Field Line ◽  
Correlation Coefficient ◽  
Total Electron Content ◽  
Electron Content ◽  
Geomagnetic Equator ◽  
Total Electron ◽  
Dipole Magnetic Field ◽  
Statistical Relationships

The paper presents the results of studies of the seasonal variability of statistical relationships between Magnetoconjugated Points (MCP) of the ionosphere. The analysis is based on the calculation of the correlation coefficients between the variations in the Total Electron Content (TEC) at points located on the same field line of the dipole magnetic field on both sides of the geomagnetic equator. Global TEC maps were used as initial data. For the four seasons of 2009 and 2015, the values of the Pearson’s correlation coefficient between the variations in the Total Electron Content in the MCP were calculated. For two levels of solar activity, we examined the seasonal features of statistical relationships between TEC variations at points located on the same field line of the dipole magnetic field on both sides of the geomagnetic equator. Pearson's correlation coefficient was calculated for the mean daily TEC variations. It was shown in the work that during the period of low solar activity, the correlation between the TEC variations in the MCP regions is weak or absent, except for autumn. In 2015, a significant correlation between magnetoconjugated regions is observed during all seasons, while in winter and summer they are localized at low latitudes and in spring and autumn at high and middle latitudes.

scholarly journals Bound Electron Transitions under the Influence of Electromagnetic Wave in Constant Magnetic Field

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1367
Author(s):  
Vladimir Zhukovsky
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Wave ◽  
Quantum Wells ◽  
Wave Equations ◽  
Gordon Equation ◽  
Classical Equation ◽  
Relativistic Case ◽  
Radiative Transitions ◽  
Klein Gordon ◽  
Klein Gordon Equation

Motion and radiative transitions of an electron in a magnetic field under the influence of an external electromagnetic wave are studied for various confining conditions in semiconductor, graphene, in quantum wells, and relativistic generalization in terms of the Klein–Gordon equation are considered. In particular, the following problems are discussed. The so-called cyclotron resonance, which may appear in graphene, is studied with indication for appearance of the so-called frequency-halving. The problem is solved for two-dimensional massless charged particle, whose gapless nature is protected by sublattice symmetry. The exact classical calculation of this effect is undertaken in the framework of a 2D classical equation for a zero-mass electron. We also find an exact solution of the Schrödinger equation for charge carriers in semiconductors under the influence of an external magnetic field and in the field of electromagnetic wave with an account for their radiative transitions. Solutions of the relativistic Klein–Gordon equation in this configuration of electromagnetic fields are found as a certain generalization of the results obtained for the non-relativistic case. These results may serve as a first step for further efforts to find exact solutions of wave equations for quasiparticles in solid state structures in external fields.

scholarly journals Hydromagnetic waves in a compressed-dipole field via field-aligned Klein–Gordon equations

2016 ◽  
Vol 34 (4) ◽  
pp. 473-484 ◽  
Author(s):  
Jinlei Zheng ◽  
Qiang Hu ◽  
Gary M. Webb ◽  
James F. McKenzie
Keyword(s):  
Magnetic Field ◽  
Amplitude Ratio ◽  
Low Frequency ◽  
Alfven Wave ◽  
Earth’S Magnetosphere ◽  
Background Magnetic Field ◽  
Earth's Magnetosphere ◽  
Klein Gordon ◽  
Field Lines ◽  
Hydromagnetic Waves

Abstract. Hydromagnetic waves, especially those of frequencies in the range of a few millihertz to a few hertz observed in the Earth's magnetosphere, are categorized as ultra low-frequency (ULF) waves or pulsations. They have been extensively studied due to their importance in the interaction with radiation belt particles and in probing the structures of the magnetosphere. We developed an approach to examining the toroidal standing Aflvén waves in a background magnetic field by recasting the wave equation into a Klein–Gordon (KG) form along individual field lines. The eigenvalue solutions to the system are characteristic of a propagation type when the corresponding eigenfrequency is greater than a critical frequency and a decaying type otherwise. We apply the approach to a compressed-dipole magnetic field model of the inner magnetosphere and obtain the spatial profiles of relevant parameters and the spatial wave forms of harmonic oscillations. We further extend the approach to poloidal-mode standing Alfvén waves along field lines. In particular, we present a quantitative comparison with a recent spacecraft observation of a poloidal standing Alfvén wave in the Earth's magnetosphere. Our analysis based on the KG equation yields consistent results which agree with the spacecraft measurements of the wave period and the amplitude ratio between the magnetic field and electric field perturbations.

Evolution of Large-Scale Coronal Structures

1994 ◽  
Vol 144 ◽  
pp. 29-33
Author(s):  
P. Ambrož
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Large Scale ◽  
Coronal Magnetic Field ◽  
Source Surface ◽  
Solar Cycles ◽  
Characteristic Relationship ◽  
The Magnetic Field ◽  
Coronal Structures

AbstractThe large-scale coronal structures observed during the sporadically visible solar eclipses were compared with the numerically extrapolated field-line structures of coronal magnetic field. A characteristic relationship between the observed structures of coronal plasma and the magnetic field line configurations was determined. The long-term evolution of large scale coronal structures inferred from photospheric magnetic observations in the course of 11- and 22-year solar cycles is described.Some known parameters, such as the source surface radius, or coronal rotation rate are discussed and actually interpreted. A relation between the large-scale photospheric magnetic field evolution and the coronal structure rearrangement is demonstrated.

A 3 T superconducting magnet for long-run magnetic Compton-scattering experiments

1998 ◽  
Vol 5 (3) ◽  
pp. 937-939 ◽  
Author(s):  
Nobuhiko Sakai ◽  
Hiroshi Ohkubo ◽  
Yasushi Nakamura
Keyword(s):  
Magnetic Field ◽  
Low Temperature ◽  
Compton Scattering ◽  
Superconducting Magnet ◽  
Field Direction ◽  
Compton Profile ◽  
Magnetic Field Direction ◽  
Long Run ◽  
Radiation Shields ◽  
The Magnetic Field

A 3 T superconducting magnet has been designed and constructed for magnetic Compton-profile (MCP) measurements with the new capabilities that the magnetic field direction can be altered quickly (within 5 s) and liquid-He refill is not required for more than one week. For the latter capability, two refrigerators have been directly attached to the cryostat to maintain the low temperature of the radiation shields and for the recondensation of liquid He. The system has been satisfactorily operated for over one week.

scholarly journals Enhanced X-ray emission arising from laser-plasma confinement by a strong transverse magnetic field

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Evgeny D. Filippov ◽  
Sergey S. Makarov ◽  
Konstantin F. Burdonov ◽  
Weipeng Yao ◽  
Guilhem Revet ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Transverse Magnetic ◽  
Radiative Properties ◽  
Magnetic Field Direction ◽  
Solid Target ◽  
Total Plasma ◽  
Plasma Confinement ◽  
X Ray ◽  
Magnetic Compression ◽  
The Magnetic Field

AbstractWe analyze, using experiments and 3D MHD numerical simulations, the dynamic and radiative properties of a plasma ablated by a laser (1 ns, 10$$^{12}$$ 12 –10$$^{13}$$ 13 W/cm$$^2$$ 2 ) from a solid target as it expands into a homogeneous, strong magnetic field (up to 30 T) that is transverse to its main expansion axis. We find that as early as 2 ns after the start of the expansion, the plasma becomes constrained by the magnetic field. As the magnetic field strength is increased, more plasma is confined close to the target and is heated by magnetic compression. We also observe that after $$\sim 8$$ ∼ 8  ns, the plasma is being overall shaped in a slab, with the plasma being compressed perpendicularly to the magnetic field, and being extended along the magnetic field direction. This dense slab rapidly expands into vacuum; however, it contains only $$\sim 2\%$$ ∼ 2 % of the total plasma. As a result of the higher density and increased heating of the plasma confined against the laser-irradiated solid target, there is a net enhancement of the total X-ray emissivity induced by the magnetization.

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