Torsional waves with force-free magnetic fields in solar plasma structures

2021 ◽  
Vol 502 (4) ◽  
pp. 4930-4934
Author(s):  
H Ebadi ◽  
S Shahmorad ◽  
S Vasheghani Farahani
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Magnetic Fields ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Torsional Wave ◽  
Eigenvalues And Eigenfunctions ◽  
Transform Method ◽  
Solar Plasma ◽  
Torsional Waves

ABSTRACT The aim here is to model torsional waves in homogeneous and expanding twisted flux tubes of solar coronal magnetic plasma structures. For the sake of simplicity, a force-free condition applicable to solar magnetic structures is presented to determine the existing three-dimensional equilibrium magnetic fields. The determined magnetic field is implemented to study the effects of the magnetic twist parameter on the eigenvalues and eigenfunctions of torsional waves. Solenoidal and force-free conditions are applied to find the three-dimensional components of the magnetic field with respect to the numerical flux function. The obtained differential equation is linear where the technique of the separation of variables is implemented in order to solve it. The equilibrium magnetic field components and appropriate vector potential are extracted. Using the provided components in the magnetohydrodynamic theory, a differential equation that governs the frequency dependence of the torsional wave is obtained, whereby the differential transform method is solved. Both eigenvalues and eigenfunctions of torsional waves are calculated numerically. The obtained values for the frequency of the fundamental mode and its first harmonic, together with appropriate functions, exhibit a fine consistency with observations, with regards to the ratio of ω2/ω1, which is estimated to be around 2. At a fixed distance from the tube axis, the ratio increases with the increase of the twist parameter. The higher the applied twist parameter, the more variations of the ω2/ω1 ratio are observed. We cannot find significant variations of the eigenfunctions of torsional waves due to the twist parameter. The consistency between analytical results and observations proves adequate for implementing a force-free equilibrium magnetic field subject to conditions in solar plasma structures regarding torsional wave propagation.

scholarly journals Magnetic and Electronic Properties of π-d Interacting Molecular Magnetic Superconductor κ-(BETS)2FeX4 (X = Cl, Br) Studied by Angle-Resolved Heat Capacity Measurements

Crystals ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 66 ◽  
Author(s):  
Shuhei Fukuoka ◽  
Sotarou Fukuchi ◽  
Hiroki Akutsu ◽  
Atsushi Kawamoto ◽  
Yasuhiro Nakazawa
Keyword(s):  
Magnetic Field ◽  
Heat Capacity ◽  
Magnetic Fields ◽  
Temperature Dependence ◽  
Three Dimensional ◽  
Magnetic Interaction ◽  
Spin Configuration ◽  
Magnetic Superconductor ◽  
Heat Capacity Measurements ◽  
Long Range Ordering

Thermodynamic picture induced by π-d interaction in a molecular magnetic superconductor κ-(BETS)2FeX4 (X = Cl, Br), where BETS is bis(ethylenedithio)tetraselenafulvalene, studied by single crystal calorimetry is reviewed. Although the S = 5/2 spins of Fe3+ in the anion layers form a three-dimensional long-range ordering with nearly full entropy of Rln6, a broad hump structure appears in the temperature dependence of the magnetic heat capacity only when the magnetic field is applied parallel to the a axis, which is considered as the magnetic easy axis. The scaling of the temperature dependence of the magnetic heat capacity of the two salts is possible using the parameter of |Jdd|/kB and therefore the origin of the hump structure is related to the direct magnetic interaction, Jdd, that is dominant in the system. Quite unusual crossover from a three-dimensional ordering to a one-dimensional magnet occurs when magnetic fields are applied parallel to the a axis. A notable anisotropic field-direction dependence against the in-plane magnetic field was also observed in the transition temperature of the bulk superconductivity by the angle-resolved heat capacity measurements. We discuss the origin of this in-plane anisotropy in terms of the 3d electron spin configuration change induced by magnetic fields.

Room Temperature Sample Scanning SQUID Microscope for Imaging the Magnetic Fields of Geological Specimens

2013 ◽  
Vol 475-476 ◽  
pp. 3-6 ◽  
Author(s):  
Qing Meng Wang ◽  
Hua Feng Qin ◽  
Qing Song Liu ◽  
Tao Song
Keyword(s):  
Magnetic Field ◽  
Low Temperature ◽  
Magnetic Fields ◽  
Liquid Helium ◽  
Quantum Interference ◽  
Three Dimensional ◽  
Input Circuit ◽  
Pickup Coil ◽  
Weak Magnetic Fields ◽  
Scanning Squid

A microscope to image weak magnetic fields using a low-temperature superconducting quantum interference device (SQUID) had developed with a liquid helium consumption rate of ~0.5L/hour. The gradient pickup coil is made by a low-temperature superconducting niobium wire with a diameter of 66 μm, which is coupled to the input circuit of the SQUID and is then enwound on the sapphire bobbin. Both of the pickup coil and the SQUID sensor are installed in a red copper cold finger, which is thermally anchored to the liquid helium evaporation platform in the vacuum space of the cryostat. To reduce the distance between the pickup coil and sample, a 100 μm thick sapphire window is nestled up to the bottom of the cryostat. A three-dimensional scanning stage platform with a 50 cm Teflon sample rack under the sapphire window had the precision of 10 μm. To test the fidelity of the new facility, the distribution of the magnetic field of basalt slice specimens was determined. Results show that the spatial resolution of the newly-designed facility is 500 μm with a gradient magnetic field sensitivity of 380fT. This opens new opportunities in examining the distribution of magnetic assemblages in samples, which bear great geological and geophysical information.

Shielding from external magnetic fields by rotating magnetic conducting cylindrical shells

2015 ◽  
Vol 34 (2) ◽  
pp. 505-513
Author(s):  
Marcin Ziolkowski ◽  
Stanislaw Gratkowski
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Static Magnetic Field ◽  
Analytical Solutions ◽  
Separation Of Variables ◽  
Shielding Effect ◽  
Magnetic Vector Potential ◽  
Content Type ◽  
Shielding Factor ◽  
Cylindrical Screen

Purpose – In many different engineering fields often there is a need to protect regions from electromagnetic interference. According to static and low-frequency magnetic fields the common strategy bases on using a shield made of conductive or ferromagnetic material. Another screening technique uses solenoids that generate an opposite magnetic field to the external one. The purpose of this paper is to discuss the shielding effect for a magnetic and conducting cylindrical screen rotating in an external static magnetic field. Design/methodology/approach – The magnetic flux density is expressed in terms of the magnetic vector potential. Applying the separation of variables method analytical solutions are obtained for an infinitely long magnetic conducting cylindrical screen rotating in a uniform static transverse magnetic field. Findings – Analytical formulas of the shielding factor for a cylindrical screen of arbitrary conductivity and magnetic permeability are given. A magnetic Reynolds number is found to be an appropriate indication of the change in magnetic field inside the screen. Useful simplified expressions are presented. Originality/value – This paper treats in a qualitative way the possibility of static magnetic field shielding by using rotating conducting magnetic cylindrical screens. Analytical solutions are given. If the angular velocity is equal to zero or the relative permeability of the shield is equal to one the shielding factor has forms well known from literature.

Changes in the Magnetic Fields of Star-Shaped JIS-SKS93 Plates Embedded in Clear Acrylic Cold Mounting Resin under Tensile Stress

2012 ◽  
Vol 457-458 ◽  
pp. 884-890
Author(s):  
Megumi Uryu ◽  
Katsuyuki Kida ◽  
Takashi Honda ◽  
Kenichi Saruwatari ◽  
Edson Costa Santos ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Stress Concentration ◽  
Magnetic Fields ◽  
Three Dimensional ◽  
Steel Specimen ◽  
Acrylic Resin ◽  
Steel Sample ◽  
Hall Probe ◽  
Film Sensor ◽  
The Magnetic Field

Fatigue failure of machine components occurs when cracks form in the stress concentration area and propagate under continued loading during component work. In order to understand the relation between the phenomena of stress concentration and crack propagation, non-destructive evaluation methods using in-situ measurements in the stress concentration areas are necessary. In the present work, a scanning Hall probe microscope (SHPM) equipped with a GaAs film sensor was developed and the three dimensional magnetic fields were observed at room temperature in air. The effect of stress on the changes in the magnetic field in steel components is reported. A steel specimen (JIS SKS93) embedded in acrylic resin were strained at different loads and the magnetic field before and after straining were observed. The obtained magnetic images clearly corresponded with the shape of the steel plate. It was possible to measure the changes in the magnetic field of the steel sample after straining under tensile loading, by neutralizing the initial magnetic field of the specimens prior to testing.

scholarly journals Guiding-centre transformation of the radiation–reaction force in a non-uniform magnetic field

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
E. Hirvijoki ◽  
J. Decker ◽  
A. J. Brizard ◽  
O. Embréus
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Uniform Magnetic Field ◽  
Reaction Force ◽  
Charged Particles ◽  
Collision Operator ◽  
Radiation Reaction ◽  
Transform Method ◽  
Lie Transform ◽  
Radiation Reaction Force

In this paper, we present the guiding-centre transformation of the radiation–reaction force of a classical point charge travelling in a non-uniform magnetic field. The transformation is valid as long as the gyroradius of the charged particles is much smaller than the magnetic field non-uniformity length scale, so that the guiding-centre Lie-transform method is applicable. Elimination of the gyromotion time scale from the radiation–reaction force is obtained with the Poisson-bracket formalism originally introduced by Brizard (Phys. Plasmas, vol. 11, 2004, 4429–4438), where it was used to eliminate the fast gyromotion from the Fokker–Planck collision operator. The formalism presented here is applicable to the motion of charged particles in planetary magnetic fields as well as in magnetic confinement fusion plasmas, where the corresponding so-called synchrotron radiation can be detected. Applications of the guiding-centre radiation–reaction force include tracing of charged particle orbits in complex magnetic fields as well as the kinetic description of plasma when the loss of energy and momentum due to radiation plays an important role, e.g. for runaway-electron dynamics in tokamaks.

On the stability of parallel flows with parallel magnetic fields

1966 ◽  
Vol 293 (1434) ◽  
pp. 342-358 ◽  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Parallel Magnetic Field ◽  
Parallel Flows ◽  
The Mean ◽  
The Stability ◽  
The Magnetic Field ◽  
Parallel Magnetic Fields

The first part of the paper is a physical discussion of the way in which a magnetic field affects the stability of a fluid in motion. Particular emphasis is given to how the magnetic field affects the interaction of the disturbance with the mean motion. The second part is an analysis of the stability of plane parallel flows of fluids with finite viscosity and conductivity under the action of uniform parallel magnetic fields. We show that, in general, three-dimensional disturbances are the most unstable, thus disagreeing with the conclusion of Michael (1953) and Stuart (1954). We show how results obtained for two-dimensional disturbances can be used to calculate the most unstable three-dimensional disturbances and thence we prove that a parallel magnetic field can never completely stabilize a parallel flow.

A numerical study of a bubble pair rising side by side in external magnetic fields

2021 ◽  
Vol 926 ◽  
Author(s):  
Jie Zhang ◽  
Ming-Jiu Ni
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Lorentz Force ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Transverse Field ◽  
Asymmetric Distribution ◽  
Streamwise Vortices ◽  
Horizontal Magnetic Field

The motion of a pair of bubbles rising side by side under the influence of external magnetic fields is numerically examined. Through solving the fully three-dimensional Navier–Stokes equations, the results reveal that the bubble interactions are rather sensitive to the field direction and strength. At first, we identify that, in a hydrodynamic flow, whether the two bubbles will bounce or coalesce depends on the developments of the counter-rotating streamwise vortices during the collision. In particular, for an originally bouncing bubble pair, a streamwise magnetic field tends to promote their coalescence by weakening the strengths of the standing streamwise vortices, and such a weakening effect is caused by the asymmetric distribution of the Lorentz force in the presence of another bubble such that a torque is induced to offset the original streamwise vortices. Under a horizontal magnetic field, on the other hand, the influences are highly dependent on the angle between the bubble centroid line and the field: a transverse field or a moderate spanwise field always leads the bubble pair to coalescence while a strong spanwise field has the opposite effect. This anisotropic effect comes from the Lorentz force induced flow diffusion along the magnetic field, which not only produces two pairs of streamwise vortices at the bubble rear, but also homogenizes the pressure along the magnetic lines. As the competition between the two mechanisms varies with the magnetic direction and strength, the interaction between the bubble pair also changes. We show that the external magnetic fields control the bubble interaction through reconstructing the vortex structures, and hence the core mechanisms are identified.

Liquid-Metal MHD Open-Channel Flows

1984 ◽  
Vol 51 (1) ◽  
pp. 13-18 ◽  
Author(s):  
P. R. Hays ◽  
J. S. Walker
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Magnetic Fields ◽  
Liquid Metal ◽  
Boundary Layers ◽  
Open Channel ◽  
Three Dimensional ◽  
Viscous Effects ◽  
Channel Bottom ◽  
Dimensional Variable

Many metallurgical applications of magnetohydrodynamics (MHD) involve open-channel liquid-metal flows with magnetic fields. This paper treats the three-dimensional, variable-depth flow in a rectangular open channel having an electrically insulating bottom and perfectly conducting sides. A steady, uniform magnetic field is applied perpendicular to the channel bottom. Induced magnetic fields and surface tension effects are neglected, while the applied magnetic field is sufficiently strong that inertial effects are negligible everywhere. Viscous effects are confined to boundary layers adjacent to the bottom, sides, and free surface. Solutions are presented for the inviscid core and the boundary layers. The locations of the free surface above the core and above the boundary layers adjacent to the sides are obtained. The side-layer variables are rescaled into universal profile functions which depend on the coordinates in the channel’s cross section and on a parameter related to the local slopes of the bottom and the free surface. The solutions for the side layers in open channels are compared to the side-layer solutions for certain rectangular closed ducts in order to reveal the effects of the free surface. This comparison leads to a qualitative correspondence principle between open-channel and closed-duct side-layer solutions. The similarities and differences between corresponding open-channel and closed-duct side layers are discussed.

Unsteady Hydromagnetic Boundary Layer in a Rotating Medium

1976 ◽  
Vol 43 (2) ◽  
pp. 205-208 ◽  
Author(s):  
P. Puri ◽  
P. K. Kulshrestha
Keyword(s):  
Magnetic Field ◽  
Porous Plate ◽  
Three Dimensional ◽  
Power Input ◽  
Transverse Magnetic ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Rotating Medium ◽  
The Laplace Transform ◽  
The Magnetic Field

The three-dimensional flow of a viscous fluid in the presence of the transverse magnetic field past an infinite porous plate moving with a time-dependent velocity in a rotating medium is investigated. An exact solution is found by using the Laplace transform method. The order of Stokes, Ekman, and Stokes-Rayleigh layers arising in the problem are derived and the influence of the magnetic field and suction (blowing) is studied. The behavior of the drag and lateral stress on the plate is discussed and the power input required to keep the plate in motion calculated. It is also found that a normal solution exists at the resonant frequency for the problem investigated here.

scholarly journals Study of magnetism cyclicity of the Sun in the framework of the macroscopic magnetohydrodynamics theory

2019 ◽  
pp. 22-32
Author(s):  
V. Krivodubskij
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Lower Half ◽  
Dynamo Model ◽  
The Sun ◽  
Solar Plasma ◽  
Radial Gradient ◽  
Magnetic Buoyancy ◽  
Global Magnetic Field

Since the mid-70s of the last century, a new direction in theoretical studies of the evolution of the global magnetism of the Sun in the framework of macroscopic MHD has been launched at the Astronomical Observatory of the Taras Shevchenko National University of Kyiv. The paper presents the results of a study of the processes of generation and restructuring of a large-scale (global) magnetic field based on the αΩ-dynamo model, taking into account new turbulent effects discovered in the theory of macroscopic MHD and data of helioseismological experiments on the internal rotation of the Sun. It was established that a sharp radial gradient of turbulent velocity in the lower half of the solar convective zone (SCZ) leads to a change in the sign of the azimuthal component of the helicity parameter α, resulting in the formation of a relatively thin layer of negative α-effect near the bottom of the SCZ. It was found that the layer of negative α-effect, together with the sign of the radial gradient of the angular velocity, detected in helioseismological experiments, makes it possible to explain the direction of migration of dynamo-waves on the solar surface. The magnetic saturation of the α-effect (alpha-quenching) in the deep layers of the SCZ was calculated. An explanation of the protracted duration of the 23rd solar cycle of about 13 years is proposed. For this, we used the observed data on a significant increase of the annual module of the magnetic fields of sunspots in the 23rd cycle. The calculated north-south asymmetry of the structure of the global magnetic field provides an opportunity to explain the phenomenon of the seeming magnetic “monopole”, which is observed during reversal of polar magnetism. It was found that the values of turbulent electrical conductivity and turbulent magnetic permeability of the solar plasma are significantly less than the corresponding gas-kinetic parameters. Therefore, the turbulent dissipation of solar magnetic fields is enhanced by 4–9 orders of magnitude compared with classical ohmic dissipation. Macroscopic turbulent diamagnetism of solar plasma was investigated. It has been found that in the lower part of the SCZ, turbulent diamagnetism acts against magnetic buoyancy, thus fulfilling the role of “negative magnetic buoyancy”. As a result of the balance of the effects of magnetic buoyancy and turbulent diamagnetism, a layer of blocked magnetic field of magnitude ≈ 3000 G is formed in the depths of the SCZ. The turbulent advection of a magnetic field in an inhomogeneous plasma density of the SCZ was studied. It was found that in the lower half of the SCZ of the equatorial domain, turbulent advection is directed upwards. As a result of the combined action of magnetic buoyancy and turbulent advection, deep strong toroidal fields are carried to the surface of the Sun in the latitudinal “royal zone” of sunspots. The role of horizontal turbulent diamagnetism in ensuring the long-term stability of sunspots was noted. To explain the observed phenomenon of double maxima of the solar spot cycle, a scenario was developed containing the generation of a magnetic field in the tachocline at the bottom of the SCZ and subsequent removal of this magnetic field from the depth layers to the surface in the latitudinal “royal zone”. The role of the radial omega-effect in the radiant zone in explaining the observed asymmetry in the amplitude of two neighbouring 11-years sunspot cycles was noted.

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