scholarly journals A Velocity Profile of a Ferrofluid in the Presence of Rotating Magnetic Fields. Pseudo-Analytical and Numerical Solutions

2020 ◽  
pp. 1-6
Author(s):  
Rodrigo Correa ◽  
Cristian Jimenez ◽  
Hermann Vargas
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Linear Model ◽  
Numerical Solutions ◽  
Velocity Profiles ◽  
Analytical Models ◽  
Parallel Plates ◽  
Rotating Magnetic Fields ◽  
Analytical Strategy ◽  
The Magnetic Field

From the beginning of ferro-hydrodynamics, several authors have proposed analytical models to describe the movement of ferrofluids in the presence of rotating external magnetic fields. To this effect they have made valid simplifications in certain and very restricted physical situations. In this work we analyze the effects of these approaches against numerical solutions that do not make use of them. A sample of ferrofluid immersed in containers with three types of geometries was considered: one of flat and parallel plates, one cylindrical and another coaxial cylindrical. Velocity ​​profiles were obtained by these two strategies. The analytical solution leads to a linear model with several simplifications, while the second, numerical in nature, generates a non-linear model, but without approximations. The simulation results showed that the simplifications made in the analytical strategy generate profiles that are valid only for magnetic field intensities lower than the respective ferrofluid saturation values. Additionally, and given the level of development of analytical modeling, it was found that the numerical solution is currently the most appropriate to evaluate the ferro-hydrodynamic model, since it does not have restrictions related to the intensity of the magnetic field. In the same way, it allows to evidence the phenomenon of saturation in the velocity profiles by increasing the intensity of the magnetic field, a situation observed experimentally, and unpredictable by means of these currently available pseudo-analytical solutions.

scholarly journals Nonlinear force-free modeling of magnetic fields in flare-productive active regions

2015 ◽  
Vol 11 (S320) ◽  
pp. 167-174
Author(s):  
M. S. Wheatland ◽  
S. A. Gilchrist
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Boundary Data ◽  
Numerical Solutions ◽  
Free Field ◽  
Active Regions ◽  
Coronal Magnetic Field ◽  
Nonlinear Force ◽  
The Magnetic Field ◽  
Force Free Field

AbstractWe review nonlinear force-free field (NLFFF) modeling of magnetic fields in active regions. The NLFFF model (in which the electric current density is parallel to the magnetic field) is often adopted to describe the coronal magnetic field, and numerical solutions to the model are constructed based on photospheric vector magnetogram boundary data. Comparative tests of NLFFF codes on sets of boundary data have revealed significant problems, in particular associated with the inconsistency of the model and the data. Nevertheless NLFFF modeling is often applied, in particular to flare-productive active regions. We examine the results, and discuss their reliability.

Rheology and Behavior of Magnetic Fluids in Alternating/Rotating Magnetic Fields

2003 ◽  
Author(s):  
Carlos Rinaldi ◽  
Xiaowei He ◽  
Adam Rosenthal ◽  
Thomas Franklin ◽  
Cory Lorenz ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Fluids ◽  
Rotating Magnetic Fields ◽  
Magnetic Field Rotation ◽  
Three Phase ◽  
Field Rotation ◽  
And Behavior ◽  
The Magnetic Field ◽  
Cylindrical Test

The rheology and behavior of magnetic fluids in the presence of time-varying magnetic fields is illustrated through three sets of experiments. The first involves measurements of ferrofluid torque on a cylindrical spindle under applied uniform rotating magnetic fields. We measure the torque required to restrain a stationary cylindrical test wall in contact with aqueous ferrofluids subjected to the rotating uniform magnetic field generated by a three-phase AC 2-pole motor stator winding. The torque is found to scale linearly with volume, and to be a function of the applied magnetic field amplitude, frequency and direction of rotation. Measurements show that for ferrofluid entirely inside the cylindrical test wall the torque points in the same direction as the magnetic field rotation pseudovector, whereas for ferrofluid entirely outside the cylindrical wall the torque points in the direction opposite to the field rotation pseudovector. The second set of experiments explores the formation of ordered ferrofluid structures in the gap of a Hele-Shaw cell subjected to simultaneous vertical DC and in-plane horizontal rotating magnetic fields. Finally, the third set of experiments illustrates the effect of applied DC fields on the shape of ferrofluid jets and sheets.

scholarly journals Directing the orientational alignment of anisotropic magnetic nanoparticles using dynamic magnetic fields

2015 ◽  
Vol 181 ◽  
pp. 449-461 ◽  
Author(s):  
Daniel Hoffelner ◽  
Matthias Kundt ◽  
Annette M. Schmidt ◽  
Emmanuel Kentzinger ◽  
Philipp Bender ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Electron Microscopy ◽  
Magnetic Properties ◽  
Magnetic Nanoparticles ◽  
Magnetic Fields ◽  
Rotating Magnetic Fields ◽  
X Ray ◽  
X Ray Scattering ◽  
Field Geometry ◽  
The Magnetic Field

The structure-directing influence of static and dynamic, i.e. rotating, magnetic fields on the orientational alignment of spindle-type hematite particles with a high aspect ratio is investigated. Structural characterization using electron microscopy and small-angle X-ray scattering confirms a nearly collinear particle arrangement with orientation of the main particle axis either parallel or perpendicular to the substrate as directed by the magnetic field geometry. The combination of large structural and magnetocrystalline anisotropies results in significantly different, strongly anisotropic magnetic properties of the assemblies revealed by directional magnetization measurements.

Numerical solutions of the kinematic dynamo problem

1973 ◽  
Vol 274 (1241) ◽  
pp. 493-521 ◽  
Keyword(s):  
Magnetic Field ◽  
Numerical Solutions ◽  
Expansion Method ◽  
Magnetic Reynolds Number ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Rotating Magnetic Fields ◽  
Induction Equation ◽  
Steady Solutions ◽  
The Magnetic Field

The expansion method of Bullard & Gellman is used to find numerical solutions of the induction equation in a sphere of conducting fluid. Modifications are made to the numerical methods, and one change due to G. O. Roberts greatly increases the efficiency of the scheme. Calculations performed recently by Lilley are re-examined. His solutions, which appeared to be convergent, are shown to diverge when a higher level of truncation is used. Other similar dynamo models are investigated and it is found that these also do not provide satisfactory steady solutions for the magnetic field. Axially symmetric motions which depend on spherical harmonics of degree n are examined. Growing solutions, varying with longitude, 0, as e1^, are found for the magnetic field, and numerical convergence of the solutions is established. The field is predominantly an equatorial dipole with a toroidal field symmetric about the same axis. When n is large the problem lends itself to a two-scale analysis. Comparisons are made between the approximate results of the two-scale method and the numerical results. There is agreement when n is large. When n is small the efficiency of the dynamo is lowered. It is shown that the dominant effect of a large microscale magnetic Reynolds number is the expulsion of magnetic flux by eddies to give a rope-like structure for part of the field. Physical interpretations are given which explain the dynamo action of these motions, and of related flows which support rotating magnetic fields.

Emergence of Twisted Magnetic Flux Related Sigmoidal Brightening

2000 ◽  
Vol 179 ◽  
pp. 263-264
Author(s):  
K. Sundara Raman ◽  
K. B. Ramesh ◽  
R. Selvendran ◽  
P. S. M. Aleem ◽  
K. M. Hiremath
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Flux ◽  
Ultra Violet ◽  
Active Regions ◽  
Morphological Properties ◽  
Energy Storage And Conversion ◽  
The Sun ◽  
X Rays ◽  
The Magnetic Field

Extended AbstractWe have examined the morphological properties of a sigmoid associated with an SXR (soft X-ray) flare. The sigmoid is cospatial with the EUV (extreme ultra violet) images and in the optical part lies along an S-shaped Hαfilament. The photoheliogram shows flux emergence within an existingδtype sunspot which has caused the rotation of the umbrae giving rise to the sigmoidal brightening.It is now widely accepted that flares derive their energy from the magnetic fields of the active regions and coronal levels are considered to be the flare sites. But still a satisfactory understanding of the flare processes has not been achieved because of the difficulties encountered to predict and estimate the probability of flare eruptions. The convection flows and vortices below the photosphere transport and concentrate magnetic field, which subsequently appear as active regions in the photosphere (Rust & Kumar 1994 and the references therein). Successive emergence of magnetic flux, twist the field, creating flare productive magnetic shear and has been studied by many authors (Sundara Ramanet al.1998 and the references therein). Hence, it is considered that the flare is powered by the energy stored in the twisted magnetic flux tubes (Kurokawa 1996 and the references therein). Rust & Kumar (1996) named the S-shaped bright coronal loops that appear in soft X-rays as ‘Sigmoids’ and concluded that this S-shaped distortion is due to the twist developed in the magnetic field lines. These transient sigmoidal features tell a great deal about unstable coronal magnetic fields, as these regions are more likely to be eruptive (Canfieldet al.1999). As the magnetic fields of the active regions are deep rooted in the Sun, the twist developed in the subphotospheric flux tube penetrates the photosphere and extends in to the corona. Thus, it is essentially favourable for the subphotospheric twist to unwind the twist and transmit it through the photosphere to the corona. Therefore, it becomes essential to make complete observational descriptions of a flare from the magnetic field changes that are taking place in different atmospheric levels of the Sun, to pin down the energy storage and conversion process that trigger the flare phenomena.

scholarly journals An 84-μG Magnetic Field in a Galaxy at Z=0.692?

2008 ◽  
Vol 4 (S254) ◽  
pp. 95-96
Author(s):  
Arthur M. Wolfe ◽  
Regina A. Jorgenson ◽  
Timothy Robishaw ◽  
Carl Heiles ◽  
Jason X. Prochaska
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Faraday Rotation ◽  
Large Scale ◽  
Dynamo Model ◽  
Magnetic Field Generation ◽  
Interstellar Gas ◽  
Splitting Technique ◽  
Average Value ◽  
The Magnetic Field

AbstractThe magnetic field pervading our Galaxy is a crucial constituent of the interstellar medium: it mediates the dynamics of interstellar clouds, the energy density of cosmic rays, and the formation of stars (Beck 2005). The field associated with ionized interstellar gas has been determined through observations of pulsars in our Galaxy. Radio-frequency measurements of pulse dispersion and the rotation of the plane of linear polarization, i.e., Faraday rotation, yield an average value B ≈ 3 μG (Han et al. 2006). The possible detection of Faraday rotation of linearly polarized photons emitted by high-redshift quasars (Kronberg et al. 2008) suggests similar magnetic fields are present in foreground galaxies with redshifts z > 1. As Faraday rotation alone, however, determines neither the magnitude nor the redshift of the magnetic field, the strength of galactic magnetic fields at redshifts z > 0 remains uncertain.Here we report a measurement of a magnetic field of B ≈ 84 μG in a galaxy at z =0.692, using the same Zeeman-splitting technique that revealed an average value of B = 6 μG in the neutral interstellar gas of our Galaxy (Heiles et al. 2004). This is unexpected, as the leading theory of magnetic field generation, the mean-field dynamo model, predicts large-scale magnetic fields to be weaker in the past, rather than stronger (Parker 1970).The full text of this paper was published in Nature (Wolfe et al. 2008).

Magnetic Field Spectroheliograms from the San Fernando Observatory

1971 ◽  
Vol 43 ◽  
pp. 329-339 ◽  
Author(s):  
Dale Vrabec
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Spiral Structure ◽  
Longitudinal Component ◽  
Solar Telescope ◽  
Solar Magnetic Fields ◽  
San Fernando ◽  
Field Lines ◽  
The Magnetic Field ◽  
Field Network

Zeeman spectroheliograms of photospheric magnetic fields (longitudinal component) in the CaI 6102.7 Å line are being obtained with the new 61-cm vacuum solar telescope and spectroheliograph, using the Leighton technique. The structure of the magnetic field network appears identical to the bright photospheric network visible in the cores of many Fraunhofer lines and in CN spectroheliograms, with the exception that polarities are distinguished. This supports the evolving concept that solar magnetic fields outside of sunspots exist in small concentrations of essentially vertically oriented field, roughly clumped to form a network imbedded in the otherwise field-free photosphere. A timelapse spectroheliogram movie sequence spanning 6 hr revealed changes in the magnetic fields, including a systematic outward streaming of small magnetic knots of both polarities within annular areas surrounding several sunspots. The photospheric magnetic fields and a series of filtergrams taken at various wavelengths in the Hα profile starting in the far wing are intercompared in an effort to demonstrate that the dark strands of arch filament systems (AFS) and fibrils map magnetic field lines in the chromosphere. An example of an active region in which the magnetic fields assume a distinct spiral structure is presented.

scholarly journals No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

Data ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Evgeny Mikhailov ◽  
Daniela Boneva ◽  
Maria Pashentseva
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Large Scale ◽  
Point Of View ◽  
Accretion Discs ◽  
Wide Range ◽  
Astrophysical Objects ◽  
Alpha Effect ◽  
The Stability ◽  
The Magnetic Field

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

scholarly journals The Origin and Dynamical Effects of the Magnetic Fields and Cosmic Rays in the Disk of the Galaxy

1970 ◽  
Vol 39 ◽  
pp. 168-183
Author(s):  
E. N. Parker
Keyword(s):  
Magnetic Field ◽  
Cosmic Rays ◽  
Magnetic Fields ◽  
Dynamical Behavior ◽  
Cosmic Ray ◽  
Interested Reader ◽  
Written Text ◽  
The Galaxy ◽  
Basic Ideas ◽  
The Magnetic Field

The topic of this presentation is the origin and dynamical behavior of the magnetic field and cosmic-ray gas in the disk of the Galaxy. In the space available I can do no more than mention the ideas that have been developed, with but little explanation and discussion. To make up for this inadequacy I have tried to give a complete list of references in the written text, so that the interested reader can pursue the points in depth (in particular see the review articles Parker, 1968a, 1969a, 1970). My purpose here is twofold, to outline for you the calculations and ideas that have developed thus far, and to indicate the uncertainties that remain. The basic ideas are sound, I think, but, when we come to the details, there are so many theoretical alternatives that need yet to be explored and so much that is not yet made clear by observations.

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