A Three-Function Variational Principle for Stationary Nonbarotropic Magnetohydrodynamics

The current paper is devoted to the introduction of simpler Eulerian variational principles from which all the relevant equations of non-barotropic stationary magnetohydrodynamics can be derived for magnetic fields which lie on surfaces. A variational principle is given in terms of three independent variables for stationary non-barotropic magnetohydrodynamic flows. This is a smaller number of variables than the eight variables which appear in the standard equations of non-barotropic magnetohydrodynamics which are the magnetic field, the velocity field, the specific entropy and the density. We further investigate the case in which the flow along magnetic lines is not ideal.

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Simplified variational principles for non-barotropic magnetohydrodynamics

Journal of Plasma Physics ◽

10.1017/s0022377816000222 ◽

2016 ◽

Vol 82 (2) ◽

Cited By ~ 12

Author(s):

Asher Yahalom

Keyword(s):

Magnetic Field ◽

Variational Principle ◽

Velocity Field ◽

Variational Principles ◽

Independent Functions ◽

The Magnetic Field

Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of non-barotropic magnetohydrodynamics can be derived for certain field topologies. The variational principle is given in terms of five independent functions for non-stationary barotropic flows. This is less than the eight variables which appear in the standard equations of barotropic magnetohydrodynamics which are the magnetic field $\boldsymbol{B}$ the velocity field $\boldsymbol{v}$, the entropy $s$ and the density ${\it\rho}$.

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Magnetic fields in massive spirals: The role of feedback and initial conditions

Astronomy and Astrophysics ◽

10.1051/0004-6361/201834153 ◽

2018 ◽

Vol 619 ◽

pp. L5 ◽

Cited By ~ 2

Author(s):

Evangelia Ntormousi

Keyword(s):

Magnetic Field ◽

Velocity Field ◽

Magnetic Fields ◽

Field Component ◽

Initial Conditions ◽

Magnetic Field Component ◽

Stellar Feedback ◽

Random Magnetic Field ◽

Supernova Feedback ◽

The Magnetic Field

Context. Magnetic fields play a very important role in the evolution of galaxies through their direct impact on star formation and stellar feedback-induced turbulence. However, their co-evolution with these processes has still not been thoroughly investigated, and the possible effect of the initial conditions is largely unknown. Aims. This Letter presents the first results from a series of high-resolution numerical models, aimed at deciphering the effect of the initial conditions and of stellar feedback on the evolution of the galactic magnetic field in isolated Milky Way-like galaxies. Methods. The models start with an ordered magnetic field of varying strength, either poloidal or toroidal, and are evolved with and without supernova feedback. They include a dark matter halo, a stellar and a gaseous disk, as well as the appropriate cooling and heating processes for the interstellar medium. Results. Independently of the initial conditions, the galaxies develop a turbulent velocity field and a random magnetic field component in under 15 Myr. Supernova feedback is extremely efficient in building a random magnetic field component up to large galactic heights. However, a random magnetic field emerges even in runs without feedback, which points to an inherent instability of the ordered component. Conclusions. Supernova feedback greatly affects the velocity field of the galaxy up to large galactic heights, and helps restructure the magnetic field up to 10 kpc above the disk, independently of the initial magnetic field morphology. On the other hand, the initial morphology of the magnetic field can accelerate the development of a random component at large heights. These effects have important implications for the study of the magnetic field evolution in galaxy simulations.

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Magnetic fields and the dynamics of molecular clouds

Symposium - International Astronomical Union ◽

10.1017/s0074180900239429 ◽

1991 ◽

Vol 147 ◽

pp. 75-81

Author(s):

J. L. Puget

Keyword(s):

Magnetic Field ◽

Star Formation ◽

Velocity Field ◽

Magnetic Fields ◽

Molecular Clouds ◽

Velocity Dispersion ◽

Small Scale ◽

Transverse Waves ◽

Analytical Approximations ◽

The Magnetic Field

Magnetic fields are believed to play an important role in the star formation process. Correlations in the velocity field in molecular filaments are indicative of dynamical interactions between clouds and parts within a cloud. The magnetic field is a likely candidate as the vector of such interactions. Perturbations of the field at large scales can feed the velocity dispersion within condensations at small scale. This mechanism is discussed in the framework of two simple analytical approximations describing transverse waves fed into plane parallel slabs.

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Simplified variational principles for barotropic magnetohydrodynamics

Journal of Fluid Mechanics ◽

10.1017/s0022112008002024 ◽

2008 ◽

Vol 607 ◽

pp. 235-265 ◽

Cited By ~ 18

Author(s):

ASHER YAHALOM ◽

DONALD LYNDEN-BELL

Keyword(s):

Magnetic Field ◽

Variational Principle ◽

Variational Principles ◽

Hamiltonian Formalism ◽

Lagrangian Formalism ◽

Independent Functions ◽

Present Formalism ◽

Branch Cuts ◽

Dynamic Variables ◽

The Magnetic Field

Variational principles for magnetohydrodynamics have been introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of barotropic magnetohydrodynamics can be derived. The variational principle is given in terms of six independent functions for non-stationary barotropic flows with trivial topologies and three independent functions for stationary barotropic flows. This is less than the seven variables which appear in the standard equations of barotropic magnetohydrodynamics, which are the magnetic field B the velocity field v and the density ρ.For non-trivial topologies it is necessary to assume that some of the variables introduced in the non-stationary formalism are non-single-valued. That is, it is necessary to introduce a number of branch cuts in order to define single-valued branches of the field variables. In turn, these cuts along with the six field variables constitute an extended number of dynamic variables. The number of cuts necessary depends on the flow. The relations between barotropic magnetohydrodynamics topological constants and the functions of the present formalism will be elucidated.The equations obtained for non-stationary barotropic magnetohydrodynamics resemble the equations of Frenkel et al. (Phys. Lett. A, vol. 88, 1982, p. 461). The connection between the Hamiltonian formalism introduced in Frenkel et al. (1982) and the present Lagrangian formalism (with Eulerian variables) will be discussed.

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Magnetic fields and the dynamics of molecular clouds

Symposium - International Astronomical Union ◽

10.1017/s0074180900198808 ◽

1991 ◽

Vol 147 ◽

pp. 75-81

Author(s):

J. L. Puget

Keyword(s):

Magnetic Field ◽

Star Formation ◽

Velocity Field ◽

Magnetic Fields ◽

Molecular Clouds ◽

Velocity Dispersion ◽

Small Scale ◽

Transverse Waves ◽

Analytical Approximations ◽

The Magnetic Field

Magnetic fields are believed to play an important role in the star formation process. Correlations in the velocity field in molecular filaments are indicative of dynamical interactions between clouds and parts within a cloud. The magnetic field is a likely candidate as the vector of such interactions. Perturbations of the field at large scales can feed the velocity dispersion within condensations at small scale. This mechanism is discussed in the framework of two simple analytical approximations describing transverse waves fed into plane parallel slabs.

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Emergence of Twisted Magnetic Flux Related Sigmoidal Brightening

International Astronomical Union Colloquium ◽

10.1017/s0252921100064630 ◽

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.

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PFG NMR measurements of flow through porous media: effects of spatial correlations of the magnetic field and the velocity field

Journal of Magnetic Resonance ◽

10.1016/s1090-7807(02)00022-8 ◽

2002 ◽

Author(s):

L Lebon

Keyword(s):

Magnetic Field ◽

Porous Media ◽

Velocity Field ◽

Media Effects ◽

Flow Through Porous Media ◽

Spatial Correlations ◽

Flow Through ◽

Pfg Nmr ◽

The Magnetic Field

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

Proceedings of the International Astronomical Union ◽

10.1017/s1743921308027439 ◽

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).

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Magnetic Field Spectroheliograms from the San Fernando Observatory

Symposium - International Astronomical Union ◽

10.1017/s0074180900022774 ◽

1971 ◽

Vol 43 ◽

pp. 329-339 ◽

Cited By ~ 30

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.

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