scholarly journals Potential vorticity in magnetohydrodynamics

2014 ◽  
Vol 81 (1) ◽  
Author(s):  
G. M. Webb ◽  
R. L. Mace
Keyword(s):  
Magnetic Field ◽  
Potential Vorticity ◽  
Conservation Law ◽  
Conservation Equation ◽  
Symmetry Generator ◽  
Generalized Potential ◽  
General Physical ◽  
Special Case ◽  
The Magnetic Field ◽  
Independent Derivation

A version of Noether's second theorem using Lagrange multipliers is used to investigate fluid relabelling symmetries conservation laws in magnetohydrodynamics (MHD). We obtain a new generalized potential vorticity type conservation equation for MHD which takes into account entropy gradients and the J × B force on the plasma due to the current J and magnetic induction B. This new conservation law for MHD is derived by using Noether's second theorem in conjunction with a class of fluid relabelling symmetries in which the symmetry generator for the Lagrange label transformations is non-parallel to the magnetic field induction in Lagrange label space. This is associated with an Abelian Lie pseudo algebra and a foliated phase space in Lagrange label space. It contains as a special case Ertel's theorem in ideal fluid mechanics. An independent derivation shows that the new conservation law is also valid for more general physical situations.

Die „adiabatische Invarianz“ des magnetischen Bahnmomentes geladener Teilchen

1957 ◽  
Vol 12 (10) ◽  
pp. 844-849 ◽  
Author(s):  
F. Hertweck ◽  
A. Schlüter
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Magnetic Moment ◽  
Relative Rate ◽  
Rate Of Change ◽  
Time Dependent ◽  
Constant Field ◽  
Relative Change ◽  
Special Case ◽  
The Magnetic Field

In einem Magnetfeld ist das magnetische Bahnmoment μ* eines geladenen Teilchens annähernd eine Konstante der Bewegung, wenn das Magnetfeld nur schwach variiert. Für den Spezialfall eines homogenen, zeitabhängigen Magnetfeldes wird gezeigt, daß die relative Änderung in μ* zwischen zwei verschiedenen Zuständen, in denen das Magnetfeld konstant ist, mindestens exponentiell in h/a gegen Null geht. Hierin ist α ein Maß für die relative Feldänderungsgeschwindigkeit und mit h ist die Gyro-Frequenz bezeichnet.The magnetic moment μ of the motion of a charged particle in a magnetic field is an approximate constant of motion in moderately varying magnetic fields. For the special case of a homgeneous time-dependent magnetic field, it is shown that the relative change in μ between two different states of constant field decreases at least exponentially in h/α if α/h tends to zero, where a represents the relative rate of change of the magnetic field and h denotes the gyro-frequency.

Slipping stream instability in anisotropic plasma with magnetic shear

1968 ◽  
Vol 2 (2) ◽  
pp. 181-187 ◽  
Author(s):  
S. S. Rao ◽  
G. L. Kalra ◽  
S. P. Talwar
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Tangential Velocity ◽  
Anisotropic Plasma ◽  
The Other ◽  
Magnetic Shear ◽  
Velocity Discontinuity ◽  
Special Case ◽  
The Magnetic Field ◽  
Stream Instability

Starting with the Chew, Goldberger & Low equations, an analysis is made of instability arising due to a tangential velocity discontinuity in a dilute plasma. The velocities on either side are parallel but oppositely directed. Two cases are considered: (i) the magnetic field is uniform and everywhere transverse to the motion, and (ii) the magnetic field vectors on either side are orthogonal, being parallel to the motion on one side and perpendicular on the other. The conditions for instability are obtained and it is found that the effect of magnetic field is destabilizing in both cases. The effect of orthogonality of magnetic fields on the conventional fire-hose instability for a uniform, static plasma is also discussed as special case.

Time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of n line currents

1968 ◽  
Vol 2 (2) ◽  
pp. 189-195
Author(s):  
D. N. Burghes ◽  
R. C. Hewson-Browne
Keyword(s):  
Magnetic Field ◽  
General Problem ◽  
Time Dependent ◽  
Special Case ◽  
The Magnetic Field

Time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of n line currents are considered. The general problem is formulated and solved in the case of an initially flat-faced cloud of flux approaching and passing the magnetic field of n line currents. The special case of a line dipole is analysed in some detail.

Axialsymmetrische magnetohydrodynamische Gleichgewichtskonfigurationen

1957 ◽  
Vol 12 (10) ◽  
pp. 850-854 ◽  
Author(s):  
R. Lüst ◽  
A. Schlüter
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Axial Symmetry ◽  
Hydrostatic Equilibrium ◽  
Gas Pressure ◽  
The Stability ◽  
Special Case ◽  
The Magnetic Field ◽  
Lines Of Force

Es werden die Bedingungen für magnetohydrodynamische Gleichgewichtskonfigurationen mit axialer Symmetrie untersucht. Das Magnetfeld wird aufgeteilt in seine meridionalen und seine toroidalen Anteile, welche durch skalare Funktionen F bzw. T beschrieben werden. Es wird gezeigt, daß der Gasdruck p und die Funktionen F und T Funktionen voneinander sein müssen. Wenn man über die Funktionen p (F) und T (F) verfügt, bekommt man eine Differentialgleichung für F. Die Fälle, in denen diese Differentialgleichung linear ist, werden betrachtet und die Differentialgleichung explizit gelöst, wenn T (F) =const ist. In einem Spezialfall werden die magnetischen Feldlinien numerisch berechnet und in einer Abbildung angegeben. Schließlich werden noch einige Bemerkungen über die Stabilität solcher Felder angefügt.The conditions for magneto-hydrostatic equilibrium are studied in the case of axial symmetry. The magnetic field is divided into its meridional and its toroidal parts which are described by the scalar functions F and T respectively. It is shown that the gas pressure p and the functions F and T have to be functions of each other. Taking in particular p(F) and T (F) as known relations, a differential equation for F is derived. The cases in which this differential equation is linear are considered and explicitly solved if furthermore T(F) = const. In a special case, the magnetic lines of force are calculated numerically and shown in a figure. Some remarks on the stability are added.

scholarly journals Charged particle dynamics near an X-point of a non-symmetric magnetic field with closed field lines

2020 ◽  
Vol 86 (2) ◽  
Author(s):  
Elena Elbarmi ◽  
Wrick Sengupta ◽  
Harold Weitzner
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Magnetic Fields ◽  
Particle Dynamics ◽  
Closed Field ◽  
Symmetric Vacuum ◽  
Field Lines ◽  
Particle Confinement ◽  
Special Case ◽  
The Magnetic Field

Understanding particle drifts in a non-symmetric magnetic field is of primary interest in designing optimized stellarators in order to minimize the neoclassical radial loss of particles. Quasisymmetry and omnigeneity, two distinct properties proposed to ensure radial localization of collisionless trapped particles in stellarators, have been explored almost exclusively for magnetic fields with nested flux surfaces. In this work, we examine radial particle confinement when all field lines are closed. We then study charged particle dynamics in the special case of a non-symmetric vacuum magnetic field with closed field lines obtained recently by Weitzner & Sengupta (Phys. Plasmas, vol. 27, 2020, 022509). These magnetic fields can be used to construct magnetohydrodynamic equilibria for low pressure. Expanding in the amplitude of the non-symmetric fields, we explicitly evaluate the omnigeneity and quasisymmetry constraints. We show that the magnetic field is omnigeneous in the sense that the drift surfaces coincide with the pressure surfaces. However, it is not quasisymmetric according to the standard definitions.

scholarly journals Mode Coupling in the Solar Corona. III. Alfvén and Magnetoacoustic Waves

1977 ◽  
Vol 30 (4) ◽  
pp. 495 ◽  
Author(s):  
DB Melrose
Keyword(s):  
Magnetic Field ◽  
Solar Corona ◽  
Acoustic Waves ◽  
Mode Coupling ◽  
Stratified Medium ◽  
Magnetoacoustic Waves ◽  
Field Lines ◽  
Hydromagnetic Waves ◽  
Special Case ◽  
The Magnetic Field

Coupling between Alfven waves and fast mode waves obliquely incident on a stratified medium is treated using the method of Clemmow and Heading (1954) within the framework of the cold plasma approximation. A result due to Frisch (1964) is rederived in the special case of vertical incidence. The coupling is strongest for nearly parallel (to the magnetic field lines) propagation, and the coupling ratio may be approximated by Q = (00 /0)" where 0 is the angle between the wave vector and the magnetic field lines, while og = A/L, with A the wavelength and L the scalelength of the inhomogeneity. This result may be of significance in connection with the heating of the solar corona by the dissipation of waves generated initially as acoustic waves in the photosphere, and perhaps with the propagation of hydromagnetic waves in the interplanetary medium.

Observing the galactic magnetic field

1967 ◽  
Vol 31 ◽  
pp. 375-380
Author(s):  
H. C. van de Hulst
Keyword(s):  
Magnetic Field ◽  
Fair Agreement ◽  
Solar Neighbourhood ◽  
Galactic Magnetic Field ◽  
The Magnetic Field

Various methods of observing the galactic magnetic field are reviewed, and their results summarized. There is fair agreement about the direction of the magnetic field in the solar neighbourhood:l= 50° to 80°; the strength of the field in the disk is of the order of 10-5gauss.

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.

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.

On the Configuration of the Magnetic Field of β CrB

1976 ◽  
Vol 32 ◽  
pp. 613-622
Author(s):  
I.A. Aslanov ◽  
Yu.S. Rustamov
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Radial Velocity ◽  
Magnetic Field Strength ◽  
Complex Shape ◽  
Rotation Period ◽  
Field Variation ◽  
Magnetic Field Variation ◽  
Secular Variations ◽  
The Magnetic Field

SummaryMeasurements of the radial velocities and magnetic field strength of β CrB were carried out. It is shown that there is a variability with the rotation period different for various elements. The curve of the magnetic field variation measured from lines of 5 different elements: FeI, CrI, CrII, TiII, ScII and CaI has a complex shape specific for each element. This may be due to the presence of magnetic spots on the stellar surface. A comparison with the radial velocity curves suggests the presence of a least 4 spots of Ti and Cr coinciding with magnetic spots. A change of the magnetic field with optical depth is shown. The curve of the Heffvariation with the rotation period is given. A possibility of secular variations of the magnetic field is shown.

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