Axisymmetric global gravitational equilibrium for magnetized, rotating hot plasma

2015 ◽  
Vol 81 (6) ◽  
Author(s):  
Peter J. Catto ◽  
Istvan Pusztai ◽  
Sergei I. Krasheninnikov
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Plasma Density ◽  
Equatorial Plane ◽  
Magnetic Energy ◽  
Plasma Pressure ◽  
Gravitational Energy ◽  
Equilibrium Solutions ◽  
Poloidal Magnetic Field ◽  
Hot Plasma

We present analytic solutions for three-dimensional magnetized axisymmetric equilibria confining rotating hot plasma in a gravitational field. Our up–down symmetric solution to the full Grad–Shafranov equation can exhibit equatorial plane localization of the plasma density and current, resulting in disk equilibria for the plasma density. For very weak magnetic fields and high plasma pressure, we find strongly rotating thin plasma disk gravitational equilibria that satisfy strict Keplerian motion provided the gravitational energy is much larger than the plasma pressure, which must be large compared to the magnetic energy of the poloidal magnetic field. When the rotational energy exceeds the gravitational energy and it is larger than the plasma pressure, diffuse disk equilibrium solutions continue to exist provided the poloidal magnetic energy remains small. For stronger magnetic fields and lower plasma pressure and rotation, we can also find gravitational equilibria with strong localization to the equatorial plane. However, a toroidal magnetic field is almost always necessary to numerically verify these equilibria are valid solutions in the presence of gravity for the cases considered in Catto & Krasheninnikov (J. Plasma Phys., vol. 81, 2015, 105810301). In all cases both analytic and numerical results are presented.

scholarly journals A rotating and magnetized three-dimensional hot plasma equilibrium in a gravitational field

2015 ◽  
Vol 81 (3) ◽  
Author(s):  
Peter J. Catto ◽  
Sergei I. Krasheninnikov
Keyword(s):  
Magnetic Field ◽  
Gravitational Field ◽  
Equatorial Plane ◽  
Three Dimensional ◽  
Rotation Frequency ◽  
High Plasma ◽  
Plasma Pressure ◽  
Hot Plasma ◽  
Field Lines ◽  
Open Magnetic Field

A rotating and magnetized three-dimensional axisymmetric equilibrium for hot plasma confined by a gravitational field is found. The plasma density and current can exhibit strong equatorial plane localization, resulting in disk equilibria with open magnetic field lines. The associated equatorial plane pinching results in magnetic field flaring, implying a strong gravitational squeezing of the plasma carrying ambient magnetic field lines toward the gravitational source. At high plasma pressure, the magnetic field becomes strongly radial outside the disk. The model predicts the rotation frequency bound, the condition for a plasma disk, and the requirement for strong magnetic field flaring.

scholarly journals Are the photospheric sunspots magnetically force-free in nature?

2010 ◽  
Vol 6 (S273) ◽  
pp. 333-337 ◽  
Author(s):  
Sanjiv Kumar Tiwari
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Magnetic Fields ◽  
Magnetic Energy ◽  
Sufficient Conditions ◽  
Field Measurements ◽  
Magnetic Behaviour ◽  
Optical Telescope ◽  
Energy Gradient ◽  
Necessary And Sufficient

AbstractIn a force-free magnetic field, there is no interaction of field and the plasma in the surrounding atmosphere i.e., electric currents are aligned with the magnetic field, giving rise to zero Lorentz force. The computation of many magnetic parameters like magnetic energy, gradient of twist of sunspot magnetic fields (computed from the force-free parameter α), including any kind of extrapolations heavily hinge on the force-free approximation of the photospheric magnetic fields. The force-free magnetic behaviour of the photospheric sunspot fields has been examined by Metcalf et al. (1995) and Moon et al. (2002) ending with inconsistent results. Metcalf et al. (1995) concluded that the photospheric magnetic fields are far from the force-free nature whereas Moon et al. (2002) found the that the photospheric magnetic fields are not so far from the force-free nature as conventionally regarded. The accurate photospheric vector field measurements with high resolution are needed to examine the force-free nature of sunspots. We use high resolution vector magnetograms obtained from the Solar Optical Telescope/Spectro-Polarimeter (SOT/SP) aboard Hinode to inspect the force-free behaviour of the photospheric sunspot magnetic fields. Both the necessary and sufficient conditions for force-freeness are examined by checking global as well as as local nature of sunspot magnetic fields. We find that the sunspot magnetic fields are very close to the force-free approximation, although they are not completely force-free on the photosphere.

scholarly journals Observing and modeling the poloidal and toroidal fields of the solar dynamo

2018 ◽  
Vol 609 ◽  
pp. A56 ◽  
Author(s):  
R. H. Cameron ◽  
T. L. Duvall ◽  
M. Schüssler ◽  
H. Schunker
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Time Lag ◽  
Solar Observatory ◽  
Toroidal Field ◽  
Solar Dynamo ◽  
Dynamo Model ◽  
Flux Emergence ◽  
Poloidal Field ◽  
Poloidal Magnetic Field

Context. The solar dynamo consists of a process that converts poloidal magnetic field to toroidal magnetic field followed by a process that creates new poloidal field from the toroidal field. Aims. Our aim is to observe the poloidal and toroidal fields relevant to the global solar dynamo and to see if their evolution is captured by a Babcock-Leighton dynamo. Methods. We used synoptic maps of the surface radial field from the KPNSO/VT and SOLIS observatories, to construct the poloidal field as a function of time and latitude; we also used full disk images from Wilcox Solar Observatory and SOHO/MDI to infer the longitudinally averaged surface azimuthal field. We show that the latter is consistent with an estimate of the longitudinally averaged surface azimuthal field due to flux emergence and therefore is closely related to the subsurface toroidal field. Results. We present maps of the poloidal and toroidal magnetic fields of the global solar dynamo. The longitude-averaged azimuthal field observed at the surface results from flux emergence. At high latitudes this component follows the radial component of the polar fields with a short time lag of between 1−3 years. The lag increases at lower latitudes. The observed evolution of the poloidal and toroidal magnetic fields is described by the (updated) Babcock-Leighton dynamo model.

scholarly journals Nonlinear equilibrium structure of thin currents sheets: influence of electron pressure anisotropy

2004 ◽  
Vol 11 (5/6) ◽  
pp. 579-587 ◽  
Author(s):  
L. M. Zelenyi ◽  
H. V. Malova ◽  
V. Yu. Popov ◽  
D. Delcourt ◽  
A. S. Sharma
Keyword(s):  
Magnetic Field ◽  
Current Sheet ◽  
Magnetic Energy ◽  
Plasma Pressure ◽  
Quasi Equilibrium ◽  
Electrostatic Effects ◽  
Current Sheets ◽  
Thin Current Sheet ◽  
Field Lines ◽  
The Magnetic Field

Abstract. Thin current sheets represent important and puzzling sites of magnetic energy storage and subsequent fast release. Such structures are observed in planetary magnetospheres, solar atmosphere and are expected to be widespread in nature. The thin current sheet structure resembles a collapsing MHD solution with a plane singularity. Being potential sites of effective energy accumulation, these structures have received a good deal of attention during the last decade, especially after the launch of the multiprobe CLUSTER mission which is capable of resolving their 3D features. Many theoretical models of thin current sheet dynamics, including the well-known current sheet bifurcation, have been developed recently. A self-consistent 1D analytical model of thin current sheets in which the tension of the magnetic field lines is balanced by the ion inertia rather than by the plasma pressure gradients was developed earlier. The influence of the anisotropic electron population and of the corresponding electrostatic field that acts to restore quasi-neutrality of the plasma is taken into account. It is assumed that the electron motion is fluid-like in the direction perpendicular to the magnetic field and fast enough to support quasi-equilibrium Boltzmann distribution along the field lines. Electrostatic effects lead to an interesting feature of the current density profile inside the current sheet, i.e. a narrow sharp peak of electron current in the very center of the sheet due to fast curvature drift of the particles in this region. The corresponding magnetic field profile becomes much steeper near the neutral plane although the total cross-tail current is in all cases dominated by the ion contribution. The dependence of electrostatic effects on the ion to electron temperature ratio, the curvature of the magnetic field lines, and the average electron magnetic moment is also analyzed. The implications of these effects on the fine structure of thin current sheets and their potential impact on substorm dynamics are presented.

scholarly journals The Steady Currents Driven in a Conducting Sphere Placed in a Rotating Magnetic Field

1984 ◽  
Vol 37 (5) ◽  
pp. 521 ◽  
Author(s):  
WN Hugrass ◽  
HA Kirolous
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Equatorial Plane ◽  
Rotating Magnetic Field ◽  
Toroidal Magnetic Field ◽  
Weakly Nonlinear ◽  
Conducting Sphere

The steady currents (and the associated steady magnetic fields) generated in a conducting sphere placed in a rotating magnetic field are calculated in the weakly nonlinear limit. It is found that the steady driven current has a poloidal and a toroidal component. The steady toroidal magnetic field associated with the driven poloidal current has opposite senses above and below the equatorial plane; the net toroidal flux is zero. The relevance of this result to some recent observations in the Rotamak experiment is discussed.

On the spontaneous magnetic field in a conducting liquid in turbulent motion

1950 ◽  
Vol 201 (1066) ◽  
pp. 405-416 ◽  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Energy ◽  
Turbulent Motion ◽  
Small Scale ◽  
Flow Equations ◽  
Metallic Conductor ◽  
Set Up ◽  
The Stability ◽  
The Magnetic Field

Several recent investigations in geophysics and astrophysics have involved a consideration of the hydrodynamics of a fluid which is a good electrical conductor. In this paper one of the problems which seem likely to arise in such investigations is discussed. The fluid is assumed to be incompressible and in homogeneous turbulent motion, and externally imposed electric and magnetic fields are assumed to be absent. The equations governing the interaction of the electromagnetic field and the turbulent motion are set up with the same assumptions as are used to obtain the Maxwell and current flow equations for a metallic conductor. It is shown that the equation for the magnetic field is identical in form with that for the vorticity in a non-conducting fluid; immediate deductions are that lines of magnetic force move with the fluid when the conductivity is infinite, and that the small-scale components of the turbulence have the more powerful effect on the magnetic field. The first question considered is the stability of a purely hydrodynamical system to small disturbing magnetic fields, and it is shown that the magnetic energy of the disturbance will increase provided the conductivity is greater than a critical value determined by the viscosity of the fluid. The rate of growth of magnetic energy is approximately exponential, with a doubling time which can be simply related to the properties of the turbulence. General mechanical considerations suggest that a steady state is reached when the magnetic field has as much energy as is contained in the small-scale components of the turbulence. Estimates of this amount of energy and of the region of the spectrum in which it will lie are given in terms of observable properties of the turbulence.

scholarly journals Tunnel Magnetoresistance of Fe3O4/MgO/Fe Nanostructures

2011 ◽  
Vol 2011 ◽  
pp. 1-3
Author(s):  
S. G. Chigarev ◽  
E. M. Epshtein ◽  
I. V. Malikov ◽  
G. M. Mikhailov ◽  
P. E. Zilberman
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Magnetic Fields ◽  
Tunnel Junction ◽  
Magnetic Energy ◽  
Magnetic Tunnel Junction ◽  
Tunnel Magnetoresistance ◽  
Unidirectional Anisotropy ◽  
Layer Orientation ◽  
Layer Magnetization

A magnetic tunnel junction Fe3O4/MgO/Fe with (001) layer orientation is considered. The junction magnetic energy is analyzed as a function of the angle between the layer magnetization vectors under various magnetic fields. The tunnel magnetoresistance is calculated as a function of the external magnetic field. In contrast with junctions with unidirectional anisotropy, a substantially lower magnetic field is required for the junction switching.

scholarly journals Velocity Shear Instabilities in the Anisotropic Solar Wind

1985 ◽  
Vol 107 ◽  
pp. 371-374
Author(s):  
Stefano Migliuolo
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Solar Wind ◽  
Magnetic Energy ◽  
Equilibrium Temperature ◽  
Acoustic Mode ◽  
Plasma Pressure ◽  
Velocity Shear ◽  
Linear Growth Rate ◽  
Quasilinear Theory

The linear and quasilinear theory of perturbations in finite-β (β is the ratio of plasma pressure to magnetic energy density), collisionless plasmas, that have sheared (velocity) flows, is developed. A simple, one-dimensional magnetic field geometry is assumed to adequately represent solar wind conditions near the sun (i.e., at R ≃ 0.3 AU). Two modes are examined in detail: an ion-acoustic mode (finite-β stabilized) and a compressional Alfven mode (finite-β threshold, high-β stabilization). The role played by equilibrium temperature anisotropies, in the linear stability of these modes, is also presented. From the quasilinear theory, two results are obtained. First, the feedback of these waves on the state of the wind is such as to heat (cool) the ions in the direction perpendicular (parallel) to the equilibrium magnetic field. The opposite effect is found for the electrons. This is in qualitative agreement with the observed anisotropies of ions and electrons, in fast solar wind streams. Second, these quasilinear temperature changes are shown to result in a quasilinear growth rate that is lower than the linear growth rate, suggesting saturation of these instabilities.

scholarly journals Statistics of Radio-X-Ray Emission and Magnetic Fields in the Intergalactic Medium

1990 ◽  
Vol 139 ◽  
pp. 414-415
Author(s):  
Hitoshi Hanami
Keyword(s):  
Magnetic Field ◽  
Cosmic Rays ◽  
Magnetic Fields ◽  
Intergalactic Medium ◽  
Relativistic Electrons ◽  
X Ray ◽  
Cooling Flows ◽  
Hot Plasma ◽  
Inverse Compton ◽  
The Magnetic Field

X-ray observations have demonstrated that the intergalactic medium in many clusters (cf. Coma, Perseus) contains a thin, hot plasma that may be produced by the accretion process in the gravitational potential of clusters with radiative cooling; this is usually called “cooling flows” (Fabian, Nulsen, and Canizares 1984; Sarazin 1986). On the other hand, the existence of radio halos in some clusters has been reported (Coma: Jaffe, Perola, and Valentijn 1976; A401: Roland et al. 1981). In addition, many elliptical galaxies in the center of clusters are also strong synchrotron radio sources. These radio emissions provide evidence for large amounts of relativistic electrons associated with the active phenomena in or around these galaxies and clusters. We can estimate the values or limits on the magnetic field in the cluster from the limits on the inverse Compton X-ray emission with the synchrotron radio emission (cf. Jaffe 1980). The intracluster field strength Bo is roughly 1 μG. It has been suggested that the influence of cosmic rays and magnetic fields is important for the properties and dynamics of the intercluster medium (Böhringer and Morfill 1988; Soker and Sarazin 1989). If cooling flows are real, this inward flow can impede the escape of the cosmic rays from the central galaxies in clusters and enhance the magnetic field. The confinement of the cosmic rays and the magnetic field in the center of clusters affects the gas of the intracluster medium.

scholarly journals Zooming in on the Formation of Protoplanetary Disks

2013 ◽  
Vol 8 (S299) ◽  
pp. 131-135 ◽  
Author(s):  
Åke Nordlund ◽  
Troels Haugbølle ◽  
Michael Küffmeier ◽  
Paolo Padoan ◽  
Aris Vasileiades
Keyword(s):  
Magnetic Field ◽  
Energy Efficient ◽  
Adaptive Mesh Refinement ◽  
Accretion Rate ◽  
Magnetic Energy ◽  
Protoplanetary Disks ◽  
Adaptive Mesh ◽  
Gravitational Energy ◽  
Solar Mass ◽  
The Magnetic Field

AbstractWe use the adaptive mesh refinement code RAMSES to model the formation of protoplanetary disks in realistic star formation environments. The resolution scales over up to 29 powers of two (~ 9 orders of magnitude) covering a range from outer scales of 40 pc to inner scales of 0.015 AU. The accretion rate from a 1.5 solar mass envelope peaks near 10−4 M⊙ about 6 kyr after sink particle formation and then decays approximately exponentially, reaching 10−6 M⊙ in 100 kyr. The models suggest universal scalings of physical properties with radius during the main accretion phase, with kinetic and / or magnetic energy in approximate balance with gravitational energy. Efficient accretion is made possible by the braking action of the magnetic field, which nevertheless allows a near-Keplerian disk to grow to a 100 AU size. The magnetic field strength ranges from more than 10 G at 0.1 AU to less than 1 mG at 100 AU, and drives a time dependent bipolar outflow, with a collimated jet and a broader disk wind.

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