Gravitationsinstabilitäten eines Plasmas bei differentieller Rotation

1967 ◽  
Vol 22 (4) ◽  
pp. 431-437
Author(s):  
R. Ebert
Keyword(s):  
Magnetic Field ◽  
Differential Rotation ◽  
Wave Length ◽  
Critical Value ◽  
Unstable Wave ◽  
Simultaneous Action ◽  
Axially Symmetric ◽  
Gas Density ◽  
Axis Of Rotation ◽  
The Magnetic Field

In this paper an instability calculation is given for an axially symmetric gas distribution which has a differential rotation and in which a magnetic field is present. It is a generalization of similar calculations given by CHANDRASEKHAR and BEL and SCHATZMAN. The generalization becomes necessary for the study of problems of the formation of planetary systems, and star formation.The instability conditions and the critical wave lengths are calculated for plane-wave-like disturbances. For disturbances running perpendicularly to the axis of rotation instability can occur only if the gas density exceeds a critical value which depends on the differential rotation at the considered distance only as long as pressure gradients and gradients of the magnetic field strength are negligible. If the gas density exceeds this critical value the shortest unstable wave length is proportional to the square root of vT2+vB2, where vT means the velocity of sound and vB the ALFVÉN-velocity.For disturbances running parallel to the axis of rotation in addition to the JEANS instability a new type of instability occurs due to the simultaneous action of the magnetic field and the differential rotation; for rigid rotation this instability vanishes.

scholarly journals Flux expulsion with dynamics

2016 ◽  
Vol 791 ◽  
pp. 568-588 ◽  
Author(s):  
Andrew D. Gilbert ◽  
Joanne Mason ◽  
Steven M. Tobias
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Lorentz Force ◽  
Differential Rotation ◽  
Time Scale ◽  
Scaling Laws ◽  
Dynamical Regime ◽  
Kinematic Evolution ◽  
Flux Expulsion ◽  
The Magnetic Field

In the process of flux expulsion, a magnetic field is expelled from a region of closed streamlines on a $TR_{m}^{1/3}$ time scale, for magnetic Reynolds number $R_{m}\gg 1$ ($T$ being the turnover time of the flow). This classic result applies in the kinematic regime where the flow field is specified independently of the magnetic field. A weak magnetic ‘core’ is left at the centre of a closed region of streamlines, and this decays exponentially on the $TR_{m}^{1/2}$ time scale. The present paper extends these results to the dynamical regime, where there is competition between the process of flux expulsion and the Lorentz force, which suppresses the differential rotation. This competition is studied using a quasi-linear model in which the flow is constrained to be axisymmetric. The magnetic Prandtl number $R_{m}/R_{e}$ is taken to be small, with $R_{m}$ large, and a range of initial field strengths $b_{0}$ is considered. Two scaling laws are proposed and confirmed numerically. For initial magnetic fields below the threshold $b_{core}=O(UR_{m}^{-1/3})$, flux expulsion operates despite the Lorentz force, cutting through field lines to result in the formation of a central core of magnetic field. Here $U$ is a velocity scale of the flow and magnetic fields are measured in Alfvén units. For larger initial fields the Lorentz force is dominant and the flow creates Alfvén waves that propagate away. The second threshold is $b_{dynam}=O(UR_{m}^{-3/4})$, below which the field follows the kinematic evolution and decays rapidly. Between these two thresholds the magnetic field is strong enough to suppress differential rotation, leaving a magnetically controlled core spinning in solid body motion, which then decays slowly on a time scale of order $TR_{m}$.

scholarly journals Two-fluid simulations of the magnetic field evolution in neutron star cores in the weak-coupling regime

2020 ◽  
Vol 498 (2) ◽  
pp. 3000-3012 ◽  
Author(s):  
F Castillo ◽  
A Reisenegger ◽  
J A Valdivia
Keyword(s):  
Magnetic Field ◽  
Neutron Star ◽  
Charged Particles ◽  
Stable Stratification ◽  
Composition Gradient ◽  
Axially Symmetric ◽  
Drag Forces ◽  
Degeneracy Pressure ◽  
The Magnetic Field ◽  
Two Fluid

ABSTRACT In a previous paper, we reported simulations of the evolution of the magnetic field in neutron star (NS) cores through ambipolar diffusion, taking the neutrons as a motionless uniform background. However, in real NSs, neutrons are free to move, and a strong composition gradient leads to stable stratification (stability against convective motions) both of which might impact on the time-scales of evolution. Here, we address these issues by providing the first long-term two-fluid simulations of the evolution of an axially symmetric magnetic field in a neutron star core composed of neutrons, protons, and electrons with density and composition gradients. Again, we find that the magnetic field evolves towards barotropic ‘Grad–Shafranov equillibria’, in which the magnetic force is balanced by the degeneracy pressure gradient and gravitational force of the charged particles. However, the evolution is found to be faster than in the case of motionless neutrons, as the movement of charged particles (which are coupled to the magnetic field, but are also limited by the collisional drag forces exerted by neutrons) is less constrained, since neutrons are now allowed to move. The possible impact of non-axisymmetric instabilities on these equilibria, as well as beta decays, proton superconductivity, and neutron superfluidity, are left for future work.

Dynamically consistent magnetic fields produced by differential rotation

1987 ◽  
Vol 178 ◽  
pp. 521-534 ◽  
Author(s):  
D. R. Fearn ◽  
M. R. E. Proctor
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Flow Field ◽  
Differential Rotation ◽  
Zonal Flow ◽  
Nonlinear Characteristic ◽  
Poloidal Magnetic Field ◽  
Self Consistent ◽  
Self Consistency ◽  
The Magnetic Field

We investigate the dynamical consequences of an axisymmetric velocity field with a poloidal magnetic field driven by a prescribed e.m.f. E. The problem is motivated by previous investigations of dynamically driven dynamos in the magnetostrophic range. A geostrophic zonal flow field is added to a previously described velocity, and determined by the requirement that Taylor's constraint (Taylor 1963) (guaranteeing dynamical self-consistency of the fields) be satisfied. Several solutions are exhibited, and it is suggested that self-consistent solutions can always be found to this ‘forced’ problem, whereas the usual α-effect dynamo formalism in which E is a linear function of the magnetic field leads to a difficult transcendentally nonlinear characteristic value problem that may not always possess solutions.

scholarly journals Magnetorotational supernovae with different equations of state

2011 ◽  
Vol 7 (S279) ◽  
pp. 357-358
Author(s):  
Sergey G. Moiseenko ◽  
Gennady S. Bisnovatyi-Kogan
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Angular Momentum ◽  
Differential Rotation ◽  
Equations Of State ◽  
Supernova Explosion ◽  
Explosion Energy ◽  
Iron Core ◽  
Wave Forms ◽  
The Magnetic Field

AbstractWe present results of the simulation of a magneto-rotational supernova explosion. We show that, due to the differential rotation of the collapsing iron core, the magnetic field increases with time. The magnetic field transfers angular momentum and a MHD shock wave forms. This shock wave produces the supernova explosion. The explosion energy computed in our simulations is 0.5-2.5 ċ 1051erg. We used two different equations of state for the simulations. The results are rather similar.

The equilibrium configuration of a slowly rotating mass of liquid in the presence of a poloidal magnetic field

1972 ◽  
Vol 55 (1) ◽  
pp. 105-112
Author(s):  
C. Sozou
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Equilibrium Configuration ◽  
Spherical Surface ◽  
Perturbation Expansion ◽  
Reverse Direction ◽  
Poloidal Magnetic Field ◽  
Inviscid Liquid ◽  
Axis Of Rotation ◽  
The Magnetic Field

The equilibrium configuration of a slowly rotating self-gravitating perfectly conducting inviscid liquid, in the presence of a small poloidal magnetic field, is considered for a case where the electric current is a simple function of the distance from the axis of rotation. Owing to the coupling of the magnetic field with the rotation the electric current may reverse direction. This could make the magnetic field zero on certain surfaces and impose restrictions on the parameters of the problem. A perturbation expansion of the nearly spherical surface of the liquid is constructed.

V.—Dissymmetrical Separations in the Zeeman Effect in Tungsten and Molybdenum

1909 ◽  
Vol 29 ◽  
pp. 75-83 ◽  
Author(s):  
Robert Jack
Keyword(s):  
Magnetic Field ◽  
Wave Length ◽  
Zeeman Effect ◽  
Normal Type ◽  
Single Spectrum ◽  
Large Numbers ◽  
Middle Component ◽  
The Absolute ◽  
The Difference ◽  
The Magnetic Field

It has been mentioned by Professor Voigt of Göttingen in his newly published book and by Professor Zeeman of Amsterdam in the Physikalische Zeitschrift, that I have found examples of strongly marked dissymmetry in studying the Zeeman Effect in tungsten and molybdenum. Professor Zeeman has also discovered and published such cases of dissymmetry in other elements. Not only have many examples of normal dissymmetry been found, but almost as many cases of abnormal dissymmetry. To explain those terms, normal and abnormal, let us consider that the single spectrum line is broken up, when the light is in the magnetic field, into the three components, 1, 2, 3, where the numbers begin from the component which has the shortest wave-length. In the normal dissymmetrical triplet the middle component is nearer the component on the red side than that on the violet one, i.e. for the normal type the interval 1–2 is greater than the interval 2–3, but in the abnormal dissymmetrical triplet 2 is nearer to 1 than to 3. These observations of Professor Zeeman and myself, which were made at the same time in the Universities of Amsterdam and Göttingen, having been communicated to Professor Voigt, he wrote and published in the above-mentioned book an extension to his and Professor H. A. Lorentz's theories of the Zeeman Effect. In his original theory Professor Voigt had shown that, considering the electrons as uncoupled, cases of normal dissymmetry might arise among the Zeeman triplets, this dissymmetry being accompanied by a greater intensity of the red component than the violet one. He pointed out also that the ‘absolute’ dissymmetry or the difference between the absolute displacements of the red and violet components should be independent of the magnetic field strength used to produce the Zeeman Effect. To explain the large numbers of complicated types of Zeeman Effect which have been found —in the study of the Zeeman Effect in tungsten I discovered lines with no fewer than 17 to 19 components, the largest numbers hitherto found—Professors Voigt and Lorentz made use in their theories of couplings between electrons of the same vibration frequencies.

scholarly journals Global properties of magnetotail current sheet flapping: THEMIS perspectives

2009 ◽  
Vol 27 (1) ◽  
pp. 319-328 ◽  
Author(s):  
A. Runov ◽  
V. Angelopoulos ◽  
V. A. Sergeev ◽  
K.-H. Glassmeier ◽  
U. Auster ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Current Sheet ◽  
Growth Phase ◽  
Timing Analysis ◽  
Wave Length ◽  
Global Properties ◽  
The Cross ◽  
Magnetic Field Variations ◽  
The Magnetic Field ◽  
Magnetotail Current Sheet

Abstract. A sequence of magnetic field oscillations with an amplitude of up to 30 nT and a time scale of 30 min was detected by four of the five THEMIS spacecraft in the magnetotail plasma sheet. The probes P1 and P2 were at X=−15.2 and −12.7 RE and P3 and P4 were at X=−7.9 RE. All four probes were at −6.5>Y>−7.5 RE (major conjunction). Multi-point timing analysis of the magnetic field variations shows that fronts of the oscillations propagated flankward (dawnward and Earthward) nearly perpendicular to the direction of the magnetic maximum variation (B1) at velocities of 20–30 km/s. These are typical characteristics of current sheet flapping motion. The observed anti-correlation between ∂B1/∂t and the Z-component of the bulk velocity make it possible to estimate a flapping amplitude of 1 to 3 RE. The cross-tail scale wave-length was found to be about 5 RE. Thus the flapping waves are steep tail-aligned structures with a lengthwise scale of >10 RE. The intermittent plasma motion with the cross-tail velocity component changing its sign, observed during flapping, indicates that the flapping waves were propagating through the ambient plasma. Simultaneous observations of the magnetic field variations by THEMIS ground-based magnetometers show that the flapping oscillations were observed during the growth phase of a substorm.

scholarly journals Large-Scale Internal Magnetic Field of the Sun

1990 ◽  
Vol 138 ◽  
pp. 391-394
Author(s):  
A.E. Dudorov ◽  
V.N. Krivodubskij ◽  
A.A. Ruzmaikin ◽  
T.V. Ruzmaikina
Keyword(s):  
Magnetic Field ◽  
Differential Rotation ◽  
Large Scale ◽  
The Sun ◽  
Poloidal Magnetic Field ◽  
The Core ◽  
Torsional Waves ◽  
Formation And Evolution ◽  
Field Lines ◽  
The Magnetic Field

The behaviour of the magnetic field during the formation and evolution of the Sun is investigated. It is shown that an internal poloidal magnetic field of the order of 104 − 105 G near the core of the Sun may be compatible with differential rotation and with torsional waves, travelling along the magnetic field lines (Dudorov et al., 1989).

scholarly journals High-energy collision of particles in the magnetic field far from black holes

2014 ◽  
Vol 29 (29) ◽  
pp. 1450151
Author(s):  
O. B. Zaslavskii
Keyword(s):  
Magnetic Field ◽  
Black Hole ◽  
Center Of Mass ◽  
High Energy ◽  
Axially Symmetric ◽  
High Energy Collision ◽  
Mass Frame ◽  
Symmetric Black Hole ◽  
Rotating Star ◽  
The Magnetic Field

We consider collision of two particles in the axially symmetric black hole metric in the magnetic field. If the value of the angular momentum |L| of one particles grows unbound (but its Killing energy remains fixed) one can achieve unbound energy in the center-of-mass frame E c.m. In the absence of the magnetic field, collision of this kind is known to happen in the ergoregion. However, if the magnetic field strength B is also large, with the ratio |L|/B being finite, large E c.m. can be achieved even far from a black hole, in the almost flat region. Such an effect also occurs in the metric of a rotating star.

Sign in / Sign up

Export Citation Format

Share Document