Influence of a Magnetic Field on the Brownian Motion of Particles with Magnetic Moment

1968 ◽  
Vol 23 (12) ◽  
pp. 1911-1913
Author(s):  
Siegfried Hess

The influence of a magnetic field on the diffusion of Brownian particles with a magnetic moment parallel to their internal angular momentum is discussed. Starting point is a generalized Fokker-Planck equation. Application of the moment method leads to a set of transport-relaxation equations. From them the diffusion tensor depending on the external field is inferred.

1971 ◽  
Vol 26 (6) ◽  
pp. 1057-1071 ◽  
Author(s):  
S. Hess ◽  
L. Waldmann

Abstract The Senftleben-Beenakker effect of the viscosity of dilute polyatomic gases is investigated theoretically for the case where an alternating magnetic field parallel to the usual static field is present. The starting point is a set of transport-relaxation equations obtained from the kinetic equation for the one-particle distribution by application of the moment method. The transport-relaxation equations are solved for the viscosity problem and the relevant viscosity coefficients averaged over many periods of the oscillating field are calculated as functions of the frequency of the alternating field and of the magnitudes of both magnetic fields. The importance of the obtained results for the dynamic behaviour of the thermomagnetic gas torque (Scott effect) is discussed.


1987 ◽  
Vol 115 ◽  
pp. 384-384
Author(s):  
S. Hinata

There is a simple relationship among moment of inertia I, rotational kinetic energy K, and momentum L given by (David Layzer, private communication), 2IK ≧ L. During the Hayashi phase a rotating protostar will amplify the trapped magnetic field by a dynamo-like process. Since the rotation is expected to be fast, many unstable modes will be excited and will grow exponentially in time until some nonlinear processes saturate the amplitude. However, it may happen that the reduction in rotational kinetic energy becomes so large that without increasing the moment of inertia the inequality given above may not be satisfied. The only way to increase the moment of inertia is to move the mass outward. This can be done by transferring the angular momentum outward through the magnetic field. So we will have a fast rotating mass shell at the outer edge of the star. Further transfer of angular momentum will push the shell against the accretion disk; the moving masses of the disk will divert the mass flow along the background magnetic field which extends perpendicular to the accretion disk. This results in the hollow cone jets from both poles because the outward motion is primarily on the equatorial plane.


The accurate experiments of Chattock and Bates prove that the angular momentum arising in a ferromagnetic substance from unit change in its magnetic moment is very nearly, if not exactly, one half the value 2 m/e = 1.13 X 10 -7 , which seemed to me the most likely when I first discussed this effect. This conclusion is supported by the fact that the improvements which have been introduced into this subject by successive experimenters in recent years have led to values showing a strong tendency to settle at the same limit m/e = 5.65 X 10 -8 . This value is also in general agreement with that deduced by Barnett from experiments on the converse effect. It seems desirable therefore to reconsider the interpretation of this ratio. The higher value 2 m/e is obtained by making rather definite assumptions, which evidently require modification, as to the nature of the phenomena. These assumptions are that the process of magnetization involves the turning of electron orbits, and that nothing else which may occur has any important influence on the phenomena. The inertia of the electrons is assumed to be entirely of the type which controls the deflection of a beam of cathode rays by a magnetic field, and any change in the motion of the positively charged part of the atom is disregarded. These assumptions are essentially the same as those of the theories of Langevin and Weiss which have been successful in dealing with purely magnetic phenomena.


1972 ◽  
Vol 27 (10) ◽  
pp. 1383-1393 ◽  
Author(s):  
W. E. Köhler ◽  
H. H. Raum

Abstract The system of transport relaxation equations obtained from the linearized Waldmann-Snider equation is the starting point for the kinetic treatment of the heat conductivity for mixtures of linear diamagnetic molecules in an external homogeneous magnetic field. The connection of the occurring collision integrals with certain molecular cross sections is discussed and order of magnitude considerations are made for molecules with small nonsphericity of their interaction. With the Kagan polarization as the decisive rotational angular momentum anisotropy term in the molecular distribution function, an expression for the heat conductivity ini the presence of a magnetic field is derived for mixtures with an arbitrary number of components. The mole fraction dependence of the saturation values is studied for binary mixtures of rotating molecules and noble gas atoms for a simplified model. As an example, the system o-D2/He is considered.


1970 ◽  
Vol 25 (8-9) ◽  
pp. 1178-1190 ◽  
Author(s):  
H.H. Raum ◽  
W.E. Köhler

Abstract A transport theory is developed for mixtures of dilute gases consisting of linear rotating diamagnetic molecules in an external homogeneous magnetic field. This formalism is adequate for a treatment of the Senftleben-Beenakker effects for gas mixtures. Starting point is the system of linearized Waldmann-Snider equations. A complete scheme of orthogonal expansion tensors in velocity and rotational angular momentum is given, up to tensors of third rank and power. The moment method is applied to solve the coupled system of Waldmann-Snider equations and the resulting system of transport relaxation equations (TRE) is stated up to third rank tensor equations. The local conservation laws - linearized in the deviation from thermal equilibrium - are derivated from the TRE.


Author(s):  
C. G. Darwin

1. In a recent paper Landau has shown that, when electrons are moving freely in a magnetic field, they exhibit, in addition to the paramagnetic effect of their spin, a diamagnetic effect due to their motion. This result is rather unexpected, since it is quite contrary to the classical case. There it might appear as though the circles described by the electrons must produce a magnetic moment, but the error was long ago pointed out by Bohr. The motion of the electrons must be confined to some region by means of a boundary wall, and the electrons near the wall describe a succession of circular arcs, repeatedly bouncing on the wall, and slowly creeping round it in the direction opposite to that of the uninterrupted circles; when the moment of these electrons is taken into account, it exactly cancels out that due to the free circles. In Landau's work it is of course necessary to consider the boundary, but he shows how allowance is to be made for it by an appropriate process. The complete justification is rather subtle, and so it may be worth considering a special case, admitting of exact solution, which takes the boundary into account, and so makes it possible to follow more closely the analogy between the classical and quantum problems. With regard to the general case with a boundary wall of any type, we shall only observe that the different results arise, because in the wave problem ψ must vanish at the bounding “potential wall,” and so will be small near it; this upsets the balance of the electric current near the wall, and yields the magnetic moment.


1975 ◽  
Vol 30 (9) ◽  
pp. 1114-1121 ◽  
Author(s):  
W. E. Köhler ◽  
J. Halbritter

A kinetic theory of thermal diffusion in binary mixtures of polyatomic gases in an external homogeneous magnetic field is presented. It is based on the transport-relaxation equations obtained from the linearized Waldmann-Snider equation with the moment method. Under the assumption that the Kagan polarization is the decisive nonequilibrium alignment an expression for the thermal diffusion tensor in terms of Waldmann-Snider collision integrals is derived. In particular, mixtures of linear molecules with noble gas atoms are treated and the mole fraction dependence of the transverse effect is studied. As examples, the mixtures N2-Ar and N2-Ne are considered. Finally the order of magnitude of the transverse Senftleben-Beenakker effect of diffusion is estimated


2012 ◽  
pp. 66-80
Author(s):  
Michał Mrozowicki

Michel Butor, born in 1926, one of the leaders of the French New Novel movement, has written only four novels between 1954 and 1960. The most famous of them is La Modification (Second thoughts), published in 1957. The author of the paper analyzes two other Butor’s novels: L’Emploi du temps (Passing time) – 1956, and Degrés (Degrees) – 1960. The theme of absence is crucial in both of them. In the former, the novel, presented as the diary of Jacques Revel, a young Frenchman spending a year in Bleston (a fictitious English city vaguely similar to Manchester), describes the narrator’s struggle to survive in a double – spatial and temporal – labyrinth. The first of them, formed by Bleston’s streets, squares and parks, is symbolized by the City plan. During his one year sojourn in the city, using its plan, Revel learns patiently how to move in its different districts, and in its strange labyrinth – strange because devoid any centre – that at the end stops annoying him. The other, the temporal one, symbolized by the diary itself, the labyrinth of the human memory, discovered by the narrator rather lately, somewhere in the middle of the year passed in Bleston, becomes, by contrast, more and more dense and complex, which is reflected by an increasinly complex narration used to describe the past. However, at the moment Revel is leaving the city, he is still unable to recall and to describe the events of the 29th of February 1952. This gap, this absence, symbolizes his defeat as the narrator, and, in the same time, the human memory’s limits. In Degrees temporal and spatial structures are also very important. This time round, however, the problems of the narration itself, become predominant. Considered from this point of view, the novel announces Gerard Genette’s work Narrative Discourse and his theoretical discussion of two narratological categories: narrative voice and narrative mode. Having transgressed his narrative competences, Pierre Vernier, the narrator of the first and the second parts of the novel, who, taking as a starting point, a complete account of one hour at school, tries to describe the whole world and various aspects of the human civilization for the benefit of his nephew, Pierre Eller, must fail and disappear, as the narrator, from the third part, which is narrated by another narrator, less audacious and more credible.


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