A CLASS OF SELF-SUSTAINING DISSIPATIVE SPHERICAL DYNAMOS

Journal Article · Fri Aug 01 04:00:00 EDT 1958 · Annals of Physics (New York) (U.S.)

DOI:https://doi.org/10.1016/0003-4916(58)90054-X· OSTI ID:4323954

Backus, G

The dynamo equations describing the effects of the internal motion of a bounded volume of incompressible fluid with nonzero ohmic resistivity on the magnetic field produced by electric currents in that fluid are rigorously treated. The procedure involves representing an arbitrary solenoidal vector field in terms of two scalars, analogous to the representation of an arbitrary irrotational field as the gradient of a single scalar. The dynamo equations are reduced to scalar heat equations for the two field scalars, the coupling between them taking the form of a heat source term. Precise results about the magnetic field can be obtained from these heat equations with the help of several variational inequalities analogous to Rayleigh's variational estimate for the fundamental frequency of a vibrating system. The main result is the explicit construction of a large class of continuously differentiable fluid velocities capable of indefinitely maintaining or amplifying the dipole moment of the external magnetic field. A critique of some previous attempts to produce dissipative self- regenerative spherical dynamos is included. The techniques which lead to the existence of self-sustaining dynamos produce other results about the dynamo equations. These results are listed. (auth) 1437l A general, first-order, linear, relativistic wave equation for a particle of arbitrary half-integral maximum spin is presented. The structure of the general theory is described briefly, while its specialization to a particle of maximum spin one is treated at greater length. The special theory describes not only the simple scalar (S), pseudoscalar (P), vector (V), and axial-vector (A) mesons, but also composite ''particles'' possessing S, P, V, and A components, all components differing in rest mass. The restriction to unique rest mass allows the wave function to satisfy the Klein-Gordon equation. The restriction to a positive-definite energy density eliminates all composite particles except the S-P, the S-A, and the P-V. The theory is invariant under the extended Lorentz group, charge conjugation, and Hermitian conjugation. (auth)

• Research Organization: Princeton Univ., N. J.
• NSA Number: NSA-12-014370
• OSTI ID: 4323954
• Journal Information: Annals of Physics (New York) (U.S.), Journal Name: Annals of Physics (New York) (U.S.) Vol. Vol: 4; ISSN APNYA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

COUPLING-- DIFFERENTIAL EQUATIONS-- ELECTRODYNAMICS-- EQUATIONS-- FLUIDS-- INTERACTIONS-- MAGNETIC FIELDS-- MATHEMATICS-- RADIATION SOURCES-- TEMPERATURE-- THERMAL RADIATION-- VECTORS
CURRENTS-- DIFFERENTIAL EQUATIONS-- ELECTRIC CONDUCTIVITY-- ELECTRODYNAMICS-- EQUATIONS-- FLUIDS-- MAGNETIC FIELDS-- MATHEMATICS-- MOTION-- PRESSURE
DIFFERENTIAL EQUATIONS-- DIPOLES-- ELECTRODYNAMICS-- EQUATIONS-- FLUIDS-- MAGNETIC FIELDS-- MATHEMATICS-- VELOCITY
DIFFERENTIAL EQUATIONS-- ELECTRODYNAMICS-- EQUATIONS-- FLUIDS-- FREQUENCY-- MAGNETIC FIELDS-- MATHEMATICS-- VARIATIONS-- VIBRATIONS
PHYSICS