XLIV. On the molecular theory of galvanic polarization

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Helicity-Rotation-Gravity Coupling for Gravitational Waves

The consequences of spin-rotation-gravity coupling are worked out for linear gravitational waves. The coupling of helicity of the wave with the rotation of a gravitational-wave antenna is investigated and the resulting modifications in the Doppler effect and aberration are pointed out for incident high-frequency gravitational radiation. Extending these results to the case of a gravitomagnetic field via the gravitational Larmor theorem, the rotation of linear polarization of gravitational radiation propagating in the field of a rotating mass is studied. It is shown that in this case the linear polarization state rotates by twice the Skrotskii angle as a consequence of the spin-2 character of linear gravitational waves.Comment: 11 pages, no figures, accepted for publication in Phys. Rev. D; v2: a few minor typos correcte

Diffraction of light by a planar aperture in a metallic screen

We present a complete derivation of the formula of Smythe [Phys.Rev.72, 1066 (1947)] giving the electromagnetic field diffracted by an aperture created in a perfectly conducting plane surface. The reasoning, valid for any excitating field and any hole shape, makes use only of the free scalar Green function for the Helmoltz equation without any reference to a Green dyadic formalism. We compare our proof with the one previously given by Jackson and connect our reasoning to the general Huygens Fresnel theorem.Comment: J. Math. Phys. 47, 072901 (2006

Variational data assimilation for the initial-value dynamo problem

The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries

Large-scale magnetic topologies of late M dwarfs

We present here the final results of the first spectropolarimetric survey of a small sample of active M dwarfs, aimed at providing observational constraints on dynamo action on both sides of the full-convection threshold (spectral type M4). Our two previous studies (Donati et al. 2008b; Morin et al. 2008b) were focused on early and mid M dwarfs. The present paper examines 11 fully convective late M dwarfs (spectral types M5-M8). Tomographic imaging techniques were applied to time-series of circularly polarised profiles of 6 stars, in order to infer their large-scale magnetic topologies. For 3 other stars we could not produce such magnetic maps, because of low variability of the Stokes V signatures, but were able to derive some properties of the magnetic fields. We find 2 distinct categories of magnetic topologies: on the one hand strong axisymmetric dipolar fields (similar to mid M dwarfs), and on the other hand weak fields generally featuring a significant non-axisymmetric component, and sometimes a significant toroidal one. Comparison with unsigned magnetic fluxes demonstrates that the second category of magnetic fields shows less organization (less energy in the large scales), similarly to partly convective early M dwarfs. Stars in both categories have similar stellar parameters, our data do not evidence a separation between these 2 categories in the mass-rotation plane. We also report marginal detection of a large-scale magnetic field on the M8 star VB 10 featuring a significant toroidal axisymmetric component, whereas no field is detectable on VB 8 (M7).Comment: 26 pages, 16 figures, 9 tables, 11 tables in appendix. Accepted for publication in MNRA

Turbulent transport in hydromagnetic flows

The predictive power of mean-field theory is emphasized by comparing theory with simulations under controlled conditions. The recently developed test-field method is used to extract turbulent transport coefficients both in kinematic as well as nonlinear and quasi-kinematic cases. A striking example of the quasi-kinematic method is provided by magnetic buoyancy-driven flows that produce an alpha effect and turbulent diffusion.Comment: 17 pages, 6 figures, topical issue of Physica Scripta on turbulent mixing and beyon

Gravitomagnetism and the Clock Effect

The main theoretical aspects of gravitomagnetism are reviewed. It is shown that the gravitomagnetic precession of a gyroscope is intimately connected with the special temporal structure around a rotating mass that is revealed by the gravitomagnetic clock effect. This remarkable effect, which involves the difference in the proper periods of a standard clock in prograde and retrograde circular geodesic orbits around a rotating mass, is discussed in detail. The implications of this effect for the notion of ``inertial dragging'' in the general theory of relativity are presented. The theory of the clock effect is developed within the PPN framework and the possibility of measuring it via spaceborne clocks is examined.Comment: 27 pages, LaTeX, submitted to Proc. Bad Honnef Meeting on: GYROS, CLOCKS, AND INTERFEROMETERS: TESTING GENERAL RELATIVITY IN SPACE (22 - 27 August 1999; Bad Honnef, Germany

On the Origin of Cosmic Magnetic Fields

We review the literature concerning how the cosmic magnetic fields pervading nearly all galaxies actually got started. some observational evidence involves the chemical abundance of the light elements Be and B, while another one is based on strong magnetic fields seen in high red shift galaxies. Seed fields, whose strength is of order 10^{-20} gauss, easily sprung up in the era preceding galaxy formation. Several mechanisms are proposed to amplify these seed fields to microgauss strengths. The standard mechanism is the Alpha-Omega dynamo theory. It has a major difficulty that makes unlikely to provide the sole origin. The difficulty is rooted in the fact that the total flux is constant. This implies that flux must be removed from the galactic discs. This requires that the field and flux be separated, for otherwise interstellar mass must be removed from the deep galactic gravitational and then their strength increased by the alpha omega theory.Comment: 90 pages and 6 figures; accepted for publication in Reports of Progress in Physics as an invited revie

On the magnetic fields generated by experimental dynamos

We review the results obtained by three successful fluid dynamo experiments and discuss what has been learnt from them about the effect of turbulence on the dynamo threshold and saturation. We then discuss several questions that are still open and propose experiments that could be performed to answer some of them.Comment: 40 pages, 13 figure