CNRS-INSU-PNP Alpha, beta and omega effects in magnetostrophic regime

As part of S. Cabanes’ thesis, supervised by H-C. Nataf and N. Schaeffer (arrow allocation University of Grenoble), we are developing a method to find in our DTS experiment the alpha, beta and omega effects that are the ingredients used by theorists to build large-scale dynamos that take into account coherent small scale fluctuations. Since Parker’s founding work (1955) there has been an effective scenario for generating a magnetic field in stars and planets : differential rotation converts the poloidal magnetic field into a toroidal field (omega effect) and non-axisymmetric fluctuations convert the poloidal field into a cold field (alpha effect), thus closing the field amplification loop. On the other hand, fluctuations also contribute to the diffusion of the large-scale field (beta effect).

After the success of the "guided" liquid sodium dynamos in Riga and Karlsruhe in 2000, all attempts to obtain turbulent experimental dynamos (Maryland, Madison, Cadarache) ended in failure (the VKS group did obtain a dynamo, but only when the device included ferromagnetic parts). It appears that instead of contributing to the appearance of the magnetic field, small scale turbulent fluctuations reduce the dynamogenic potential of the large scale flow. Several teams estimated these effects in turbulent flows, imposing a weak magnetic field and studying the fluid response. Thus, the VKS and Madison teams obtained alpha effect measurements for their von Karman flows. The Perm group obtained a measure of the beta effect (turbulent diffusion) by imposing an oscillating field on their sodium torus.

In planetary dynamos, flows are strongly constrained by the magnetic field and it is crucial to predict the effects of small scales on the dynamo in this case. With our DTS experience of a spherical duvet rotating with an imposed magnetic field, we have the opportunity to examine this question in the case of a flow where Lorentz force plays a dominant role. But then it is necessary to map the flow in situ, rather than relying on the flow measured in a water model. Thanks to significant instrumental advances, we have begun to do this by combining flow velocity measurements along ultrasonic Doppler profiles that grid the fluid (Brito et al, 2011).

We also measured the induced magnetic field, and calculated the omega effect produced by the flow. The difference comes from the contribution of fluctuations that can be put in the form of an alpha effect.

The small differences in the axisymmetry of the magnetic field (mainly dipole) imposed by the rotating seed produce an oscillating signal at the rotational period of the seed, which we have also mapped. Using the numerical code developed by N. Schaeffer, S. Cabanes (Cabanes et al, SEDI 2012) seeks to report observations in terms of omega effect and turbulent diffusivity (beta effect). The method developed can be used for other experiments (BigSister in Maryland) and in numerical simulations.

For the first time, we could determine the alpha, beta and omega effects of a real flow in spherical geometry with a strong magnetic field. This would represent an important step towards the community of theorists who have studied extensively the behaviour of dynamos parameterized with ad hoc alpha and omega effects.

We have a sufficient dataset in case the external sphere is at a standstill. We would like to obtain data when the external sphere rotates, in a more "global" regime. We must therefore embark on an electronic digitization process. This electronics is in the test phase, and we are asking for funding (8 k€) to build the mechanical modules that will allow this electronics to be embedded, and to carry out a series of rotating measurement campaigns. We are also asking for mission funding (€3k), mainly to continue the collaborations with Dan Lathrop at the University of Maryland.