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Magnetohydrodynamic waves play a central role in most geophysical and astrophysical systems involving conducting fluids and magnetic fields. For example, in the solar corona, they underpin the oscillatory behaviour of coronal loops. In the liquid core of the Earth, their propagation from the solid inner core to the outer core-mantle boundary drives variations in the length of days. The journey to the formal understanding of these waves started in 1942 with Alfv茅n's simple 1D, theory for a linear transversal MHD wave, in a homogeneous, incompressible fluid pervaded by a homogeneous magnetic field. In real systems, however, inhomogeneities, nonlinearities, background flows and multi-modality are essential ingredients whose impact is difficult to study in isolation.

Since Lundquist's fist attempt to produce Alfv茅n's waves (AW) in mercury in 1949, liquid metal experiments have been hindered by the large magnetic dissipation inherent to metals. They struggled to produce even simple linear waves and have been practically abandoned. The advent of plasma Technology in the 1950's offered a more successful alternative, with the first convincing experimental evidence of AW, followed by more complex waves with inhomogeneities and nonlinear interactions. Plasma devices are, however very complex and make it difficult to control flow conditions. Furthermore, the compressibility of plasmas make it difficult to disentangle the different types of waves they bear.

In this talk, I will show that well-controlled MHD waves can be generated in liquid metals after all, by means of a technique previously used to produce MHD turbulence. The idea relies on very high magnetic fields that enable MHD waves to propagate before they dissipate, and consists in forcing the waves with electric current of adjustable distribution. With this technique, we obtain AW, inhomogeneous waves, and produce nonlinear interactions between MHD waves in liquid metal for the first time. The vast possible variations around the principle of these experiments provide a new alley to individually study complex aspects of MHD wave involving inhomogeneity, nonlinearity, but also background flows and other ingredients relevant to geo and astrophysical systems.

S. Lalloz, L. Davoust, F. Debray and A. Poth茅rat, "Alfven waves at low magnetic Reynolds number: transitions between diffusion, dispersive Alfv茅n waves and nonlinear propagation", J. Fluid Mech. 1003, A19 (2025)