Experimental Observation of Spatially Localized Dynamo Magnetic Fields

We report the first experimental observation of a spatially localized dynamo magnetic field, a common feature of astrophysical dynamos and convective dynamo simulations. When the two propellers of the von Kármán sodium experiment are driven at frequencies that differ by 15%, the mean magnetic field’s energy measured close to the slower disk is nearly 10 times larger than the one close to the faster one. This strong localization of the magnetic field when a symmetry of the forcing is broken is in good agreement with a prediction based on the interaction between a dipolar and a quadrupolar magnetic mode.

Figure 1

Energy fraction close to disk 1 as a function of the dimensionless symmetry-breaking amplitude. All stationary dynamos obtained for $\max (F_1,F_2)\ge 22.75\mathrm{Hz}$ are shown. Inset: sketch of the experiment: two impellers counterrotate at frequencies $F_1$ and $F_2$. When $F_1=F_2$ the setup is invariant to ${\mathcal{R}}_{\pi }$ rotation. The vertical thick lines indicate the locations of the two arrays of three-axis Hall probes which measure the magnetic field close to each disk.

Figure 2

Asymmetry factor of the magnetic field as a function of the dimensionless symmetry-breaking amplitude. At $|ϵ|\simeq 15\%$, the magnetic energy close to the slower disk is roughly 10 times larger than the one close to the faster disk. Inset (top): parameter space of the measurement points used for this graph (●: steady magnetic field; ■: randomly reversing magnetic field); (bottom): amplitudes of the dipolar and quadrupolar components evaluated by the sum and difference of axial fields measured by the deepest probe of each array (●: $d$; $+$: $q$).

Figure 3

Time series in reversing regime at $F_1=18\mathrm{Hz}$ and $F_2=24\mathrm{Hz}$ (Top: axial field close to disk 1; middle: magnetic energy density for a zoom on the last two reversals; bottom: ratio of these two energies.) Before computing the energies, we use a sliding average on 500 ms to remove high frequency fluctuations. The magnetic field is localized close to the slower disk during the phases of given polarity. It gets briefly localized close to the faster disk during a reversal.

Figure 4

Evolution in phase space ($B_x^{(1)}$, $B_x^{(2)}$) as the symmetry-breaking amplitude increases. The symbols are the time averages ${\overline{B}}_x^{(1)}$ and ${\overline{B}}_x^{(2)}$ for $+$: $(F_1,F_2)=(21\mathrm{Hz},21\mathrm{Hz})$; *: $(F_1,F_2)=(19.5\mathrm{Hz},22.5\mathrm{Hz})$; ■: $(F_1,F_2)=(19\mathrm{Hz},24\mathrm{Hz})$. The line is a trajectory during reversals at $(F_1,F_2)=(18\mathrm{Hz},24\mathrm{Hz})$, and the circles are the corresponding averages computed for each polarity ($\pm M$).