Mode Conversion and Period Doubling in a Liquid Rubidium Alfvén-Wave Experiment with Coinciding Sound and Alfvén Speeds

We report Alfvén-wave experiments with liquid rubidium at the Dresden High Magnetic Field Laboratory. Reaching up to 63 T, the pulsed magnetic field exceeds the critical value of 54 T at which the Alfvén speed coincides with the sound speed. At this threshold, we observe a period doubling of an applied 8 kHz cw excitation, which is consistent with the theoretical expectation of a parametric resonance between magnetosonic waves and Alfvén waves. Similar mode conversions are discussed as a possible mechanism for heating the solar corona.

Figure 1

Experimental setting. (a) Stainless-steel container filled with rubidium. (b) Holder with four pickup coils (PU 1–PU 4) and four compensation coils (CC). (c) Geometrical details of the construction. PP 1–PP 4 denote four electric-potential probes soldered on the container. The three orange triangles indicate the rim contacts (RCs) encircling the bottom part of the container. LC is the lower contact. All sizes are in millimeters. (d) Schematic for the driving of the torsional Alfvén wave in the lower part of the container.

Figure 2

(a) Time dependence of the pulsed magnetic field and (b) of the voltage measurements at the lower contact. The red dashed lines indicate the instants where the critical field strength of 54 T is crossed. The insets of (b) detail the two transition regions, where the double-period signal starts and ceases to exist. (c) Gabor transform of the signal from (b), with a von Hann window width of 5 ms. Amplitude of the (d) 8 and (e) 4 kHz stripe from (c), for different choices of the von Hann window width. The PSD units of (d) and (e) are arbitrary, but consistent among each other.

Figure 3

(a) Time dependence of the applied magnetic field and (b) of the (compensated) voltage measurement at the pickup coil PU 2. The red dashed lines indicate the instants where the critical field strength of 54 T is crossed. The inset of (b) shows the region of highest field, where a significant contribution of a 16 kHz signal is visible. (c) Gabor transform of the signal from (b), with a von Hann window width of 5 ms. Amplitudes of the (d) 8, 16, 24, and 32 kHz stripes and (e) the 4, 12, and 20 kHz stripes from (c). The PSD units of (d) and (e) are arbitrary, but consistent among each other.

Figure 4

Dependence of various measured signals on the magnetic field. (a) PSD of the 8 and 4 kHz coefficients of the voltage $U_{\mathrm{LC}-\mathrm{RC}}$ from Figs. 2 and 2 for three different von Hann windows. (b) PSD of the 8, 16, and 24 kHz signals from Fig. 3 and of the 4, 12, and 20 kHz signals from Fig. 3. The arrows indicate rising and falling branches of the pulsed magnetic field.