Magnetic field self-excitation in the
Riga dynamo experiment

Agris Gailitis, Olgerts Lielausis, Ernests Platacis
Institute of Physics, Latvian University
LV-2169 Salaspils 1, Riga, Latvia

Gunter Gerbeth, Frank Stefani
Forschungszentrum Rossendorf
P.O. Box 510119 D-01314 Dresden, Germany

Magnetic fields of planets, stars, and galaxies are generated by motion of electrically conducting fluids. Whereas the corresponding theory of homogeneous dynamos has been widely elaborated in the last decades, an experimental verification of magnetic field self-excitation in conducting fluids was still missing until recently. Besides a few other experimental approaches in the world the Riga dynamo facility is one of the large sodium facilities devoted to the investigation of magnetic field self-excitation. Figure 1 shows the main parts of the facility, comprising a propeller driven central spiral flow (with a velocity up to 15 m/s), a straight back-flow and sodium at rest in two additional coaxial tubes of stainless steel. In order to reach self-excitation with the limited power ressources, the whole facility had been optimized in a long iterative process of pump design and numerical simulations (Figure 2 shows a snapshot of the expected magnetic field close to the innermost wall resulting from a 2D-solver for the induction equation).

Fig. 1: The Riga dynamo facility: 1 - Two motors (55 kW each), 2 - Propeller, 3 - Spiral flow, 4 - Back-flow, 5- Sodium at rest, * - Flux-gate sensor, x - Six Hall sensors
Fig. 2: Impression of the self-excited magnetic field at the innermost wall

In November 1999, a first dynamo experiment was carried out. After heating up the sodium to 300C it was pumped slowly through the tubes for more than a day in order to ensure good electrical contact with the walls. While cooling down the system, three experiments were planned at 250C, 200C, and 150C. However, the experiment at 150C where the conductivity is highest and hence the best conditions for magnetic-field self-excitation were expected could not be carried out due to some technical problem with the seal during the experiment at 200C. At this temperature, the amplification of an applied magnetic field (produced by a 1 Hz current in a helical coil wound around the dynamo) was measured for various rotation rates of the propeller (Fig. 3). All points in Fig. 3, except the rightmost one, are calculated from sinusoidal field signals (measured at the innermost sensor) with the same 1 Hz frequency as the excitation current. At the highest rotation rate of 2150, however, a second signal with a frequency of 1.3 Hz appeared on the background of the amplified 1 Hz signal (Fig. 4). This signal is exponentially growing in time with a small growth rate of p=0.03/s , i.e. the threshold of self-excitation was just crossed for that highest rotation rate. After switching off the excitation current at a slightly decreased rotation rate of 1980 rpm, a slowly decaying signal with a frequency of 1.1 Hz and a negative growth rate of p=-0.3/s was detected. The signals of the six outer Hall sensors for that case are shown in Fig. 5.

Fig. 3: Dependence of the magnetic field amplification on the propeller rotation rate. The ordinate shows the inverse relation of the measured magnetic field to the current in the excitation coils.
Fig. 4: Decomposition of the fit of the measured magnetic field at 2150 rpm in two signals with different frequencies.

Fig. 5: Magnetic field signals recorded at six outer Hall sensors after switching off the excitation current at 1980 rpm.
Fig. 6: Numerical predictions for growth rates p and frequencies f of the dynamo eigenmode in dependence on the rotation rate for three different temperatures, and measured values.

These two measured values for rotation rates of 1980 rpm and 2150 rpm can be compared with numerical prognoses which were made for the three said temperatures (Fig. 6). Considering some simplifications used in the numerical computations the agreement between prognoses and measured values is very good.

For the first time, magnetic field self-excitation in a moving liquid metal has been demonstrated experimentally. Future experiments at lower temperature are expected to provide a stronger magnetic field self-excitation. Than the back-reaction of the magnetic field on the flow will lead to interesting saturation effects.

(12.01.2000) Frank Stefani