Feasible homopolar dynamo with sliding liquid-metal contacts

We present a feasible homopolar dynamo design consisting of a flat, multi-arm spiral coil, which is placed above a fast-spinning metal ring and connected to the latter by sliding liquid-metal electrical contacts. Using a simple, analytically solvable axisymmetric model, we determine the optimal design of such a setup. For small contact resistance, the lowest magnetic Reynolds number, Rm≈34.6, at which the dynamo can work, is attained at the optimal ratio of the outer and inner radii of the rings Ri/Ro≈0.36 and the spiral pitch angle 54.7°. In a setup of two copper rings with the thickness of 3 cm, Ri=10cm and Ro=30cm, self-excitation of the magnetic field is expected at a critical rotation frequency around 10 Hz.