An electromagnet with Hall excitation

Abstract

In 1911 Corbino showed that if a disk with a current flowing to the axis is placed in a magnetic field parallel to the axis of the disk, then due to the Hall emf the initially straight line of electric current is turned into a spiral. This leads to an increase in the length of the current line and thus to an increase in the disk resistance. The change in the disk resistance in a magnetic field was used in [1] to switch the current in the circuit of an inductive energy store. If the electric current carriers move from the edge of the disk to the axis, the azimuthal Hall current is accompanied by an increase in the magnetic field inside the disk compared with that outside it [2]. The same processes occur in a hydromagnet [3–5], in which the radial flow of a conducting liquid in an axial magnetic field is used to amplify a magnetic field. In the papers mentioned earlier the transients which occur when the steady magnetic field is established were not considered. To produce a magnetic field, and particularly for switching, the switch-on time of the device is of considerable importance. Hence, in this paper we consider the nonstationary problem of the amplification of a magnetic field. The amplification of the field is obtained and the time taken for the stationary state to build up is found. Both quantities depend exponentially on the magnetic Reynolds number. For a hydromagnet it is shown that the steady-state magnetic field differs considerably from that obtained in [4, 5]. The disagreement between the results is due to the fact that the boundary conditions in [4, 5] were arbitrarily chosen.