12.1.1 Generalities

In this chapter, we are interested in the growth of an electromagnetic instability produced by the motion of an electrically conducting fluid. Let us take an initially non-zero magnetic field. Let us consider a stationary flow and assume that we can regulate the intensity of the flow without changing its geometry. We observe that the magnetic field is deformed by the flow. Let us suppose that subsequently the initial source of magnetic field is abruptly removed, two cases are then possible:

• either the magnetic intensity disappears over time. This is called magnetic diffusion;

• or the magnetic intensity does not decrease over time. This is then a dynamo instability ^[1].

^[1]

Let us consider for example the case of the deformation of a uniform field by a fluid in rotation. In order to simplify the problem, the flow will be taken as a cylinder in rotation around its revolution axis [PAR 66] [WEI 66]. An initial field perpendicular to the rotation axis of the cylinder is chosen. The motion of the cylinder generates an electric current density. This current density induces a magnetic field which is added to the initial field. If the cylinder rotation rate is constant, then the magnetic field reaches a stable state. The final configuration of the field depends on the cylinder rotation rate (Figure 12.1). For a high rotation rate (the 4 ^th image in Figure 12.1), the magnetic field is expelled towards the periphery of the cylinder.