Impact of a shearless flow and cylindricity on interchange instability in magnetized plasma

The stability of magnetically confined plasmas is sometimes examined using the so-called "slab" model, where the toroidal geometry of the problem is approximated locally by the Cartesian one. In the present paper, a (more accurate) cylindrical approximation is considered and shown to yield results which are qualitatively different from those of the slab model. In particular, if the slab model is applied to the outboard region of the tokamak (where the gradient of the plasma's density and that of the magnetic field are of the same sign), disturbances remain unstable at all times. In the cylindrical model, on the other hand, the E×B flow carries disturbances around the cylinder and they alternate between the unstable and stable regions. Naturally, this reduces the growth rate of instability and makes it dependent on the angular velocity of the flow.