Fundamentals of Plasma Physics

10.7 Qualitative description of free-boundary instabilities 325

weaker azimuthal

magnetic field

stronger azimuthal

magneticfield

surface

current

Figure 10.7: Kink instability can occur when the equilibrium magnetic fieldis helical

The sausage instability can be prevented by surrounding the plasma with aperfectly
conducting wall or by immersing the plasma in a strong axial vacuum magnetic field gen-
erated by currents in external solenoid coils coaxial with the plasma. Ifa plasma with
embedded axial field attempts to sausage, the axial rippling of the plasma would have to
bend the embedded axial field since this axial field is frozen into the plasma.Any bending
of a magnetic field requires work and so the free energy available to drive the sausage insta-
bility would also have to do work to bend the axial field. If bending the axial magnetic field
absorbs more energy than liberated by the sausaging motion, the plasma is stabilized. The
axial field stabilizes the plasma in a manner analogous to a steel reinforcing rod embedded
in concrete. The other method for stabilization, a close-fitting conductingwall, works be-
cause image currents induced in the wall by the sausage motion produce a magneticfield
which interacts with the plasma current in such a way as to repel the plasma away from the
wall.

10.7.2Qualitative examination of the kink instability

The axial magnetic fieldBzcombined with the azimuthal magnetic fieldBθproduced by
the plasma current results in a magnetic field that is helical. This helical magnetic field is
susceptible to the helical kink instabilities sketched in Fig.10.7. At the concave parts of
the plasma surface there is a concentration of the azimuthal field resulting in a magnetic
pressure that increases the concavity. Similarly, at the convex portions of the surface, the