Introduction

All of the analysis contained in Chapters 313 is premised on the assumption that the geometry of a tokamak plasma can be adequately approximated as a periodic cylinder. In this final chapter, we shall move beyond this simplistic approach, and take into account the fact that tokamak plasmas are actually toroidal in shape. Moreover, as illustrated in Figure 14.1, the poloidal cross-section of the equilibrium magnetic flux-surfaces in a typical tokamak plasma are not circular, as is assumed in the cylindrical model. Instead, they are highly elongated in the vertical direction, and somewhat triangular. Finally, the outermost closed magnetic flux-surface in a tokamak plasma possesses a magnetic X-point (see Figure 14.1), which implies that the corresponding value of the safety-factor is infinite. (See Figure 14.2.) The aim of this chapter is to explore how the true geometry of the equilibrium magnetic flux-surfaces in a tokamak plasma affects the dynamics of any tearing modes to which the plasma is subject.