Figure 14.1 shows contours of the poloidal magnetic flux for a typical plasma discharge in the KSTAR tokamak [42].
It can be seen that there are a number of differences from the idealized tokamak pictured in Figure 1.5. The first main difference
is that the flux-surfaces in Figure 14.1 do not have circular cross-sections. In particular, the flux-surfaces are highly *vertically elongated*. It turns out
that this feature allows the toroidal plasma current driven in a tokamak discharge to be increased without violating the Kruskal-Shafranov
criterion. (See Section 1.10.) Hence, all modern tokamaks have strongly-shaped, vertically-elongated cross-sections. The second main difference is that the edge of the plasma is defined by a *last closed
magnetic flux-surface* that features a magnetic X-point (i.e., a hyperbolic null in the poloidal magnetic field). Plasma that crosses the last closed flux-surface is rapidly conducted along magnetic
field-lines, in a thin *scrape-off layer*, to divertor plates located below the plasma. The purpose of this feature is to mitigate the interaction of the
plasma with the plasma-facing components, and, thereby, help limit the flux of impurities into the plasma [44]. Hence, all modern tokamaks have magnetic X-points. Given that the poloidal magnetic field-strength
at the X-point is zero, the safety-factor value on the last closed flux-surface is infinite. [See Equation (1.76).] Experimentally, it is found that the safety-factor value
on the magnetic flux-surface that encloses 95% of the poloidal magnetic flux enclosed by the last closed flux-surface, which is known as , plays an
analogous role to the edge safety-factor value, , in a tokamak without a magnetic X-point [64]. (See Section 14.4.) Thus, the rule of thumb for safe operation,
,
is replaced by
. (See Section 1.9.)
In the type of highly-shaped plasma equilibrium pictured in Figure 14.1, tearing modes with the same toroidal mode number, but different poloidal mode numbers, are coupled together [13,23]. Somewhat confusingly, this effect is known as *toroidal mode coupling*. Toroidal mode coupling allows magnetic island
chains resonant on different rational surfaces within the plasma to interact. The interaction is expected to be mutually destabilizing [23]. However, sheared plasma
rotation acts to prevent such interaction. (See Chapter 14.)