Table 5.1 gives estimates for the values of the various parameters that characterize the rescaled reduced drift-MHD model, (8.16)–(8.20), in a low-field and a high-field tokamak fusion reactor. (See Chapter 1.) These estimates are made using the following assumptions: (low-field) or (high-field), , , (where and are the deuteron and triton masses, respectively), , , , (where is the minor radius of the plasma), , , , and . It is clear from Table 5.1 and Equations (8.25)–(8.34) that all of the parameters appearing in the rescaled, reduced, drift-MHD equations are less than unity, in accordance with Equation (8.47), provided that the radial width of the magnetic island chain that develops in the inner region exceeds a few centimeters.

The orderings and are a direct consequence of the fact that conventional tokamak fusion reactors have large aspect-ratios (i.e., ), and confine low- plasmas (i.e., ). As will become apparent, the ordering ensures that the island chain is sufficiently wide that ion acoustic waves propagating parallel to the magnetic field are able to smooth out any variations in the normalized plasma pressure, , around magnetic flux-surfaces [9]. The orderings , , and ensure that the island chain is sufficiently wide that the perpendicular diffusion of magnetic flux, momentum, and energy are not dominant effects in the rescaled, reduced, drift-MHD equations. Finally, the ordering ensures that the island chain is sufficiently wide that parallel energy transport smooths out any variations in the normalized plasma pressure, , around magnetic flux-surfaces [3].

Finally, suppose that

(8.48) |