The first term on the right-hand side of Equation (13.4) is the linear tearing stability index, . The second term is a stabilizing (i.e., negative) saturation term . The third term is a destabilizing (i.e., positive) term that is due to the loss of the bootstrap current within the magnetic separatrix of the island chain consequent on the flattening of the plasma pressure profile in this region . The fourth term is a stabilizing term due to magnetic field-line curvature [13,18]. The fifth term represents the stabilizing effect of the ion polarization current induced in the vicinity of the rational surface when the ion fluid is diverted around the island chain's magnetic separatrix [7,25,26,27]. The sixth and seventh terms are additional ion polarization terms that arise from the modified ion flow in the immediate vicinity of the island chain when the chain is subject to an externally generated electromagnetic torque [10,27]. The final term is due to the direct interaction between the island chain and the resonant magnetic perturbation .
It is convenient to rewrite Equation (13.4) in the formHere, , , and , where is the plasma minor radius. Moreover, , , , and are defined in Equations (12.23)–(12.26), respectively, whereas
Table 12.1 gives estimates for the various dimensionless parameters that characterize the right-hand side of the generalized Rutherford equation, (13.7), for the case of 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), , , , , , and . The plasma equilibrium is assumed to be of the Wesson type with , , and . (See Section 9.4.)