Normalization of Neoclassical Fluid Equations

(2.354) | ||

(2.355) | ||

(2.356) | ||

(2.357) | ||

(2.358) | ||

(2.359) | ||

(2.360) | ||

(2.361) |

It is helpful to define the following dimensionless parameters:

Here, is the ion magnetization parameter defined in Equation (2.110), whereas is defined in Equation (1.23). Table 2.6 gives estimates for the dimensionless parameters defined in Equations (2.363)–(2.369) for a low-field and a high-field fusion reactor. As before, these estimates are made assuming that , , and .

Our neoclassical fluid equations, (2.326), (2.331), and (2.338)–(2.340), can be written

Here, the factors , , , et cetera, indicate that the terms they precede are larger or smaller than terms preceded by no factor by the dimensionless parameter contained within the square brackets.According to Table 2.6, the dominant parallel diffusivity term in the electron energy conservation equation, (2.373), yields

In other words, the parallel electron energy diffusivity in a tokamak fusion reactor is sufficiently large to ensure that the electron temperature is uniform on magnetic flux-surfaces. Likewise, according to Table 2.6, the dominant parallel diffusivity term in the ion energy conservation equation, (2.374), gives In other words, the parallel ion energy diffusivity in a tokamak fusion reactor is sufficiently large to ensure that the ion temperature is uniform on magnetic flux-surfaces. According to Table 2.6, the dominant terms in the plasma equation of motion, (2.371), yield In other words, the plasma in a tokamak fusion reactor exists in a state of approximate force balance. The previous equation suggests that . When combined with Equations (2.375) and (2.376), this relation gives We conclude that the electron number density, the electron pressure, and the ion pressure are all uniform on magnetic flux-surfaces in a tokamak fusion reactor. According to Table 2.6, the dominant terms in the plasma Ohm's law, (2.372), yield where use has been made of Equations (2.377) and (2.378). Thus, we conclude that the plasma in a tokamak fusion reactor satisfies the so-called