It is helpful to define the species- toroidal magnetization parameter,
Drift and Transport Orderings
the species- poloidal magnetization parameter,
and the (modified) species- collisionality parameter,
As is apparent from Table 2.4, these dimensionless parameters are all
much less than unity for both electrons and ions in a tokamak fusion reactor.
In the following, we shall adopt the following fundamental ordering assumptions :
Equation (2.113) is known as the drift ordering [18,29], and serves to rule out the rapid plasma motions associated
with ideal magnetohydrodynamical instabilities . Equation (2.114) is known as the transport
ordering. According to this ordering, any time dependence of plasma quantities is due to the action of perpendicular
transport, viscous heating, and frictional heating.
The drift and transport orderings, combined with the analysis contained in the following two sections,
Equations (2.103)–(2.109) yield
where we have written 
In the previous five equations, we have neglected terms that are
smaller than the leading-order terms, while retaining terms that are
, which is only
. As is shown in Table 2.4, the inequality
satisfied for electrons in a tokamak fusion reactor, but is only barely satisfied for ions.
factors in the previous equations are there to
remind us that the terms they precede are
smaller than the leading-order terms.
Finally, it is helpful to define