As is well known, the smallness of the toroidal magnetization parameter, , ensures that the dominant parallel
viscosity tensors,
and
, take the socalled ChewGoldbergerLow forms [11,29]:
where
. Incidentally, it is clear from Equation (2.60) that the parallel viscosity tensor in the classical closure scheme does indeed take this form.
Now, if
takes the ChewGoldbergerLow form then
These results follow because
.
Furthermore,
where, in Cartesian coordinates,

(2.157) 
and use has been made of the fact that
is a symmetric tensor. In fact, it can be shown that [19]

(2.158) 
Hence, we deduce that
Making use of Equation (2.150), we obtain

(2.160) 
However, if
takes the ChewGoldbergerLow form then
,
because
. It follows that [32,34]

(2.161) 
Likewise, if
takes the ChewGoldbergerLow form then

(2.162) 