### 15.2 The mean field reference system

The mean field reference system (see Figure 103) reduces the problem of cross-talking between the
components, due to the fact that the interplanetary magnetic field is not oriented like the axes of the
reference system in which we perform the measurement. As a consequence, any component will experience a
contribution from the other ones.
Let us suppose to have magnetic field data sampled in the RTN reference system. If the large-scale mean
magnetic field is oriented in the direction, we will look for a new reference system within the RTN
reference system with the axis oriented along the mean field and the other two axes lying on a plane
perpendicular to this direction.

Thus, we firstly determine the direction of the unit vector parallel to the mean field, normalizing its
components

so that is the orientation of the first axis, parallel to the ambient field. As second direction
it is convenient to choose the radial direction in RTN, which is roughly the direction of the solar
wind flow, . At this point, we compute a new direction perpendicular to the plane

Consequently, the third direction will be

At this point, we can rotate our data into the new reference system. Data indicated as in
the old reference system, will become in the new reference system. The transformation is
obtained applying the rotation matrix

to the vector , i.e., .