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The simplification of the method proposed in GS and implemented here lies in the reduction to a 1d integration, made possible through the use of the scalar approximation and an isotropic distribution. However we can attempt to estimate the anisotropy - i.e. the random velocities parallel and perpendicular to the magnetic field - and interpret the result as two temperature components
and
. Here we describe the estimation.
The
element of the measured pressure tensor
can be expressed
 |
(4.23) |
which can be decomposed in terms of the unit magnetic field vector
in the case of a gyrotropic distribution:
 |
(4.24) |
The trace of
is then
 |
(4.25) |
Finally the measured anisotropy
is found as
 |
(4.26) |
We make the assumption that this measured anisotropy is an approximation to the underlying anisotropy and so we can partition the corrected temperature
according to:
 |
(4.27) |
with
 |
(4.28) |
As a check we rotate
into a field-aligned frame such that:
In practice the off-diagonal terms are not identically zero and we use the ratio of these to the diagonal terms as an error check. Additionally
provides a second check.
Next: Estimation parameters
Up: The algorithm
Previous: Adding high energy moments
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Steve Schwartz
2005-03-26