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We calculate three estimation parameters which describe how much the measured on-board moments were over- or under-estimated:
 |
(4.29) |
 |
(4.30) |
 |
(4.31) |
 |
(4.32) |
These parameters trace the effect that various environments have on the measured moments. A more general estimation parameter
is yielded by the Pythagorean combination of the three parameters above. Generally
(that is,
% correction on all moments). As mentioned above, the amplitude of the over- or under-estimation is determined by environment, however their general behaviour is also a function of spacecraft potential (which itself is somewhat influenced by the characteristics of the ambient plasma). GS describe how the estimation parameters vary for a range of potentials in three plasma environments: the solar wind, magnetosphere and magnetosheath. Those authors conclude that the moments are affected worst in the solar wind, where
can exceed 60%. In the other regions the moments are affected to a lesser extent, but in general still require correcting. GS and Salem et al (2001) also describe the existence of a critical potential,
, for which the ratio
is zero, and no correction is required (no such critical point exists in general for the temperature or velocity). In this circumstance the energy range truncation (resulting in an under-sampled distribution) is compensated by the potential broadening caused by
such that, despite truncation and the presence of a potential, the density integration over
returns the correct value.
Next: Calibration
Up: The algorithm
Previous: Temperature anisotropy estimation
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Steve Schwartz
2005-03-26