next up previous contents
Next: Calibration Up: The algorithm Previous: Temperature anisotropy estimation   Contents

Estimation parameters

We calculate three estimation parameters which describe how much the measured on-board moments were over- or under-estimated:
\begin{displaymath}
r_N = \frac{N_m - N_f}{N_f}
\end{displaymath} (4.29)


\begin{displaymath}
r_V = \frac{V_{m} - \vert{\bf V}_f\vert}{\vert{\bf V}_f\vert}
\end{displaymath} (4.30)


\begin{displaymath}
r_T = \frac{{\rm Tr}({\bf p}_m)/3N_mk - T_f}{T_f}
\end{displaymath} (4.31)


\begin{displaymath}
I_e = \sqrt{r_N^2 + r_V^2 + r_T^2}.
\end{displaymath} (4.32)

These parameters trace the effect that various environments have on the measured moments. A more general estimation parameter $I_e$ is yielded by the Pythagorean combination of the three parameters above. Generally $I_e < 1$ (that is, $<60$% 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 $I_e$ 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, $\Phi_{{\rm crit}}$, for which the ratio $r_N$ 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 $\Phi_{{\rm crit}}$ such that, despite truncation and the presence of a potential, the density integration over $f(v)$ returns the correct value.


next up previous contents
Next: Calibration Up: The algorithm Previous: Temperature anisotropy estimation   Contents
Steve Schwartz 2005-03-26