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Spacecraft moments: introduction

Chapters 2-4 are adapted from Geach et al. (2004)

The space physicist - interested in the moments of the electron distribution around the Earth - must strike a balance between the advantages and disadvantages of on-board calculations of the moments. Under most circumstances there is insufficient telemetry to transmit samples from the distribution function itself at a high time resolution, but there is ample bandwidth to transmit the moments, which encode basic information about the distribution in just a few numbers.

Moments calculated on-board spacecraft typically over- or under-estimate the values of the `true' moments, because they convolve effects caused by the presence of a potential (from the spacecraft itself) and lower and upper energy truncation imposed by the detector. Furthermore, the plasma environment determines the formation of photo- and secondary electrons, which can return to the spacecraft and enter the detector, therefore contaminating the measured moments. Conversely, full-distribution telemetry can be treated on the ground, using more sophisticated computation than is available on the spacecraft.

Generation of spacecraft potential is determined by the balance of the currents flowing away from the craft carried by liberated electrons, and the incident electrons and ions from the ambient plasma. The value of the potential is therefore determined by the plasma environment, specifically the density and temperature (Pedersen (1995), Escoubet et al (1997)). Attempts have been made to dynamincally control the potential, such as ASPOC (Active Spacecraft POtential Control) on three of the Cluster spacecraft (Riedler et al (1997)), which aims to stabalise the potential by emitting a positive (indium) ion beam. Devices such as ASPOC can limit the build up of potential (which can reach values of 70 V) to just a few Volts (Schmidt et al (1995)), and in general aim to constrain the potential to less than 10 V (Torkar et al (2001)). While the charging of the spacecraft can be limited, no real detector is free from the constraints of a finite energy range and calibration defects, the latter of which are very difficult to correct after convolution by the on-board calculation. All on-board calculated moments must therefore be treated with caution.

Song et al (1997) present the concept of a perfect plasma detector, which is free from calibration defects, for which the uncertainties in the on-board moments are solely caused by the spacecraft potential, a truncated energy range and the presence of secondary and photo-electrons. Those authors indicate that in the case of electrons, the lower energy cut-off should be calculated as the detector's nominal lower energy limit minus the spacecraft potential, although they present results for a null potential. Génot and Schwartz (2004, hereafter GS) further this idea of a perfect detector and present a method to disentangle the effects of potential and energy range truncation using a non-linear numerical routine (though it is imporatant to note that it is not possible to correct for the effects of contamination of secondary electrons - for a discussion on this topic see Szita et al (2001)). GS demonstrate that the measured moments can be expressed as functions of the true moments and the spacecraft potential, where the true moments are those which would be measured by a perfect detector. We implement the technique proposed by GS such that, given a set of measured moments and knowledge of the spacecraft potential and detector limits, the true moments can be recovered; we call these the corrected moments.

The magnitude of the difference between the on-board and corrected moments is a function of both environment and potential. GS show that the solar wind is a region where the moments are seriously affected. For a potential ranging from zero to 10 Volts, the density can be under-estimated by 60% for low potentials to over-estimation of 75% for high potentials. In general the other moments are over-estimated. Those authors make the interesting point that there exists a critical potential for which the on-board density moment equals the corrected one (see GS and Salem et al (2001)), though no such regime exist for the other moments for typical plasma environments. In other regions such as the magnetosheath and magnetosphere, the moments are less severely compromised as in the solar wind, but the effects there are by no means negligible, with up to a 40% under-estimation of the density in the magnetosheath and 10% in the magnetosphere during nominal operating conditions. Fundamentally the presence of a potential affects the width of the distribution function, such that for a naturally broad (i.e. hot) distribution, the extra broadening caused by spacecraft effects is slight; the opposite is true for cool distributions.

A PEACE (Plasma Electron and Current Experiment) instrument is flying on each of the four Cluster spacecraft, each one capable of measuring the three dimensional velocity distribution of electrons in a range from 1 eV to 25 keV. The energy range is divided into 88 levels - in general the lower energies measured by the LEEA sensor head, and the higher energies by the HEEA sensor head, mounted on the opposite side of the spacecraft. Every half-spin (about 2 seconds), PEACE calculates moments of the electron distribution. Under normal-mode telemetry, these data are transmitted to the ground, together with pitch angle distributions and a low energy distribution. Under burst-mode, 3-dimensional distribution data can be transmitted.

Encoded into the moments are quantities related to the physical characteristics of the ambient plasma such as density, temperature and velocity. The telemetered moments are perturbed by the spacecraft potential, and this must be corrected before the Maxwellian values can be inferred. QTMC performs this correction, and also compensates for unsampled energy ranges and photoelectron contamination.


next up previous contents
Next: Definitions Up: qtmc_manual Previous: QTMC - User guide   Contents
Steve Schwartz 2005-03-26