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Subsections

Calibration

Energy look-up tables

The PEACE energy range is split into 88 bins, characterised by the central energy of a bin, together with its width $\Delta E$. The exact energy levels of the $i$th level $(E_i \pm \Delta E_i/2)$ to be used are specific to both LEEA and HEEA and to each spacecraft. Further more, the instrument can operate in any one of three modes (LAR, MAR & HAR - Low, Medium and High Angular Resolutions), which also determine the exact energy to use (see Figure 5.1). To account for this we read in the telemetry value (from 0 to 89, `89' designating `off') and look-up (in hard-coded tables in ./src/truncated_moment_corrector.c) the correct lower or upper edge energy of the bin to apply in the calculation.

Overlap moments separation and sum

The overlap moments (L1L2 from LEEA and H1H2 from HEEA) are moments from the coincident energy ranges of the two sensors. Their raw format is slightly different to other data series we encounter because the data is tagged every half-spin. This means that, for LEEA say, L1 is data taken in the first half of the spin and L2 is data taken in the second half of the spin. In order to get this into a concurrent format, we must separate L1 and L2 and sum them. The result of this will be a data sequence which sums over the whole spin.

Some care must be taken at this stage. An identifier (the spin mode) indicates whether the data record comes from the first half or second half of the spin (note that these tags indicate the start of data, i.e. L1 is the start of the spin, and L2 is exactly halfway through the spin). With this information we can create a mask to subset the data sequence into two child sequences - one containing just the L1 data, and the other just the L2 data. We decide as a convention that all our data are to be spin-centred, that is, the time-tag will be placed half-way through a spin interval. L2 is already at this position, so we shift the L1 tags half a spin spacing (2 seconds) forward in time. Now the tags line up, we can simply add matching L1 and L2 tags together. This gives us the final L1+L2 sequence which conforms to all the other PEACE data we have. Note that gaps (intervals greater than 4 seconds without tags), are removed.

Figure 5.1: The specific energy level to be used is determined by the operating mode (LAR, MAR or HAR), the bin index and whether we wish to use the lower or upper edge of the bin. In the above example, level 04, the difference between operating modes can have an effect of several eV. At the low energy end of the integration this can have a non-negligible effect on the corrected moments.

Image levels

Gain correction factors

All PEACE on-board moments data is subject to a `correction factor' of 2 which is a multiplactive factor applied to all the moments as they pass through the routine. Furthermore, there is a time-dependent gain correction factor which applies to the LEEA and HEEA sensors for each spacecraft which is a further factor which varies on a time-scale of approximately 24 hours. The user supplies the location of the calibration files which must be in the following whitespace delimited format:

UT Start Time, UT End Time, GF Fiddle Factor, GF version no.
1930-01-01T00:00:00.000Z 2001-02-10T06:44:00.000Z 0.926227861 01_(00g01)
2001-02-10T06:44:00.000Z 2001-02-11T00:00:00.000Z 0.926227861 02_(01g01)
etc.


and have the names CLN_L(H)EEA.cal, where N is the spacecraft number 1-4. These are expected to reside in the location given by the user. The correct calibration file is loaded given the input arguments.

Frame transformation

The moments as seen by PEACE are measured in a frame (hereafter the P-frame) in which the x-axis ($X_p$) is aligned with the HEEA sensor head and $Z_p$ is the spin-axis. A schematic representation of the principle PEACE geometry is shown in Figure 5.2. This system is different from the engineered `body coordinates' (B-frame). In the B-frame the $X_b$ is the spin axis and $Y_b$ is 26.2 degrees antispinward of the Sun sensor. We wish to output our data in the physically informative GSE frame, so we must use attitude (AUX) data with the knowledge of the geometry of the various measurement frames to transform from the spacecraft to GSE frame.

Figure 5.2: Schematic showing the principle geometry of the PEACE experiment.

Image coords3

In general, a tensor ${\bf A}$ can be transformed to a new frame ${\bf A}^{\prime}$ by:
\begin{displaymath}\bf A^{\prime}=\bf R\bf A\bf R^{\rm T} \end{displaymath} (5.1)


where ${\bf R}$ is a transformation matrix. The transformation from the raw P-frame to the GSE-frame consists of four steps. Firstly there is a 60 degree rotation about $Z_p$ to take $Y_p$ into $Y_b$, described by:

\begin{displaymath}
\left[ \begin{array}{ccc}
\cos(60) & -\sin(60) & 0 \\
\sin(60) & \cos(60) & 0 \\
0 & 0 & 1
\end{array} \right]
\end{displaymath}


Next there is a 90 degree flip to take $X_p$ into $X_b$ - this is a 90 degree rotation about $Y_b$:

\begin{displaymath}
\left[ \begin{array}{ccc}
0 & 0 & 1 \\
0 & 1 & 0 \\
-1 & 0 & 0
\end{array} \right]
\end{displaymath}


Now we are in the B-frame, we must transform into the GSE frame. The inputs of latitude $\lambda$ and longitude $\phi$, and knowledge of the Sun's azimuthal position at PEACE's 0 degree (22.4 degrees) allow construction of two transformation matrices which deal with the spin axis orientation:

\begin{displaymath}
\left[ \begin{array}{ccc}
\cos(\lambda)\cos(\phi) & \beta(\s...
...cos(\phi)) & -\beta\cos(\lambda)\sin(\phi)
\end{array} \right]
\end{displaymath}


and the offset between $Y_b$ and the PEACE 0 degree azimuthal:

\begin{displaymath}
\left[ \begin{array}{ccc}
1 & 0 & 0 \\
0 & \cos(22.4) & \sin(22.4) \\
0 & -\sin(22.4) & \cos(22.4)
\end{array} \right]
\end{displaymath}


The normalisation factor $\beta$ is
\begin{displaymath}\beta = (\sin^2(\lambda) + \cos^2(\lambda)\sin^2(\phi))^{-1/2}\end{displaymath} (5.2)


This choice of factor accounts for the constraint that the $t=0$ $Y_p$ axis is 22.4 degrees spinward of $Y_b$ and must have a positive $X_{\rm {GSE}}$ component.

Applied in the above sequence, the above matrices transform a tensor or vector from the raw P-frame into the desired GSE frame. All outputs from the solver are in GSE coordinates.


next up previous contents
Next: Useful information Up: qtmc_manual Previous: The algorithm   Contents
Steve Schwartz 2005-03-26