PEPE Calibration ---------------- ---------------- Overview: ========= The PEPE instrument produces four types of science data: Electrion (ELC), ion singles (ION), ion mass over charge (MQ) and ion time of flight spectra (TOF). This document describes methods of calibrating and converting these data to physically meaningful quantities. Ion logicals spectra are also produced, but are designed to monitor the instrument's time-to-digital converter (TDC) and help correct for dead time effects. As a result, uncalibrated counts or counts per second are the natural units for logicals, and logicals are not covered by this document. Calibration of PEPE data consists of two steps. First, background and instrumental artifacts should be removed or corrected for. This gives the particle flux within a given energy-angle passband. Second, this flux is converted to physical units (e.g. phase space density). In some cases, it is not possible to convert flux to physical units without making a priori assumptions (e.g. of the ion mass to charge ratio.) In these cases, the data should be analyzed by calculating model spectra, converting the model spectra from physical units to counts per second, and varying parameters to obtain the best fit to the data. Sources of calibration values: ============================== The PEPE instrument, and the entire DS1 project, was focused on developing and validating new and inovative technology, with science as a secondary and extended mission goal. As a result of this focus, the short development schedule and limited funding, there were minimal pre-flight calibrations of the PEPE instrument. These calibrations established the functionallity of the instrument, verified the location and shape of the eneryg-angle passbands, and provided some data on the locations of time-of-flight peaks. Pre-flight calibrations did not, however, provide useful data on the instrument's absolute sensitivity. To supplement the pre-flight calibrations, this document relies on flight data and numerical modeling of the instrument. The flight data include the instrument's initial checkout (ICO) period, and measurements immediately before and during the Borrelly encounter. The numerical modeling consist of Monte Carlo ray tracing of the instrument optics. Scattering in the TOF entrance foil was modeled using both fits to laboratory data and simulations using the TRIM [ref Ziegler] software package. Both techniques give similar results for the location and amplitude of TOF peaks, but disagree in the details of the line shape. During the ICO period the spacecraft was within 250 R_E of the Earth. This allowed an intercalibration between PEPE and instruments on the ACE and WIND spacecraft. During ICO, PEPE was operated with a post-acceleration voltage of 8 kV. During the Borrelly encounter, the instrument was operated with a 11 kV post-acceleration voltage. This has a significant affect on the TOF and MQ spectra (improving resolution and sensitivity) The change in post- acceleration voltage should not affect the ION spectra. As a result, ICO are used the geometric factor for ION data but not the MQ and TOF data. MQ and TOF calibration values are derived from numerical modeling and from comparisons between ION and MQ spectra during the encounter. In addition, pre-encounter solar wind data were used to determine the azimuthal point spread function of the ION data. Background Subtraction: ======================= In most of the Borrelly data, zero volts were applied to electrostatic analyzer during energy steps 60-63. When the spacecraft's ion propulsion system was in use, zero volts were applied during energy steps 55-63. This provides a direct measure of background, e.g. from penetrating energetic particles, at every azimuth and elevation. Note that PEPE's ion sensor has variable-size azimuth pixels. This results in different background levels in each azimuth pixel. Ion ION point spread function: ============================== The ion ION data are energy-angle spectra of all measured start counts. As ions enter the time-of-flight system, they pass through a ultra-thin carbon foil. Although necessary to produce secondary electrons (and resulting start signals), the foil causes the ions to scatter. Some fraction of the ions scatter enough to miss the stop detector and hit a start pixel. This causes an additional start count in an incorrect azimuthal pixel. To first approximation this point spread function may be considered isotropic. This allows to spectra to be corrected by: Counts(corrected, az=i) = Counts(uncorrected, az=i) - b * Sum(j=0,15)[ Counts(uncorrected, az=j)] * AZ_width(az=i) / 360 The current, best estimate of b is given in table 1 and az is the azimuthal width of the pixel. Note that this value of b was calculated using solar wind protons. Although f is a function of ion species and energy, no other values are currently avaliable. TOF repeated pattern noise: =========================== The PEPE TOF spectra contain repeated pattern noise, with a 16 bin period. The instrument computes time of flight using a clock with 12 nanosecond ticks and an electronic vernier which provides 16, approximately 0.75 picosecond sub-ticks within each clock cycle Due to irregularities in the electronic vernier, the time-of-flight spectra contain repeared pattern noise, with a 16 bin period. This repeated pattern may be represented as Counts(uncorrected,i) = Counts(actual,i) * P(i MOD 16) P may be determined from the data by analyzis of TOF bins 512-1023. These bins contain either the exterme, low amplitude wings of low-mass species, or heavy ions such as Xe from the ion propulsion system. In either case, no real structure is present on scales of order 16 bins or shorter. These data are averaged over 16 bins to create a coarse, 64-bin spectrum with no repeated pattern noise. The full resolution data are then modeled as a linear interpolation of the coarse spectra times P(i MOD 16), and finding the 16 values which give the best, chi^2 fit to the data. Applying this process to the 21 spectra obtained within 10,000 of the Borrelly closest approach gives the values in table 1. Conversion of counts per second to phase space density: ======================================================= For ELC, ION and MQ data, counts per second may be converted to phase space density according to the following equation = Counts(i) * (m/q)^2 / (2 * tau * eta * G * E(i)^2) Where is the average phase space density within energy/angle passband i, Counts(i) are the measured counts, m and q are the mass and charge of the species, tau is the integration time, eta is the efficiency of detecting a particle, G is the instrument's geometric factor, and E is the energy at the center of the passband. Table 1 gives tau at both instrument telemetry rates. Tables 1, 2 and 3 give G for ELC, ION and MQ/TOF data. Since azimuth/elevation bins cover different solid angles, G is a function of azimuth and elevation. Table 1 gives normalized ELC and ION geometric factors (i.e. with units of cm^2-eV/eV) while Tables 2 and 3 give the solid angle as a function of elevation (for ELC) and elevation and azimuth (for ION). The geometric factor for ELC and MQ/TOF are estimated based on numerical modeling, while the geometric factor for ION data is calculated from IOC flight data and the assumption of eta=1. For ELC, the correct value of eta is not known, but could be calculated from ICO flight data and comparisons to WIND and ACE observations. For MQ/TOF data, eta is a strong function of species (see below.) For ION data, eta should not depend on species. For ELC data there are no difficulties converting counts to phase space density, since electrons are the only species measured. For ION, MQ and TOF data, several species may contribute to the counts in a given passband. As a result, m, q and eta are not known a priori. The MQ data represent counts selected on the basis of time-of-flight value. They probably, but not necessarily, represent counts from single species (or several species with similar mass to charge ratios) and may or may not include all counts from that species. These data may be converted to phase space density, but this may result in some artifacts. In contrast, the TOF data is summed over energy, making it impossible to convert to phase space density, while the ION data contain no composition information. These data are best analyzed by using a model velocity distribution to calculate generating model counts from Counts(model,i) = (2 * tau * eta * G * E(i)^2) * / (m/q)^2 and fitting the model to the data. Efficiency as a function of species has been calculated from numerical modeling and from comparisons of ION and MQ spectra obtained during the Borrelly encounter. Table 2 lists the estimated efficiencies and whether they are flight or numerical estimates. All valuse are for low energy (i.e. E << 11 keV) ions. Location of peaks in TOF spectra: ================================= Based on pre-flight calibrations and simulations, the location of a time-of-flight peak is approximately TOF(bin) = 70*(m/q)^0.55*(11/(11+E))^0.5 where m/q is the mass to charge ratio and E is the energy of the ion in keV. This applies to "straight through" peaks, i.e. ions which exit the start foil with a no charge. In the Borrelly data there is no clear evidence of LEF peaks (i.e. peaks from ions which exit the foil with a positive charge) with the exception of protons. There is a clear, negative, water group peak (i.e. from ions which exited the foil with a negative charge.) No analytic expressions for the LEF and negative peaks are available at this time. ------------------------------------------------------------------------- Table 1. PEPE calibration values ------------------------------------------------------------------------- Name Symbol Value Units ------------------------------------------------------------------------- ION PSF constant b 0.00055 TOF pattern noise P(0) 0.566 P(1) 1.246 P(2) 1.075 P(3) 0.755 P(4) 0.627 P(5) 0.860 P(6) 0.652 P(7) 0.827 P(8) 0.849 P(9) 0.947 P(10) 0.892 P(11) 1.237 P(12) 1.137 P(13) 1.149 P(14) 1.131 P(15) 1.403 Integration time,50 bps tau(50) 572.4 ms Integration time,1 kbps tau(1000) 28.62 ms Geometric factor, ELC G(ELC) 4.5e-3 cm^2-eV/eV Geometric factor, ION G(ION) 8.6e-4 cm^2-eV/eV Geometric factor, MQ/TOF G(MQ/TOF) 6.7e-3 cm^2-sr-eV/eV ----------------------------------- Table 2: ELC solid angles ----------------------------------- Elevation Solid angle [sr] 0,3 0.51 1,2 0.60 ------------------------------------------------------ Table 3: ION solid angles ------------------------------------------------------ Azimuth Elevation Solid angle [sr] 0-3 0,7 0.030 0-3 1,6 0.034 0-3 2,5 0.037 0-3 3,4 0.038 4 0,7 0.120 4 1,6 0.135 4 2,5 0.145 4 3,4 0.150 5-7 0,7 0.240 5-7 1,6 0.270 5-7 2,5 0.295 5-7 3,4 0.305 ----------------------------------------------------------- Table 4: Estimated TOF efficiency ----------------------------------------------------------- Species Value Source ----------------------------------------------------------- H+ 0.250 Flight C+ 0.139 Simulation N+ 0.106 Simulation O+ 0.061 Simulation "water group" 0.071 Flight