Accessing Spectral Data from the ARC Plasma Analyzers Aboard the Pioneer 10 and 11 Spacecraft P. R. Gazis, NASA Ames Research Center, Moffett Field, CA 94035, (650) 604-5704, pgazis@mail.arc.nasa.gov Contents 1.0 Introduction 2.0 Instrument Description 2.1 Instrument Response Function 3.0 Data Processing: Historical Overview 4.0 Pioneer Spectral Files: Format and Organization 4.1 Spectral Header 4.2 MFM Data Records 4.3 FSM Energy Cycle Header Records: 4.4 FSM Data Records 5.0 Pioneer Spectral Files: Usage 5.1 Extracting individual spectra 5.2 Converting Earth received time to spacecraft ephemeris time 5.3 Transforming from spacecraft co-ordinates to RTN co-ordinates 5.4 Converting Energy Step Numbers to E/q or velocity values 5.5 Converting instrument units to currents and fluxes 5.6 Identifying noise and bad spectra 5.7 Deconvolving the Instrument Response Function 1.0 Introduction NASA's Pioneer 10 spacecraft, launched in 1972, was the first spacecraft to encounter the planet Jupiter (1973) and until the end of its mission in 1997, was the farthest man-made object from the Sun. Data from this spacecraft span more than 2 solar cycles and 65 AU. The Pioneer 11 spacecraft, launched a year after Pioneer 10, reached Jupiter in 1974 and was the first spacecraft to encounter Saturn (1979). By July 1995, exhaustion of the spacecraft power supplies had reached the point that most of the scientific instruments could no longer be operated, but over the preceding 21 years, Pioneer 11, like Pioneer 10, has provided a very large body of interplanetary data. The ARC plasma analyzers aboard the Pioneer 10 and 11 spacecraft measure the velocity distribution, or 'spectra', of solar wind plasma in a velocity range (protons) between approximately 138 - 1858 km/s. Bulk plasma parameters, such as velocity, density, and temperature are obtained by a least-squares fit of a convected spherical Maxwellian to this velocity distribution. Plasma data from Pioneer 10 and 11 has been used to study the global structure and short-and long-term variations of the solar wind for comparison with existing models of solar wind dynamics, evolution, and the interaction of the solar wind with the interstellar medium, to examine the consequences of this structure and variability for the behavior of the solar wind termination shock, and to examine the energy balance of the solar wind. 2.0 Instrument Description The plasma analyzers aboard Pioneers 10 and 11 each contain two separate instruments: Detector A and Detector B. Each of these detectors consists of an entrance aperture, followed by a nested pair of concentric 90 degree quadraspherical plates and an array of sensors: channeltrons for Detector A and electrometers for Detector B. Particles that pass through the entrance aperture will move on Keplerian orbits in the electrostatic field produced by applying a voltage across the plates. Most of these particles will impact one of the plates and be lost, but particles with a suitable range of energy/charge (E/Q) and arrival direction will survive to pass through the exit aperture, to be measured by the sensors. By varying the voltage difference, and hence the strength of the electrostatic field between the plates, a range of E/Q values can be covered for both positive ions and electrons. If this range of E/Q values is sufficiently large, the complete particle spectrum will be measured. The incident direction of the incoming particles is determined from the spacecraft roll angle and the response from the sensors. The spacecraft spin axis is pointed towards the Earth, and thus approximately towards the Sun. The multiple sensors resolve directions parallel perpendicular to the spacecraft's spin axis while the rotation of the spacecraft provides a scan through a full 360 degrees of azimuth. In this way, the instrument can provide direct observation of the three-dimensional velocity distribution of incident ions and electrons. The Pioneer plasma analyzers have several different modes of operation. These modes determine the particle species (ion or electron), energy range (high or low), and conditions (suppressed or unsuppressed) under which the incident plasma is measured. These modes of operation are described below: Ion versus electron mode. In the ion mode, both Detectors A and B are used to measure the incident ion flux. In the electron mode, Detector B is used to measure the incident electron flux. Due to noise and sensitivity limitations, electron measurements were of limited utility, and most measurements were made in the ion mode. High-energy versus low-energy mode. In high-energy mode, the detector voltage advances in 64 steps to measure particles with E/q between 99.5 and 8,000 volts for Detector A and between 99.4 and 18,000 volts for Detector B. In low-energy mode, voltage steps were designed to measure particles with lower E/q. Because the low-energy mode did not have sufficient range to encompass an entire solar wind velocity distribution, most solar wind measurements were made in high-energy mode. Suppressed versus unsuppressed. Detector B was equipped with a suppressor grid that could be biased to minimize the effects of secondary electron gain from the current collectors at some cost in sensitivity. After the spacecraft was launched, it was found that the advantages of increased sensitivity outweighed whatever advantages might be obtained by use of the suppressor grid, so the instruments were operated in the unsuppressed mode. The Pioneer plasma analyzers also have two commandable modes of data collection: maximum flux mode (MFM) and full scan mode (FSM). In the maximum flux mode the instrument steps through its E/Q steps, one step per spacecraft rotation, to determine the maximum flux, the collector (or target) number, and the azimuthal angle for which the maximum flux occurs for each E/Q step. In the full scan mode, the instrument makes one E/Q step per spacecraft rotation and returns data from as many angular sectors as the telemetry will allow, without regard to the direction of maximum flux. The plasma analyzers can return spectra for Detectors A or B. Each record of a Detector B spectrum consists of roll direction in the form of a sector number followed by measurements from the 5 electrometers. Each record of a Detector A spectrum consists of a sector number followed by the counts measured by channeltrons 1-13, 14-26, or 1-26 depending on details of the data collection mode. 2.1 Instrument Response Function Because the separation of the plates is finite, the analyzer accepts particles from a finite range of kinetic energies. The acceptance range also depends on the azimuth of the incoming particles. Standard analytic expressions admit computation of the range of acceptance angle and energy [e.g., Gosling et al., 1984]. For Detector B, the range of acceptance angles turns out to be approximately 14 degrees, and the energy acceptance range is about 35% of the central energy; the acceptance is somewhat narrower for Detector A. While the acceptance range of the Pioneer plasma analyzers is quite wide, the actual resolution of these instruments is distinct from, and much narrower than, the acceptance range. The ideal response of Detector B to a cold beam of plasma incident along the axis of the instrument is only non-zero over the energy range from 4% below to 5% above the central energy. This energy range corresponds to orbits that graze the inner and outer plates of the plasma analyzer. The instrument response function is a function of energy, roll angle (sector number), and polar angle (detector number). Each measured spectrum is a convolution between the instrument function and the actual velocity distribution of the incident plasma. 3.0 Data Processing: Historical Overview Data from the experiments aboard the Pioneer spacecraft was delivered to investigators in the form of experimenter data records (EDR data). This EDR data consisted of actual data from the relevant instrument interspersed with engineering data and timing information. EDR data from the Pioneer plasma analyzers was reformatted to produce reformatted EDR data (REDR files). The resulting REDR files were stored on magnetic tape and formed the primary archive of Pioneer plasma data. For MFM data, these REDR files contain one or more MFM data records for each instrument cycle. Each MFM data record contains a series of adjacent energy steps. When one or more adjacent steps are missing, a new record is begun for the next series of steps. Each record contains header information followed by the data for each energy step. The data for each energy step consist of the sector number and the counts of particles collected by each electrometer of detector B or by each CCM (continuous channel multiplier) of detector A. For FSM data, these REDR files contain several records for each instrument cycle. First, there is an FSM energy cycle header record which contains information about the cycle, including the number of energy steps the cycle contains. The succeeding records are FSM data records which contain data for the individual energy steps. Each FSM data record contains data for a single energy step and consists of a header with information about that energy step, followed by data for each roll direction, or 'slice', for which data were collected. The data for an individual 'slice' consists of the sector number and the counts collected by each target or each CCM. The REDR files also contained additional records that hold data condition indicators (DCI's). Each MFM or FSM data record in an REDR file is followed by an associated DCI record. The EDR and REDR data could not be read without specialized software specific to the Pioneer plasma analyzers. Interpretation of these files was further complicated by the many generations of computer technology, and the many changes in software and data processing standards that occurred over the 25-year lifetime of the Pioneer spacecraft. For this reason, a new format, known as 'spectral files', was developed in the late 1980's. These spectral files record all of the Pioneer spectra, along with the relevant engineering data associated with the Pioneer plasma analyzers in a compact format that can be read without specialized software. Due to limitations of data storage technology at the time of their creation, these 'spectral files' were originally written as 2-byte integer words in VMS binary format. These data have since been re-written as ASCII files. Now that the EDR tapes, REDR tapes, and their associated software are no longer maintained, these 'spectral files' constitute the primary archive of data from the Pioneer plasma analyzers. The Pioneer 10 and 11 spectral files serve a dual purpose. They were intended for use in data analysis, but they were also intended to serve as an archive. Because of this archival function, the content of the data was kept as close as possible to the content of the original EDR and REDR files. In particular, several possible processing steps were deliberately omitted. 1) Times are recorded in Earth received time (ERT) as they were on the original EDR tapes rather than spacecraft ephemeris time (SCET). 2) Attitude information is in spacecraft co-ordinates rather RTN co-ordinates. 3) Spectral files record the raw spectra in the original instrument units. No attempt has been made to account for Detector A gain factors, secondary electron gain in Detector B, and the instrument response function, or convert to units to cgs. 4) Every measurement of every spectrum is included. No attempt has been made to flag bad data or eliminate noise. 4.0 Pioneer Spectral Files: Format and Organization A Pioneer 10 or 11 spectral file consists of a 4-line file header followed by a succession of spectra. Each line of the header begins with a comment character, '%'. The first line contains the file name, the second line contains the version number, the third line lists the name of the relevant documentation file, and the fourth line is deliberately left blank. A typical file header is shown below: % File name: p10Spe1972_074_120a.txt % Version: 1.0 % Documentation in: B3SpectralFiles.txt % Each spectrum consists of two or more logical records. There are four types of logical records: spectral headers, MFM data records, FSM step headers, and FSM data records. An MFM spectrum consists of a spectral header followed by a single MFM data record that contains all of the data for every energy step in the spectrum. An FSM spectrum consists of a spectral header followed by successive pairs of FSM step header and FSM data records that correspond to successive energy steps of the spectrum. Each logical record consists of a succession of lines of text terminated by a carriage returns. The longest line of an FSM data record would consist of an energy step, a sector number, and 26 measurements (for CCMs 1-26) written as 28 5-digit integer words (140 characters plus an end-of-record character), so any line of any record can be read as a 150-element character array. 4.1 Spectral Header Each spectral header consists of a two-line record separator, followed by a header line, followed by two lines that contain a total of 21 or 22 words of spectral header information. Because the two-line record separator is unique to spectral headers, and spectral headers only occur at the beginning of a spectrum, it can also be used to identify the beginning of a spectrum. A typical spectral header is shown below: % ********************************************************************** % Record Separator: MFM mode, 47 steps ******************************* % Pioneer 10, Detector B, MFM mode, HE ion, 1972 341 00:24:27.850 ****** 274 1 6036 2600 2600 0 1 64 1 42 1 3 7 10 72 341 0 24 27 850 256 18 The first line of the record separator is a dummy line consisting of a comment character followed by a space and a string of '*'s. The second line of the record separator consists of a comment character, followed by the words 'Record Separator', followed by a description of the type of spectrum and either the number of lines in the spectrum if this is an MFM spectrum or the number of energy steps in the if this is an FSM spectrum. The header line consists of a comment character, followed by the spacecraft name, followed by a description of the type of spectrum and instrument operating mode, followed by the Earth received time (ERT) at the beginning of the spectrum. The first line of header data consists of 12 6-digit integer words that contain the first 12 words (words 0-11) of header information: Index Name Contents --------------------------------------------------------------------- 0 NWORDS Number of words in the record 1 SMODE Data collection mode: for MFM data - 1 for detector B 2 for detector A, CCM 1 - 13 only 3 for detector A, CCM 14 - 26 only 4 for detector A, CCM 1 - 26 inclusive for FSM data - -5 for detector B -6 for detector A, CCM"S 1 - 13 -7 for detector A, CCM"S 14 - 26) 2 --- Electronics temperature 3 --- High voltage power supply step, left bank of CCM's 4 --- High voltage power supply step, right bank of CCM's 5 ISUP Suppression ( 0 for no, 1 for yes ) 6 EMODE Ion or electron mode (0 for electron, 1 for ion) 7 --- Number of energy steps programmed 8 IHV High voltage (0 for off, 1 for on ) 9 NSTEPS Actual number of energy steps in the cycle 10 --- Integration period (number of sectors) 11 --- Number of half revolutions per step. The second line of header data consists of either 10 6-digit integer words for an MFM spectrum or 11 6-digit integer words for an FSM spectrum. These contain the final 9 or 10 (words 12-20 or 12-21) of the header: Index Name Contents --------------------------------------------------------------------- 12 ISTEP The number of the first step in the record 13 ISC Spacecraft number (10 or 11) TIME of receipt of the energy cycle segment: 14 IYR year (2-digits, but note that IYR <= 95)) 15 IDY day 16 IHR hour 17 IMIN minute 18 ISEC second 19 MSEC millisecond 20 --- Transmission rate in bits per second 21 --- Sector angle correction (in millidegrees) at the step with the peak count. Note that this word is only present for MFM spectra. 4.2 MFM Data Records Each MFM record consists of one header line followed by several lines of data in multi-column format. The header line consists of a comment character, '%' followed by words that describe the contents of each column of data. Each line of data consists of a succession of 5-digit integer words that contain the energy step number, followed by a sector number, followed by the counts or currents measured by the relevant detector (Detector A or B). A sample MFM data record is shown below: % EN SN t1 t2 t3 t4 t5 ************************************ 7 305 68 14 0 0 0 8 157 62 0 0 0 0 9 423 61 5 0 0 0 10 95 63 1 0 0 0 11 371 59 25 0 0 0 12 227 65 29 0 0 0 13 330 65 0 0 13 0 14 58 64 0 0 8 0 15 284 60 17 0 0 0 16 254 63 31 0 20 0 17 357 61 0 0 0 0 18 240 60 14 0 0 0 19 372 62 14 0 0 0 20 249 45 0 104 0 0 21 269 0 11 169 0 0 22 229 0 0 219 0 0 23 343 0 116 229 0 0 24 409 39 181 235 1 0 25 58 30 0 230 20 0 26 508 54 39 179 0 0 27 5 31 9 92 0 0 28 407 68 17 0 0 0 29 232 65 11 0 0 0 30 266 37 35 95 0 0 31 175 60 34 134 0 0 32 352 14 39 118 0 0 33 69 52 11 141 0 0 34 488 49 0 102 0 0 35 11 75 0 0 0 0 36 296 73 6 0 5 0 37 88 62 0 0 0 0 38 425 67 9 0 0 0 39 183 68 34 0 20 0 40 444 77 0 0 0 0 41 449 60 3 0 0 0 42 241 62 0 0 0 0 43 376 62 16 0 0 0 44 79 68 0 0 2 0 45 374 61 22 0 0 0 46 173 69 6 0 0 0 47 359 64 0 0 0 0 48 254 65 41 0 0 0 This MFM data record corresponds to the spectral header shown in section 4.1. It contains data from Detector for 47 energy steps between steps 7-48. The peak of this spectrum occurred in the vicinity of energy steps 24 (this corresponds to a proton speed of approximately 357 +/- 6 km/s) in the direction of sector 405. There was also an alpha particle peak in the vicinity of energy step 33 (this corresponds to an alpha particle speed of approximately 364 +/- 6 km/s) in the direction of sector 69. 4.3 FSM Energy Step Header Records: Each FSM energy step header consists of one header line followed by two lines of header information. The header line consists of a comment character followed a three word description unique to FSM step headers, followed by the total number of lines in this FSM step header and the associated FSM data record that follows it. The two lines of header information contain 22 words of information for this FSM energy step. Note that much of this information may duplicate the information in the spectral header record for this spectrum. A typical FSM step header is shown below: % FSM step header: 32 lines ****************************************** 190 5 6036 2600 2600 0 1 64 1 28 1 2 36 10 72 342 10 49 33 936 256 56 The first line of header information consists of 12 6-digit integer words. These contain the first 12 words (word 0-11) 0 f the FSM energy step header: Index Name Contents --------------------------------------------------------------------- 0 NWORDS Number of words in the record 1 SMODE Data collection mode for FSM data - 5 for detector B 6 for detector A, CCM"S 1 - 13 7 for detector A, CCM"S 14 - 26 2 --- Electronics temperature 3 --- High voltage power supply step, left bank of CCM's 4 --- High voltage power supply step, right bank of CCM's 5 ISUP Suppression (0 for no, 1 for yes) 6 EMODE Ion or electron mode (0 for electron, 1 for ion ) 7 --- Number of steps programmed 8 IHV High voltage (0 for off, 1 for on) 9 NSLICE Number of 'slices' (azimuthal angles) in this energy step 10 --- Integration period (number of sectors) 11 --- Number of half revolutions per step The first line of header information consists of 12 6-digit integer words. These contain the first 12 words (word 0-11) of the FSM energy step header: Index Name Contents --------------------------------------------------------------------- 12 ISLICE The number of the first slice in the record 13 ISC Spacecraft number (10 or 11) Earth received time (ERT) for this FSM energy step 15 IYR year (2-digits, but note that IYR <= 95) 16 IDY day 17 IHR hour 18 IMIN minute 19 ISEC second 20 MSEC millisecond 21 --- Transmission rate in bits per second 22 --- Sector angle correction (in millidegrees) at the slice with the peak count. 4.4 FSM Data Records Each FSM step record consists of one header line followed by several lines of data in multi-column format. The header line separator consists of a comment character, '%' followed by words that describe the contents of each column of data. Each line of data consists of an energy step number (note that because this record only contains data from a single FSM energy step, all of the step numbers will be the same!) and a sector number followed by the counts or currents measured by the relevant detector (A or B). A typical FSM data record is shown below. This is the data record associated with the FSM step header described in Section 4.3. It contains measurements for 28 different azimuthal directions for energy step 36 (this corresponds to a proton speed of approximately 585 +/-24 km/s). The peak signal of 54 was observed in sector angle 355 in target 3. % EN SN t1 t2 t3 t4 t5 ************************************ 36 36 0 0 0 0 0 36 102 10 0 17 0 0 36 110 0 36 7 0 0 36 119 0 0 0 0 0 36 155 0 0 15 0 0 36 163 0 9 0 0 0 36 172 3 0 0 0 0 36 180 0 0 24 0 0 36 216 0 0 0 0 0 36 224 0 0 0 0 0 36 233 0 0 0 0 0 36 241 0 0 0 0 0 36 277 0 0 0 0 0 36 285 9 0 0 0 0 36 294 0 9 0 0 0 36 303 0 11 0 0 6 36 338 1 0 14 0 0 36 347 0 0 6 0 0 36 355 0 7 54 0 0 36 364 0 0 52 0 0 36 399 0 0 38 3 0 36 408 0 0 8 0 9 36 416 41 0 0 0 0 36 425 0 0 12 0 0 36 460 7 0 1 8 0 36 469 0 0 10 0 0 36 478 0 0 6 0 0 36 486 0 0 8 0 0 5.0 Pioneer Spectral Files: Usage The Pioneer spectral files contain velocity distributions measured by the plasma analyzers aboard the Pioneer 10 and 11 spacecraft in instrument units and co-ordinates. These spectra can be processed to recover the actual velocity distributions of the incident solar wind plasma. They can also be integrated to obtain solar wind bulk parameters such as velocity, density, and temperature. These spectral files also serve as the primary archive of solar wind data from the Pioneer plasma analyzers. Because these spectral files are intended for archival purposes as well as data analysis, their content was kept as close as possible to the content of the original EDR and REDR files from which they were created. These files can be examined in their current form with a text editor or a simple read statement, but there are several additional processing steps a user might wish to undertake before using the data. These processing steps are listed below. A detailed discussion of the relevant procedures is beyond the scope of this document, but a general discussion of these processing steps is provided in in Sections 5.2 - 5.5 1) Extracting individual spectra 2) Converting Earth received time to spacecraft ephemeris time 3) Transforming from spacecraft co-ordinates to RTN co-ordinates 4) Converting Energy Step Numbers to E/q or velocity values 5) Converting instrument units to currents and fluxes 6) Identifying noise and bad spectra 7) Deconvolving the Instrument Response Function 5.1 Extracting Individual Spectra Because of the long duration of the Pioneer missions (25 years), the enormous range of incident flux over which measurements were made (more than 4 orders of magnitude), and comparative lack of sophistication of the telemetry system onboard the Pioneer spacecraft compared with modern missions, the length and content of Pioneer 10 and 11 spectra are highly variable. Individual spectra from the Pioneer plasma analyzers can come in several different modes, with sizes that range from a minimum of 6 lines and less than 50 words to a possible maximum of more than 18,000 lines and 500,000 words. For this reason, it was not practical to store spectra as individual records of fixed length and format, and individual spectra were stored as collections of records as described in Section 4. To extract individual spectra, a read routine must locate and identify the header records at the beginning of each spectrum, determine the type of spectrum and the format of the associated data records from the information in that header, and then read the associated data records. This involves the following steps: 1.0 Find the beginning of the next spectrum 2.0 Examine the header to determine the data collection mode (MFM or FSM) 2.1 If this is an MFM spectrum, read the associated MFM data record 2.2 If this is an FSM record: 2.21 Examine the header to determine the number of energy steps 2.22 Read one FSM step header followed by one FSM data record for each energy step 3.0 Return to step 1.0 The association of these processing steps with individual spectra lends itself to an object-oriented approach, and a sample C++ routine to read and write spectral data is provided in the file B3Spectra.cpp. This routine contains extensive internal documentation. An equivalent FORTRAN routine will be provided with a future release of this document. 5.2 Converting from Earth received time to spacecraft ephemeris time All times in the original EDR and REDR data were provided as Earth received times (ERT). This convention was preserved in the Pioneer spectral files. ERT can be converted to spacecraft ephemeris time (SCET), by subtracting the light travel time from the spacecraft to Earth. To determine the light travel time for a given epoch, it is necessary to determine the distance between the spacecraft and Earth for that epoch. This can be determined in a straightforward way from the ephemeris data for the Pioneer spacecraft available from the National Space Science Data Center (NSSDC). Tables 1 and 2 provide spacecraft ephemeris information, the longitude of Earth, the longitudinal separation between the spacecraft and Earth, components of the spacecraft-Earth vector in RTN co-ordinates, and light travel time for Pioneer 10 and 11. Table 1. Spacecraft ephemeris information, the longitude of Earth, longitudinal separation between the spacecraft and Earth, spacecraft-Earth vector in RTN co-ordinates, and light travel time for Pioneer 10 Year DOY R_SC Lon_SC Lat_SC Lon_E DLon DR E/W N/S LTT --------------------------------------------------------------------------- 1972 85 1.05 189.7 -0.96 184.4 0.0 0.11 -57.8 8.2 0.02 1972 138 1.46 236.1 -1.99 236.2 360.0 0.45 0.3 4.5 0.06 1972 279 2.71 281.3 -1.82 11.9 270.0 2.90 20.2 -0.1 0.40 1973 16 3.46 295.3 -1.52 115.7 180.0 4.44 -0.1 -0.3 0.62 1973 115 4.05 304.3 -1.28 214.7 90.0 4.16 -14.0 0.0 0.58 1973 216 4.55 311.3 -1.06 311.5 360.0 3.53 0.0 0.3 0.49 1973 314 4.95 317.1 -0.88 47.4 270.0 5.05 11.3 0.0 0.70 1974 50 5.12 329.2 -0.13 150.0 180.0 6.11 -0.1 0.0 0.85 1974 156 5.39 343.4 0.65 254.0 90.0 5.48 -10.7 0.0 0.76 1974 263 5.84 356.0 1.31 356.7 360.0 4.84 0.1 -0.3 0.67 1974 362 6.39 5.7 1.77 95.9 270.0 6.46 8.8 0.0 0.90 1975 95 7.00 13.8 2.12 194.6 180.0 8.00 -0.1 0.3 1.11 1975 195 7.69 20.6 2.38 291.0 90.0 7.75 -7.5 0.0 1.07 1975 294 8.41 26.2 2.57 27.0 360.0 7.42 0.1 -0.3 1.03 1976 22 9.12 30.7 2.70 121.1 270.0 9.18 6.2 0.0 1.27 1976 116 9.84 34.5 2.80 214.9 180.0 10.85 0.0 0.3 1.50 1976 214 10.61 38.0 2.88 308.9 90.0 10.64 -5.5 0.0 1.48 1976 309 11.36 40.9 2.94 41.7 360.0 10.37 0.1 -0.3 1.44 1977 34 12.09 43.3 2.98 134.0 270.0 12.14 4.7 0.0 1.68 1977 127 12.83 45.5 3.02 226.3 180.0 13.84 -0.1 0.2 1.92 1977 223 13.60 47.5 3.05 318.2 90.0 13.63 -4.3 0.0 1.89 1977 316 14.34 49.3 3.07 49.5 360.0 13.36 0.0 -0.2 1.85 1978 41 15.06 50.8 3.08 140.9 270.0 15.10 3.8 0.0 2.09 1978 134 15.81 52.2 3.10 232.9 180.0 16.82 0.0 0.2 2.33 1978 229 16.57 53.6 3.11 323.8 90.0 16.59 -3.5 0.0 2.30 1978 322 17.31 54.8 3.12 55.3 360.0 16.32 0.0 -0.2 2.26 1979 47 18.02 55.8 3.12 146.7 270.0 18.06 3.1 0.0 2.50 1979 139 18.75 56.8 3.13 237.5 180.0 19.76 0.0 0.2 2.74 1979 234 19.50 57.8 3.13 328.3 90.0 19.52 -3.0 0.0 2.71 1979 326 20.22 58.6 3.13 59.1 360.0 19.24 0.0 -0.2 2.67 1980 50 20.92 59.4 3.14 149.5 270.0 20.95 2.7 0.0 2.90 1980 143 21.65 60.1 3.14 241.1 180.0 22.66 0.0 0.1 3.14 1980 237 22.39 60.9 3.14 331.0 90.0 22.41 -2.6 0.0 3.11 1980 329 23.10 61.5 3.14 61.9 360.0 22.12 0.0 -0.1 3.07 1981 52 23.80 62.1 3.14 152.3 270.0 23.82 2.4 0.0 3.30 1981 144 24.51 62.7 3.14 242.8 180.0 25.52 0.0 0.1 3.54 1981 239 25.24 63.2 3.14 333.7 90.0 25.26 -2.3 0.0 3.50 1981 331 25.95 63.8 3.14 64.7 360.0 24.97 0.0 -0.1 3.46 1982 55 26.64 64.2 3.13 155.1 270.0 26.67 2.1 0.0 3.70 1982 147 27.35 64.7 3.13 245.4 180.0 28.36 0.0 0.1 3.93 1982 241 28.07 65.1 3.13 335.4 90.0 28.08 -2.1 0.0 3.89 1982 333 28.77 65.5 3.13 66.4 360.0 27.78 0.0 -0.1 3.85 1983 57 29.45 65.9 3.13 156.8 270.0 29.48 1.9 0.0 4.09 1983 149 30.15 66.3 3.13 247.1 180.0 31.16 0.0 0.1 4.32 1983 243 30.86 66.7 3.12 337.1 90.0 30.87 -1.9 0.0 4.28 1983 334 31.55 67.0 3.12 67.2 360.0 30.57 0.0 -0.1 4.24 1984 58 32.23 67.3 3.12 157.6 270.0 32.25 1.8 0.0 4.47 1984 150 32.92 67.7 3.12 247.8 180.0 33.93 0.0 0.1 4.70 1984 245 33.64 68.0 3.12 338.8 90.0 33.64 -1.7 0.0 4.66 1984 336 34.32 68.3 3.11 69.0 360.0 33.34 0.0 -0.1 4.62 1985 59 34.99 68.5 3.11 159.3 270.0 35.02 1.6 0.0 4.85 1985 151 35.68 68.8 3.11 249.5 180.0 36.69 0.0 0.1 5.09 1985 245 36.39 69.1 3.11 339.5 90.0 36.39 -1.6 0.0 5.04 1985 336 37.07 69.3 3.11 69.8 360.0 36.08 0.0 -0.1 5.00 1986 60 37.73 69.5 3.10 160.1 270.0 37.75 1.5 0.0 5.23 1986 152 38.42 69.8 3.10 250.2 180.0 39.43 0.0 0.1 5.47 1986 246 39.12 70.0 3.10 340.2 90.0 39.13 -1.5 0.0 5.42 1986 337 39.79 70.2 3.10 70.5 360.0 38.81 0.0 -0.1 5.38 1987 61 40.45 70.4 3.10 160.9 270.0 40.47 1.4 0.0 5.61 1987 153 41.13 70.6 3.10 251.0 180.0 42.15 0.0 0.1 5.84 1987 247 41.83 70.8 3.09 341.0 90.0 41.84 -1.4 0.0 5.80 1987 338 42.50 71.0 3.09 71.3 360.0 41.52 0.0 -0.1 5.75 1988 62 43.16 71.2 3.09 161.6 270.0 43.18 1.3 0.0 5.98 1988 154 43.84 71.4 3.09 251.7 180.0 44.85 0.0 0.1 6.22 1988 248 44.53 71.6 3.09 341.7 90.0 44.54 -1.3 0.0 6.17 1988 339 45.20 71.7 3.09 72.1 360.0 44.21 0.0 -0.1 6.13 1989 62 45.85 71.9 3.08 162.4 270.0 45.87 1.2 0.0 6.36 1989 154 46.52 72.0 3.08 252.4 180.0 47.53 0.0 0.1 6.59 1989 248 47.21 72.2 3.08 342.4 90.0 47.22 -1.2 0.0 6.54 1989 339 47.87 72.3 3.08 72.8 360.0 46.89 0.0 -0.1 6.50 1990 63 48.52 72.5 3.08 163.2 270.0 48.55 1.2 0.0 6.73 1990 155 49.19 72.6 3.08 253.1 180.0 50.21 0.0 0.1 6.96 1990 249 49.88 72.8 3.07 343.2 90.0 49.88 -1.2 0.0 6.91 1990 340 50.54 72.9 3.07 73.6 360.0 49.56 0.0 -0.1 6.87 1991 64 51.19 73.0 3.07 163.9 270.0 51.21 1.1 0.0 7.10 1991 156 51.86 73.2 3.07 253.9 180.0 52.87 0.0 0.1 7.33 1991 250 52.54 73.3 3.07 343.9 90.0 52.54 -1.1 0.0 7.28 1991 341 53.20 73.4 3.07 74.4 360.0 52.21 0.0 -0.1 7.24 1992 64 53.83 73.5 3.07 163.7 270.0 53.85 1.1 0.0 7.46 1992 156 54.50 73.6 3.06 253.6 180.0 55.51 0.0 0.1 7.69 1992 251 55.19 73.7 3.06 344.6 90.0 55.18 -1.0 0.0 7.65 1992 341 55.83 73.9 3.06 74.1 360.0 54.85 0.0 -0.1 7.60 1993 64 56.48 74.0 3.06 164.4 270.0 56.49 1.0 0.0 7.83 1993 156 57.14 74.1 3.06 254.4 180.0 58.15 0.0 0.1 8.06 1993 250 57.82 74.2 3.06 344.4 90.0 57.82 -1.0 0.0 8.01 1993 341 58.47 74.3 3.06 74.9 360.0 57.49 0.0 -0.1 7.97 1994 65 59.11 74.4 3.06 165.2 270.0 59.13 1.0 0.0 8.20 1994 157 59.77 74.5 3.05 255.1 180.0 60.78 0.0 0.1 8.43 1994 251 60.44 74.6 3.05 345.1 90.0 60.44 -1.0 0.0 8.38 1994 342 61.10 74.6 3.05 75.7 360.0 60.11 0.0 0.0 8.33 1995 65 61.73 74.7 3.05 164.9 270.0 61.74 0.9 0.0 8.56 1995 157 62.39 74.8 3.05 254.9 180.0 63.40 0.0 0.0 8.79 1995 252 63.07 74.9 3.05 345.9 90.0 63.06 -0.9 0.0 8.74 1995 342 63.71 75.0 3.05 75.4 360.0 62.73 0.0 0.0 8.69 Table 1. Spacecraft ephemeris information, the longitude of Earth, longitudinal separation between the spacecraft and Earth, spacecraft-Earth vector in RTN co-ordinates, and light travel time for Pioneer 11 Year DOY R_SC Lon_SC Lat_SC Lon_E DLon DR E/W N/S LTT --------------------------------------------------------------------------- 1973 102 1.01 203.5 -0.40 202.0 0.0 0.03 -81.4 14.4 0.00 1973 176 1.50 273.2 -2.98 273.3 360.0 0.49 0.3 6.2 0.07 1973 313 2.72 316.0 -2.64 46.4 270.0 2.90 20.0 -0.2 0.40 1974 50 3.46 329.9 -2.20 150.0 180.0 4.45 0.0 -0.5 0.62 1974 151 4.07 339.0 -1.83 249.2 90.0 4.19 -14.0 -0.1 0.58 1974 253 4.59 346.0 -1.51 346.9 360.0 3.59 0.3 0.4 0.50 1974 349 4.90 351.7 -0.78 82.6 270.0 5.01 11.3 0.0 0.69 1975 84 4.45 3.1 2.39 183.7 180.0 5.45 -0.1 0.4 0.76 1975 192 4.07 17.9 6.26 288.1 90.0 4.19 -14.1 0.2 0.58 1975 304 3.81 36.1 10.37 36.9 360.0 2.84 0.3 -3.6 0.39 1976 47 3.74 55.7 13.53 146.4 270.0 3.88 15.2 0.5 0.54 1976 159 3.86 76.2 15.16 256.4 180.0 4.85 0.0 3.1 0.67 1976 272 4.17 94.8 15.05 5.0 90.0 4.28 -14.0 0.4 0.59 1977 10 4.56 109.1 13.93 109.6 360.0 3.62 0.1 -3.8 0.50 1977 111 5.02 120.5 12.42 210.8 270.0 5.12 11.6 0.3 0.71 1977 215 5.52 130.1 10.76 310.6 180.0 6.52 -0.1 1.7 0.90 1977 315 6.03 137.7 9.23 48.5 90.0 6.10 -9.5 0.1 0.85 1978 44 6.52 143.7 7.89 143.9 360.0 5.54 0.0 -1.4 0.77 1978 141 7.02 149.0 6.63 239.6 270.0 7.10 8.2 0.1 0.98 1978 240 7.53 153.6 5.48 334.4 180.0 8.53 -0.1 0.6 1.18 1978 335 8.01 157.5 4.47 68.4 90.0 8.05 -7.1 0.0 1.12 1979 62 8.47 160.8 3.59 161.8 360.0 7.48 0.1 -0.5 1.04 1979 157 8.94 163.9 2.77 254.7 270.0 9.01 6.5 0.0 1.25 1979 254 9.38 167.1 2.19 347.7 180.0 10.38 -0.1 0.2 1.44 1979 350 9.35 172.8 3.87 83.4 90.0 9.39 -6.0 0.0 1.30 1980 79 9.40 178.4 5.45 178.5 360.0 8.41 0.0 -0.6 1.17 1980 178 9.51 184.1 7.04 274.6 270.0 9.57 6.1 0.0 1.33 1980 277 9.69 189.8 8.50 9.9 180.0 10.68 0.0 0.8 1.48 1981 6 9.92 195.0 9.78 105.6 90.0 9.96 -5.7 0.0 1.38 1981 100 10.21 199.9 10.91 200.0 360.0 9.23 0.0 -1.2 1.28 1981 199 10.56 204.8 11.95 295.3 270.0 10.61 5.6 0.1 1.47 1981 296 10.94 209.3 12.82 29.5 180.0 11.92 0.0 1.1 1.65 1982 24 11.35 213.4 13.53 123.7 90.0 11.39 -5.1 0.0 1.58 1982 118 11.80 217.2 14.14 217.4 360.0 10.83 0.0 -1.3 1.50 1982 216 12.29 220.9 14.67 311.3 270.0 12.34 4.9 0.1 1.71 1982 311 12.80 224.2 15.09 44.3 180.0 13.76 0.0 1.1 1.91 1983 38 13.31 227.2 15.42 137.6 90.0 13.34 -4.4 0.0 1.85 1983 132 13.84 230.0 15.71 230.7 360.0 12.87 0.1 -1.2 1.78 1983 229 14.41 232.7 15.94 323.6 270.0 14.46 4.2 0.1 2.00 1983 323 14.98 235.2 16.12 56.1 180.0 15.93 -0.1 1.0 2.21 1984 48 15.53 237.3 16.26 147.5 90.0 15.56 -3.8 0.0 2.16 1984 142 16.12 239.4 16.37 240.1 360.0 15.15 0.1 -1.1 2.10 1984 238 16.73 241.4 16.46 332.0 270.0 16.77 3.6 0.0 2.32 1984 331 17.32 243.2 16.53 63.9 180.0 18.27 0.0 0.9 2.53 1985 55 17.91 244.8 16.57 155.3 90.0 17.93 -3.3 0.0 2.48 1985 148 18.51 246.4 16.60 246.6 360.0 17.54 0.0 -0.9 2.43 1985 244 19.14 247.9 16.62 338.5 270.0 19.18 3.1 0.0 2.66 1985 336 19.75 249.2 16.63 69.8 180.0 20.70 0.0 0.8 2.87 1986 61 20.35 250.5 16.63 161.1 90.0 20.36 -2.9 0.0 2.82 1986 154 20.97 251.7 16.62 252.2 360.0 20.00 0.0 -0.8 2.77 1986 249 21.61 252.9 16.61 343.1 270.0 21.64 2.8 0.0 3.00 1986 341 22.23 254.0 16.59 74.6 180.0 23.17 0.0 0.7 3.21 1987 66 22.83 254.9 16.56 165.9 90.0 22.84 -2.6 0.0 3.17 1987 159 23.46 255.9 16.54 256.7 360.0 22.49 0.0 -0.7 3.12 1987 254 24.11 256.8 16.51 347.7 270.0 24.14 2.5 0.0 3.35 1987 345 24.72 257.7 16.48 78.4 180.0 25.67 0.0 0.6 3.56 1988 69 25.33 258.5 16.45 168.6 90.0 25.34 -2.3 0.0 3.51 1988 162 25.96 259.3 16.41 259.3 360.0 24.99 0.0 -0.7 3.46 1988 257 26.60 260.0 16.38 350.4 270.0 26.63 2.3 0.0 3.69 1988 348 27.22 260.7 16.34 81.2 180.0 28.17 0.0 0.6 3.90 1989 71 27.83 261.4 16.30 171.4 90.0 27.85 -2.1 0.0 3.86 1989 165 28.47 262.0 16.27 262.9 360.0 27.50 0.0 -0.6 3.81 1989 259 29.11 262.7 16.23 353.1 270.0 29.14 2.1 0.0 4.04 1989 350 29.73 263.3 16.19 84.0 180.0 30.68 0.0 0.5 4.25 1990 74 30.34 263.8 16.16 174.1 90.0 30.35 -2.0 0.0 4.21 1990 167 30.97 264.4 16.12 264.6 360.0 30.00 0.0 -0.5 4.16 1990 262 31.62 264.9 16.08 355.8 270.0 31.65 1.9 0.0 4.39 1990 352 32.23 265.4 16.04 85.8 180.0 33.18 0.0 0.5 4.60 1991 76 32.84 265.8 16.01 175.9 90.0 32.85 -1.8 0.0 4.55 1991 170 33.48 266.3 15.97 267.2 360.0 32.50 0.0 -0.5 4.51 1991 264 34.12 266.8 15.93 357.5 270.0 34.14 1.8 0.0 4.73 1991 354 34.73 267.2 15.90 87.6 180.0 35.67 0.0 0.4 4.94 1992 78 35.33 267.6 15.87 177.6 90.0 35.35 -1.7 0.0 4.90 1992 172 35.97 268.0 15.83 268.9 360.0 34.99 0.0 -0.5 4.85 1992 266 36.61 268.4 15.80 359.2 270.0 36.64 1.6 0.0 5.08 1992 356 37.22 268.8 15.76 89.4 180.0 38.17 0.0 0.4 5.29 5.3 Transforming from spacecraft co-ordinates to RTN co-ordinates All directions in the Pioneer spectral files are given in spacecraft co-ordinates. The roll angle (azimuthal angle) for any given measurement is expressed as a sector number, which can range between 1 and 512. The polar angle is related to the channeltron (Detector A) or electrometer (Detector B) by which that measurement was made. The polar angles for the different channeltrons and electrometers of Detectors A and B are listed in Table 3 and Table 4. Table 3. Polar angles for Detector A channeltrons Channeltron Angular position (deg) -------------------------------------- 1 50.4 2 42.1 3 34.8 4 28.2 5 25.0 6 21.9 7 18.8 8 15.9 9 12.9 10 10.0 11 7.1 12 4.3 13 1.4 14 -1.4 15 -4.3 16 -7.1 17 -10.0 18 -12.9 19 -15.9 20 -18.8 21 -21.9 22 -25.0 23 -28.2 24 -34.8 25 -42.0 26 -50.4 Table 4. Polar angles for Detector B electrometers Electrometer Angular position (deg) Angular view (deg) ------------------------------------------------------------ 1 46.25 47.5 2 15.0 15.0 3 0.0 15.0 4 -15.0 15.0 5 -46.25 47.5 The transformation from spacecraft to RTN co-ordinates is not straightforward. It requires knowledge of the spacecraft's spin axis, which varied over the course of the mission as the spacecraft was realigned to keep its high-gain antenna pointed at the Earth. The relevant spacecraft attitude information is available from the NSSDC. A detailed discussion of this co-ordinate transformation is beyond the scope of this document, but the spacecraft attitude frame can be approximated, particularly later in the mission when the spacecraft were at heliocentric distances much greater than 1 AU, by assuming that the spacecraft spin axis is pointed at the Sun and a particular sector (for Pioneer 10, this was typically sector 385) corresponds to a direction pointing East in the Ecliptic plane. 5.4 Converting Energy Step Numbers to E/q values Tables 5 and 6 show the nominal plate voltages, E/q values, and proton speeds for successive energy steps of Detectors A and B. The width of each energy step is determined by the instrument response function, and is approximately equal to the separation between the energy steps. Due to problems with the telemetry system onboard Pioneer 10, some energy steps for Detector A were not reported correctly after 1985. These problems were corrected during data production and only occurred at very low step numbers (< 8), so they should not have a significant effect on the solar wind portion of a spectrum. The actual plate voltages also varied slightly with instrument temperature. This variation was extremely small (<< 1%). A routine to correct for this variation will be provided with a future release of this document. Table 5. Energy step numbers, voltages, E/q values, and velocities for Detector A Energy Step Voltage E/q (V) Velocity (km/s) ---------------------------------------------------------------- 1 5.5345 99.64 138.16 2 5.924 106.65 142.94 3 6.3535 114.38 148.03 4 6.8195 122.77 153.36 5 7.3085 131.57 158.76 6 7.835 141.05 164.38 7 8.3995 151.21 170.20 8 9.0055 161.12 175.69 9 9.7135 174.87 183.03 10 10.383 186.92 189.23 11 11.135 200.46 195.97 12 11.945 215.04 202.97 13 12.815 230.70 210.23 14 13.745 247.45 217.73 15 14.73 265.2 225.40 16 15.79 284.3 233.38 17 16.895 304.2 241.41 18 18.085 325.6 249.75 19 19.405 349.3 258.68 20 20.805 374.5 267.85 21 22.325 401.9 277.48 22 23.935 430.9 287.31 23 25.665 462.0 297.50 24 27.515 495.3 308.04 25 29.42 529.6 318.52 26 31.50 567.1 329.61 27 33.79 608.3 341.37 28 36.24 652.4 353.53 29 38.875 699.9 366.17 30 41.685 750.4 379.15 31 44.695 804.6 392.61 32 47.915 862.6 406.51 33 51.465 926.5 421.30 34 55.105 992.0 435.94 35 59.095 1063.8 451.44 36 63.38 1141.0 467.53 37 67.985 1223.9 484.22 38 72.89 1312.2 501.38 39 78.14 1406.7 519.12 40 83.78 1508.3 537.54 41 90.21 1624.0 557.78 42 96.59 1738.9 577.17 43 103.60 1865. 597.73 44 111.10 2000. 618.99 45 119.10 2126. 638.19 46 127.70 2299. 663.65 47 136.90 2465. 687.19 48 146.75 2642. 711.43 49 157.0 2826. 735.79 50 168.05 3025. 761.26 51 180.2 3244. 788.33 52 193.25 3479. 816.38 53 207.3 3732. 845.55 54 222.45 4005. 875.93 55 238.65 4296. 907.19 56 256.05 4610. 939.76 57 273.9 4931. 971.93 58 293.45 5283. 1106.02 59 314.9 5669. 1042.13 60 337.8 6081. 1079.33 61 362.35 6523. 1117.87 62 388.5 6994. 1157.52 63 416.3 7494. 1198.19 64 446.2 8033. 1240.53 Table 6. Energy step numbers, voltages, E/q values, and velocities for Detector B Energy Step Voltage E/q (V) Velocity (km/s) ---------------------------------------------------------------- 1 8.28 99.35 137.97 2 8.9985 107.98 143.83 3 9.767 117.20 149.85 4 10.605 127.26 156.14 5 11.51 138.12 162.67 6 12.51 150.12 169.59 7 13.575 162.90 176.66 8 14.74 176.88 184.08 9 16.015 192.18 191.88 10 17.405 208.86 200.03 11 18.90 226.80 208.45 12 20.51 246.12 217.15 13 22.26 267.12 226.22 14 24.195 290.34 235.85 15 26.255 315.06 245.68 16 28.52 342.24 256.06 17 31.115 373.38 267.46 18 33.815 405.78 278.82 19 36.71 440.5 290.51 20 39.85 478.2 302.68 21 43.25 519.0 315.33 22 47.01 564.1 328.75 23 51.015 612.2 342.47 24 55.42 665.0 356.94 25 60.015 720.2 371.45 26 65.225 782.7 387.24 27 70.815 849.8 403.49 28 76.86 922.3 420.36 29 83.435 1001.2 437.97 30 90.68 1088.2 456.59 31 98.41 1180.9 475.65 32 106.90 1282.8 495.74 33 116.15 1393.8 516.75 34 126.25 1515.0 538.75 35 137.05 1644.6 561.32 36 148.70 1784.4 584.69 37 161.40 1936.8 609.14 38 175.40 2105. 635.01 39 190.40 2285. 661.61 40 206.80 2481. 689.51 41 224.80 2698. 718.90 42 244.10 2929. 749.12 43 265.00 3180. 780.53 44 287.55 3451. 813.06 45 312.15 3746. 847.13 46 339.35 4072. 883.27 47 368.25 4419. 920.11 48 400.05 4801. 959.01 49 436.25 5235. 1001.46 50 474.15 5690. 1044.06 51 515.90 6191. 1089.06 52 559.90 6719. 1134.55 53 607.80 7294. 1182.08 54 660.55 7927. 1232.31 55 716.45 8597. 1283.40 56 778.60 9343. 1337.90 57 843.20 10118. 1392.30 58 916.1 10993. 1451.24 59 994.9 11939. 1512.37 60 1080. 12960. 1575.72 61 1172. 14064. 1641.47 62 1273. 15276. 1710.73 63 1382. 16584. 1782.47 64 1501. 18012. 1857.63 5.5 Converting instrument units to currents and fluxes The Pioneer plasma analyzers returned their measurements in the form of 'instrument counts'. The relationship between instrument counts and incident flux was roughly logarithmic. To determine the actual incident fluxes, it is necessary to convert instrument units to currents and divide these currents by the effective aperture of the relevant detector. For Detector A, the count values must first be converted to the actual count rate measured by the individual channeltrons, these count rates must be corrected to account for the gain factors for different channeltrons, and finally the corrected count rate must be divided by the integration time to obtain the currents. For Detector B, counts are converted to currents through use of a look-up table. The necessary software, gain factors, and look-up tables to perform these conversions will be provided in a separate document. 5.6 Identifying noise and bad spectra Because the Pioneer 10 and 11 spectral files were intended for archival purposes, no editing was done, and every spectrum in the original EDR files was retained. The i/o software included with this document (B3Spectra.cpp) checks each spectrum for problems with the format, header information, and invalid count values, but it does not make any additional tests, and it is the responsibility of the user to identify noise and bad spectra. This can be accomplished in two ways: 1) The velocity of the proton peak can be estimated by calculating the first moment of the spectrum or by determining the velocity corresponding to the peak of the spectrum. This velocity can be compared with the solar wind speed obtained from the Pioneer 10 and 11 parameter files for a corresponding time period. (These parameter files, which are available from the NSSDC, have been edited to remove bad data.) If the velocity of the proton peak agrees with the solar wind speed to within 10-20 km/s, the spectrum is probably good. If the two velocities disagree by more than approximately 20 km/s, the spectrum should be regarded with suspicion. 2) The spectrum can be examined directly, either in graphical form or by an automated analysis routine, to identify signals in the non-thermal part of the spectrum that can be attributed to noise. 5.7 Deconvolving the Instrument Response Function The Pioneer plasma analyzers return instrument spectra. These instrument spectra are a convolution of the instrument response function with the solar wind velocity distribution rather than a direct measurement of the solar wind velocity distribution itself. Because the width of the response function is fairly small, the instrument spectrum is usually a fairly good approximation of the actual velocity distribution, and there are many applications for which the effects of the instrument response function can safely be neglected. For example, it is possible to calculate plasma bulk parameters from directly from the instrument spectra. It may also be possible to identify qualitative features of the velocity distribution, or to estimate quantities such as the proton/alpha ratio or anisotropy, by examination of the instrument spectra. The approximate width of the instrument response function is described in Table 7. Table 7. Approximate width of the instrument response function Axis Width ----------------------------------------------------------------- Energy The instrument response function defines an energy step. The width of the edges of the response function is << the width of an energy step. Polar angle Detector A: < 1 channeltron Detector B: << 1 target Azimuth Approximately 4-8 sectors If a more precise measurement of the velocity distribution is required, it is necessary to deconvolve the instrument response function from the instrument spectra. This can be accomplished using the CLEAN algorithm [Hogbom, 1974]. A detailed discussion of the CLEAN algorithm and other deconvolution techniques is beyond the scope of this document. A discussion of the instrument response function and a sample deconvolution routine will be provided in a separate report.