FORMAT DESCRIPTION FOR LOCKHEED ISEE ED-, MD-, AND PF-FILES.


                             1. INTRODUCTION

The following descriptions are for a subset of one of the ISEE archival data
sets deposited in the NSSDC.  The complete set consists of five kinds of ASCII
text files (tables) for each calendar day, each file having a name containing
the date as year (two digits) followed by day of year (three digits).  The file
name begins with either of the prefixes ED, MD, MC, MS, or EX.  Two of these
files, the ED- and MD-files, are described below, along with a third file whose
name begins with the prefix PF.  This is a brief version of the MC-file, con-
taining data from only three of the 32 instrument energy channels (the three
channels with the three highest count rates). 

At the time of this writing (November 1994) the archived data set covers a time
period beginning on day 312 of 1977 and ending on day 61 of 1980.  This period
may be extended later to end on day 79 of 1982.  There are some days missing in
current period, because of instrument operating modes having too limited a
coverage of either spin angle or energy to provide standard-type velocity
moments, and any given day may have gaps for the same reason or because of
telemetry problems.  Only the ED-, MD-, and PF-files are currently kept on
computer disk at Lockheed in Palo Alto, California.  The complete set at NSSDC
is being stored on magnetic tape in a format (VAX Backup) that requires copying
to disk before it can be placed on new tapes or other medium. 

If these data are to be used for quantitative analysis, the User is urged to
consult the complete guide, called "Guide" below, which describes all five
kinds of data files.  It lists the currently known problems and limitations of
these data. 


                             2. THE ED-FILE

This file contains data from a particle counter called the "energy detector",
or "ED", which intersects the ions after energy analysis but before mass analy-
sis.  The count rates have been converted to certain velocity moments assuming
that all counts are due to protons.  These moments are thus not directly compa-
rable to any of the moments in the MD-files, unless the protons are indeed the
dominant species.  Even in that case, there may often be significant differences
between the ED and MD proton moments, because the ED and MD particle counters
respond to ions with slightly different external angles of motion (see Guide),
and the two sets of count rates are usually averaged over different times.

Since the ED count rates are independent of the mass channel selection, and the
energy channels are normally scanned at a higher rate than are the mass chan-
nels, it is usually possible to obtain several consequtive sets of ED moments
during each complete instrument scan cycle.  This advantage has been utilized
whenever possible, and the ED averaging intervals are more or less independent
of the phase of the instrument cycle.  The criterion most commonly used for de-
fining the ED intervals is to have a "sufficiently dense" coverage in energy
and spin phase angle.  This criterion varies with different types of energy and
mass scan patterns, but typically amounts to having at least every other energy
channel sampled in each of 12 spin angle sectors (30 deg wide sectors).  The
missing matrix points are filled in by interpolation between adjacent points
before the moments are calculated.

The criterion for ending each ED averaging interval is modified when the instru-
ment is in low sensitivity mode (usually set by automatic triggering at extreme
count rates) and, at the same time, the count rates show strong (10-fold or
stronger) spin phase modulation.  At such times the ED intervals are made equal
to the instrument scan cycle.  This situation occurs most often in the solar
wind.  The purpose is to suppress artificial oscillations in the moments caused
(in some modes) by spin phase dependent energy samplings.  The modification has
not been applied uniformly throughout the entire data set, however, so there are
periods of "strange" and non-physical modulations in the ED moments, especially
in the densities.  At any rate, all data taken in low sensitivity mode should
be treated with care; they are not intended to represent accurate quantitative
measurements, but they have been included to complete the gross qualitative
picture and to provide continuity between times of normal magnetospheric data.
All low sensitivity data are flagged as such (see below).

Unlike the MD data, the ED data have not been corrected for background counts
due to penetrating radiation (not measured), but they are known to be much less
affected by that problem than are the MD data (different kinds of detectors).
The ED data also differ from the MD data in that no standard deviations are cal-
culated from the combination of counts (a saving in CPU time and output volume).
If necessary, approximate upper limits on the ED standard deviations can be es-
timated from the corresponding standard deviations in the MD-file (the MD data
have additional variance associated with background correction).


2.1 File Format

The ED-file has been written by a formatted sequential FORTRAN WRITE:

      WRITE(9,210)IYYDDD,IUTSEC,BXED,BYED,BZED,BTED,ITHETB,IPHIB,
     *EDDNS,EDEMN,EDVEL,IEDANG,ACSEC,XCSEC,ENRG1,ENRG2,RX,RY,RZ

  210 FORMAT(2I6,4F8.1,I4,I5,3(1PE10.2),I5,2(0PF8.2),2F5.1,3F6.1)

The variable names represent the following quantities:

IYYDDD is the year (two digits) and day of year (three digits).

IUTSEC is the universal time in seconds at the midpoint of the averaging
       interval.  The nominal length of each interval is defined by the
       distance between adjacent midpoints, but the actual length may vary
       somewhat because of time gaps (noise) in the data (see ACSEC below).

BXED, BYED, BZED, and BTED are the GSE components and absolute value, respec-
       tively, of the measured magnetic field, each averaged over the ED
       interval (for data quality check, see next section).  The unit is
       "nanotesla" ("nT"), or equivalently, "gamma".

ITHETB and IPHIB are, respectively, the magnetic field elevation and longitude
       angles in GSE coordinates.  ITHETB ranges from -90 deg (southward) to
       +90 deg (northward), IPHIB from -180 deg (antisunward) to +180 deg (anti-
       sunward), with 0 deg being sunward and 90 deg duskward.  These angles
       have been calculated from the time averaged field components, and are
       rounded to the nearest integer.

EDDNS  is the ion number density in "/cm3" (assuming protons) contained in the
       nominal energy range from 100 eV to about 16 keV (see also next section).

EDEMN  is the "thermal" ion energy in "keV", that is the mean energy (0.1 - 
       16 keV) minus the energy associated with the common drift motion.

EDVEL  is the common drift speed in "km/sec" in a plane parallel to the s/c
       spin plane, that is approximately in the solar ecliptic plane.

IEDANG is the longitudinal direction angle of that same drift, with 0 deg
       being sunward, and 90 deg duskward (-180 deg to +180 deg).

ACSEC  is the number of seconds of data included in the moments.  This number
       is normally at least 6% smaller than the length of the averaging inter-
       val, since neither the lowest nor the highest energy channels are in-
       cluded (may be further reduced by data gaps).

XCSEC  is the number of seconds during the averaging interval when the ED detec-
       tor was in low sensitivity mode.  This number is almost always zero in
       the magnetosphere, but usually nonzero in the magnetosheath and solar
       wind.  If nonzero, it implies that at least some of the count rates have
       been multiplied by a crude scaling factor (= 130) to compensate for the
       reduced sensitivity.

ENRG1 and ENRG2 are, respectively, the lower and upper energy limits used in the
       moment calculations, in units of "keV".  These are normally 0.1 and 16.1,
       but may be modified in some modes (cf. comments on energies in Guide).

RX, RY, and RZ are the GSM coordinates of the s/c (at midpoint of interval) in
       units of "earth radii".  On the rare occasions when the GSM coordinates
       are unavailable (due to faulty ephemeris tape) the GSE coordinates are
       used instead (available on raw data tape).  Those occasions are flagged
       in the EX-file (also flagged in the MC-, PF-, MD-, and MS-files).


2.2 Further Explanations of Certain Variables.

The magnetic field values provided here may to some extent duplicate what has
already been archived at the NSSDC by the magnetometer principal investigator
(Prof. C. T. Russell; NSSDC identification number 77-102A-04), but are not in-
tended to supplant those.  The values derived here may not have been adequately
screened against telemetry noise or adjusted for instrument anomalies, so it is
recommended that the PI provided data be consulted whenever there is doubt about
accuracy.  There are two types of errors known to occur here:

a.     When the magnetometer is commanded to low gain on the inbound leg of
       the s/c orbit, usually between R = 8 Re and = 5 Re, the corresponding
       flag may show up slightly too late on the raw data tape, resulting in
       a brief underrepresentation of the field by a factor of 32.  This may
       last for about a minute or less (part of one major frame) and affects
       a single ED interval.  This error ought to be fairly obvious in the ED
       data, and therefore traceable in the MD data as well (by comparing the
       times).  The corresponding mismatch at high gain command on the out-
       bound leg, that is a sudden 32-fold increase of the field, is usually
       discovered as "unreal" and corrected.

b.     Occasionally it appears that the wrong antenna flip status has been
       inferred from the raw data behavior (pertains to the s/c Y and Z co-
       ordinates), resulting in anomalous modulations of the GSE components.
       These modulations cause the sum BXED**2+BYED**2+BZED**2 to be much
       smaller than the square of the time-averaged absolute field strength
       BTED**2.  It is recommended that the two measures of field strength
       be compared routinely, and that other magnetic field data be consulted
       if those two differ by more than a few percent.  An additional (or
       alternative) check can be made using certain MD data (see below).

The velocity moments have been calculated from a 32 energy channel (covering the
entire range from 10 eV to about 18 keV) by 12 spin angle sector (30 deg each)
matrix of time-averaged count rates in the following steps:

I.     A phase space density is assigned to each matrix point, using the
       local count rate when available, or interpolating between adjacent
       count rates if the point has not been sampled.  The bottom and top
       energy channels are included in the interpolation procedure, when
       necessary, but not in the integration (summation) over energy.

II.    Within each energy channel the phase space densities are weighted
       by cosines or sines of the spin angle (center of sector) and summed
       over angle to form two orthogonal projections.  These projections
       are in turn weighted by energy and by an energy bandwidth (see below)
       and summed over energy channels, forming two orthogonal components,
       approximately the GSE X and Y components, of a vector that is pro-
       portional to number flow density.  Both components are then divided
       by a total (scalar) sum of phase space densities weighted by the
       energy bandwidth and by the square root of the energy, that is by a
       sum proportional to number density, to form (approximate) X and Y
       drift velocity components, and an angle IEDANG.

III.   A spherical coordinate system is envisioned with its polar axis along
       the drift velocity vector, that is in the GSE X-Y plane.  It is now
       assumed that the phase space density has azimuthal symmetry in this
       coordinate system (rotational symmetry around drift velocity vector).
       The number density, drift speed (but not angle), and mean energy are
       recalculated by summing over solid angle and energy in this system.
       The solid angle weighting factors in this case are zones on a unit
       sphere, each defined at the intersection with the GSE X-Y plane by the
       boundaries of a 30 deg spin angle sector, or by one boundary and the
       drift velocity vector.  These zones are partially overlapping, and
       summing over 12 spin angle sectors (typically = 14 zones) means cover-
       ing the unit sphere twice, so a factor 1/2 is applied to each sum.
       The drift speed (EDVEL) and mean energy (EDEMN) are obtained by divid-
       ing flow density and energy density, respectively, by the number den-
       sity (EDDNS).  The mean energy is converted to "thermal" energy by
       subtracting the equivalent drift energy.

If the drift speed in step II is less than 14 km/sec (less than 1 eV energy),
the coordinate system is instead aligned with the X-Y projection of the magnetic
field, that is with the angle IPHIB, provided the elevation angle ITHETB is be-
tween -45 and +45 deg.  If the latter is not the case, and if the drift speed is
below 14 km/sec, the coordinate system is aligned with the s/c spin axis, and
the phase space densities are treated as isotropic.  Only density and mean en-
ergy are recalculated in these two cases.

The summation over energy treats each energy channel, except the second one
(first channel not included), as a point measurement at the center energy, and
takes the energy bandwidth to be the distance between adjacent channels in the
trapezoidal fashion.  At the second channel an extra term is added to extend the
integral from the center energy downward to about 0.1 keV, assuming the flux to
be a constant.  This addition brings the mathematical energy range in better
agreement with the instrumental range of acceptance.

The variable ACSEC is a sum of elementary time segments associated with each
commanded setting of the power supplies controlling energy and mass channels.
These elementary times are 1/4 sec during low bit rate operation (about 80% of
the time) and 1/16 sec during high bit rate operation.  These times include the
resetting of the power supplies, however, and are slightly longer than the times
associated with particle counting.  For simplicity, the particle counting is
interrupted for about 12% of the elementary time segments in both low and high
bit rate operation to allow for resetting.  The ACSEC therefore exceeds the ac-
tual particle counting time by about 14% in both cases.


                             3. THE MD-FILE

This file contains data from a particle counter called the "mass detector", or
"MD", which receives the ions after both energy and mass analysis.  Count rates
of the four principal magnetospheric ion species, the H+, He++, He+, and O+,
have been sorted by 32 energy channels (10 eV/e to 18 keV/e), 12 spin angle sec-
tors (30 deg each) and 9 pitch-angle ranges (20 deg each) and averaged over each
complete energy/mass scan cycle of the instrument.  At the end of each cycle the
averaged count rates have been converted to certain velocity moments using two
different assumptions:  the velocity distributions have rotational symmetry a-
round either (A) the bulk flow vector or (B) the local magnetic field direction
(see below).  Note: the ion labels are applied to certain M/Q values (the in-
strument does not measure mass per se) and may be inappropriate in the magneto-
sheath and solar wind, especially at M/Q= 4 (He+).

The energy/mass scan cycles vary in length from a few minutes to about 20 min
or more, depending on the instrument mode of operation.  Each cycle may cover
only a few mass channels and a reduced energy range, or it may cover the full
energy range at each of 64 mass channels (load mode).  The most common modes in
the magnetosphere provide for multiple energy scans at each of 5 to 7 mass chan-
nels (including a background channel at M/Q < 1), where each energy scan may
sample a different subset of the 32 energy channels (e.g. every fourth channel
in four interleaving scans), and each energy channel is maintained for about
four seconds (1.3 s/c spin cycles).  In addition, each cycle may contain a few
scans through all 64 mass channels at a few energies, as well as one or two
brief scans through the RPA voltages in the lowest energy channel (cold plasma
measurements not included here).  In order to simplify tabulation of moments,
no distinction is made here between different phases of a given cycle.  That is,
all moments are treated as averages over the same cycle, although different ions
were in fact sampled at different phases (the same ion often more than once per
cycle).

All MD moments have been corrected for background counts due to penetrating
radiation (mostly MeV electrons and associated bremsstrahlung).  This has been
done by subtracting an average background, that is the average sampled during
a given energy/mass scan cycle, from the average ion count rates in each energy
and angle bin.  As a consequence, normally non-negative moments such as number
density may end up negative, when the count rate of a given ion is very close to
background levels, and the count rate in the background channel happens to be on
the high side due to normal statistical or temporal fluctuations.  This is to be
expected, and negative values ought to be included in any statistical averaging
of number densities from these files, in order not to bias the result.

All MD moments have a standard deviation assigned to them.  This one accounts
for purely statistical uncertainties, those associated with Poisson counting
statistics.  In all cases but one, the tabulated value is an integer number be-
tween 0 and 999, which represents the ratio in percent (%) between the standard
deviation and the absolute value of the moment itself, rounded downward (values
greater than 999 assumed irrelevant).  The one exception is the bulk flow angle
(drift direction angle) in the GSE X-Y plane (spin plane), where the standard
deviation is expressed as an angle between 0 and 360 deg, rounded to the nearest
integer.

The variance (square of standard deviation) of a given moment, or a given com-
bination of moments (as in bulk velocity and mean energy), has been calculated
in a customary fashion by taking the partial derivative with respect to the
count rate in each energy and angle bin included in the moment (in both numera-
tor and denominator, where applicable), squaring the derivative, multiplying it
with the variance of the associated count rate, and adding such terms over all
bins.  If the same count rate is used twice, in order to replace a missing sam-
ple in an adjacent bin (see below), its contribution to the variance is adjusted
so as to reflect the reduced number of independent samplings.  All standard de-
viations, except the one assigned to bulk flow angle (see below), include a con-
tribution from the variance of the background measurement.  The reason for the
exception is that the background measurement, although subtracted from all other
count rates, is a scalar (single number) that cancels out from the calculation
of flow angle.

For various reasons, the data may be statistically insufficient to allow a given
moment (or combination of moments) to be calculated.  If the number density has
been calculated to be a negative number (background measurement too high), for
example, it makes no sense to even attempt to calculate a mean energy.  And if
only a few energy channels have been sampled (due to noisy data), it makes no
sense to calculate any of the moments, since the output format presumes a cer-
tain degree of consistency.  Whenever a moment calculation fails, the corre-
sponding standard deviation is set equal to -1.


3.1 File Format

The MD-file has been written in groups of five lines (records), using
formatted sequential FORTRAN WRITE statements as follows:

The first of five lines is a title line:

      WRITE(8,230)IYYDDD,JSTART,JSTOP,RX,RY,RZ,RT,DZ,IMLAT,TLOCL,
     *BXMD,BYMD,BZMD,BTMD,BETA,IDBETA,BCTR,MDTCR,
     *ENEMAX,IRATE,RSEY,RSEZ

  230 FORMAT(I6,2I5,5F6.1,I4,F5.1,4F8.1,1PE10.2,I3,1PE10.2,I3,
     *0PF5.1,I2,2F6.1)

The variable names represent the following quantities:

IYYDDD is the year (two digits) and day of year (three digits).

JSTART is the universal time in minutes at the beginning of the averaging
       interval, that is the time of the first good data in that interval.
       This is normally at the start of an energy/mass scan cycle, unless
       some initial data in that cycle are bad.

JSTOP  is the universal time in minutes at the end of the averaging interval,
       that is the time of the last good data in that interval.  This is
       normally at the end of an energy/mass scan cycle, unless the last
       data in that cycle are bad.

RX, RY, RZ, and RT are, respectively, the GSM X, Y, Z, and radial distance
       at the midpoint of the averaging interval, all in units of "earth
       radii" ("Re").  RY and RZ are set to 999. if GSM coordinates not
       available (RX same in GSE).

DZ     is the distance in "earth radii" (at midpoint) from the nominal neutral
       sheet in the geotail according to Fairfield and Ness [J.Geophys. Res.,
       75, 7032, 1970].  This is only displayed for GSM X < -11 Re, otherwise
       set to 999.  If no GSM coordinates available, it is set to 0.

IMLAT  is the geomagnetic latitude in degrees (at midpoint), rounded to the
       nearest integer.  This is set to 0, if no ephemeris tape available.

TLOCL  is the geographic local time in hours and 1/10 hours (at midpoint).
       This is set to 0.0, if no ephemeris tape available.

BXMD, BYMD, BZMD, and BTMD are the GSE components and absolute value, respec-
       tively, of the measured magnetic field, each averaged over the whole
       MD interval (for data quality check, see next section).  The unit is
       "nanotesla" ("nT"), or equivalently, "gamma".

BETA and IDBETA are a simplified representation of the ion plasma beta and its
       standard deviation (% of absolute value).  Its definition is explained
       in the next section.

BCTR   is the average background count rate in counts/sec.

MDTCR  is a flag showing which of two detector pulse hight triggering levels
       has been used (= 2 in these data; will be set = 1 in later data).

ENEMAX is the maximum energy sampled, in units of "keV/e", or equal to 16.1,
       whichever is smaller (16.1 is maximum in moments).  Even if it is listed
       as 16.1 (typical) the moments of some ion species may sometimes be lim-
       ited to lower energies, depending on the energy/mass scan mode (see next
       section).

IRATE  is a flag showing which of two data accumulation (and telemetry trans-
       mission) rates has been used.  The low or normal rate (80% of the time)
       is shown by IRATE = 1, the high rate by IRATE = 4.  Note: low rate means
       four (4) samplings/sec, high rate means sixteen (16) samplings/sec.

RSEY and RSEZ are the GSE Y and Z (at midpoint of averaging interval) in units
       of "earth radii".


The next four lines list, respectively, the moments for H+ (K= 1), He++ (K= 2),
He+ (K= 3), and O+ (K= 4) (that is actually for M/Q= 1, 2, 4, and 16):

      DO 270 K=1,4

      WRITE(8,240)DNS5,ID0,DNS8,ID1,EMN8,ID2,
     *VDRFT,ID3,IDRFT,ID4,
     *BGD,ID6,ACSEC,XCSEC,
     *IPAMIN,IPAMAX,DENS8,ID7,EPER8,ID8,EPAR8,ID9

  240 FORMAT(4(1PE10.2,I3),I5,I4,1PE10.2,I3,0PF7.2,0PF6.2,
     *I4,I4,1PE10.2,I3,2(1PE9.2,I3))

  270 CONTINUE

The variable names represent the following quantities:

DNS5 and ID0 are the number density in "/cm3" and standard deviation (% of ab-
       solute value) of ions with energies between 10 eV/e and about 100 eV/e,
       that is of ions in the lowest energy channel (with RPA voltage fixed at
       10 V).

DNS8 and ID1 are the number density in "/cm3" and standard deviation (% of ab-
       solute value) of ions with energies between about 100 eV/e and 16 keV/e
       (normally).

EMN8 and ID2 are the mean energy in "keV" and standard deviation (%) of ions in
       the nominal energy range from 100 eV/e to 16 keV/e.  Note: this is total
       energy, including bulk motion, and it is in units of "keV", not "keV/e".

VDRFT and ID3 are the common (among those ions) drift speed (bulk flow speed)
       in "km/sec" and standard deviation (%) of ions in that same energy range
       (100 eV/e - 16 keV/e).  This drift speed is in the s/c spin plane, that
       is approximately in the GSE X-Y plane.

IDRFT and ID4 are the longitudinal direction angle of that same drift and its
       standard deviation, both in "degrees".  IDRFT = 0 is sunward and = 90 is
       duskward (-180 deg to +180 deg).  ID4 is between 0 and 360 deg.

These moments, from DNS5 through IDRFT, assume that the velocity distribution
has rotational symmetry around the drift (flow) vector (in the GSE X-Y plane).

BGD and ID6 are the equivalent isotropic density in "/cm3", over the 100 eV/e
       to 16 keV/e range, and standard deviation (%) corresponding to the meas-
       ured average background count rate.  That is, BGD is equal to the total
       background correction of DNS8 (a number already subtracted from DNS8).
       The ID6, when expressed in absolute terms, is part of ID1.

ACSEC  is the number of seconds of data included in the moments for that ion
       species.  This number is normally a small fraction of the length of the
       averaging interval (energy/mass scan cycle).

XCSEC  is the number of seconds during the averaging interval when the MD detec-
       tor was in low sensitivity mode and, at the same time, was sampling that
       particular ion species.  This number is almost always zero in the magne-
       tosphere, but usually nonzero for H+ in the magnetosheath and solar wind.
       In the latter cases it is often nonzero for He++ ions as well.  If it is
       not zero, it implies that at least some of the count rates of that ion
       species have been multiplied by a crude scaling factor (= 65 for MDTCR
       = 2) to compensate for the reduced sensitivity.

IPAMIN and IPAMAX are the minimum and maximum pitch angles in "degrees" sampled
       for those ions, rounded to the nearest integer.  Note: if the magnetic
       field is properly measured and corrected for magnetometer offsets, then
       the sum of these angles, IPAMIN + IPAMAX, should range between about
       170 deg and 190 deg.

DENS8 and ID7 are the number density in "/cm3" and standard deviation (% of ab-
       solute value) of ions in the 100 eV/e - 16 keV/e range, assuming that the
       velocity distribution has rotational symmetry around the local magnetic
       field vector (see next section for further explanations).

EPER8 and ID8 are the mean perpendicular energy (perpendicular to magnetic
       field; two degrees of freedom) in "keV" and standard deviation (%) of
       ions in the 100 eV/e - 16 keV/e range, assuming that same kind of
       symmetry.

EPAR8 and ID9 are the mean parallel energy (parallel to magnetic field; one
       degree of freedom) in "keV" and standard deviation (%) of ions in the
       100 eV/e - 16 keV/e range, assuming that same kind of symmetry.


3.2 Further Explanations of Certain Variables.

The magnetic field values provided here may to some extent duplicate what has
already been archived at the NSSDC by the magnetometer principal investigator
(Prof. C. T. Russell; NSSDC identification number 77-102A-04), but are not in-
tended to supplant those.  The values derived here may not have been adequately
screened against telemetry noise or adjusted for instrument anomalies, so it is
recommended that the PI provided data be consulted whenever there is doubt about
accuracy.  There are two types of errors known to occur here:

a.     When the magnetometer is commanded to low gain on the inbound leg of
       the s/c orbit, usually between R = 8 Re and = 5 Re, the corresponding
       flag may show up slightly too late on the raw data tape, resulting in
       a brief underrepresentation of the field by a factor of 32.  This may
       last for about a minute or less (part of one major frame) and affects
       a single MD interval.  This error ought to be fairly obvious in the ED
       data, and therefore traceable in the MD data as well (by comparing the
       times).  The corresponding mismatch at high gain command on the out-
       bound leg, that is a sudden 32-fold increase of the field, is usually
       discovered as "unreal" and corrected.

b.     Occasionally it appears that the wrong antenna flip status has been
       inferred from the raw data behavior (pertains to the s/c Y and Z co-
       ordinates), resulting in anomalous modulations of the GSE components.
       These modulations cause the sum BXMD**2+BYMD**2+BZMD**2 to be much
       smaller than the square of the time-averaged absolute field strength
       BTMD**2.  It is recommended that the two measures of field strength
       be compared routinely, and that other magnetic field data be consulted
       if those two differ by more than a few percent.  An additional (or
       alternative) check can be made by summing IPAMIN and IPAMAX.  If the
       sum is several degrees smaller than 170 deg or several degrees larger
       than 190 deg, then the magnetic field should be in doubt.

The velocity moments have been calculated two ways, A and B, using either of two
energy-angle matrices.  Both matrices consist of 32 energy channels (covering
the entire range from 10 eV/e to about 18 keV/e), but one has 12 spin angle sec-
tors (30 deg each) and no pitch angles, the other has 9 pitch-angle sectors (20
deg each) and no spin angles.  In method A, using 12 spin angle sectors, the
calculations consist of the following steps:

A.I    A phase space density and a corresponding standard deviation are
       assigned to each matrix point that has been sampled, using the
       local average count rate, minus an average background count rate,
       and the number of samplings.  No interpolations are made at this
       stage.

A.II   Within each energy channel that has been sampled (usually all have),
       except the bottom and top ones, the phase space densities are weighted
       by cosines or sines of the spin angle (center of sector) and summed
       over angle to form two orthogonal projections.  At this stage the
       phase space densities are interpolated in angle, if some angular bins
       have no samples.  These projections are in turn weighted by energy and
       by an energy bandwidth (see below) and summed over energy channels,
       forming two orthogonal components, approximately the GSE X and Y com-
       ponents, of a vector that is proportional to number flow density.
       Both components are then divided by a total (scalar) sum of phase
       space densities weighted by the energy bandwidth and by the square
       root of the energy, that is by a sum proportional to number density,
       to form (approximate) X and Y drift velocity components, and a drift
       angle IDRFT.  Similar summations are carried out with the variances
       (square of standard deviations), using the corresponding partial de-
       rivatives (squared) as weights, to derive the standard deviation of
       the drift angle (ID4).

A.III  A spherical coordinate system is envisioned with its polar axis along
       the drift velocity vector, that is in the GSE X-Y plane.  It is now
       assumed that the phase space density has azimuthal symmetry in this
       coordinate system (rotational symmetry around drift velocity vector).
       The number density, flow density (but not angle), and energy density
       are recalculated by summing over solid angle and energy in this system.
       The solid angle weighting factors in this case are zones on a unit
       sphere, each defined at the intersection with the GSE X-Y plane by the
       boundaries of a 30 deg spin angle sector, or by one boundary and the
       drift velocity vector.  These zones are partially overlapping, and
       summing over 12 spin angle sectors (typically = 14 zones) means cover-
       ing the unit sphere twice, so a factor 1/2 is applied to each sum.
       The drift speed (VDRFT) and mean energy (EMN8) are obtained by dividing
       flow density and energy density, respectively, by the number density
       (DNS8).  No drift energy is subtracted from this mean energy.  The cor-
       responding standard deviations (ID3, ID2, and ID1) are derived from
       similar sums of variances, using partial derivatives as weights.

A.IV   The partial number density of ions in the bottom energy channel (DNS5)
       and the corresponding standard deviation (ID0) are also calculated in
       this coordinate system, although in this case the energy "sum" has a
       single term covering the channel width (10 eV/e to about 100 eV/e).

If the drift speed in step A.II corresponds to less than 1 eV (less than 14
km/sec for H+, less than 4 km/s for O+, etc.), then the coordinate system is
instead aligned with the X-Y projection of the magnetic field (calculated from
BXMD and BYMD), provided the field elevation angle (including BZMD) is between
-45 and +45 deg.  If the latter is not the case, and if the drift speed is be-
low minimum, the coordinate system is aligned with the s/c spin axis, and the
phase space densities are treated as isotropic.  Only density and mean energy
are recalculated in these two cases.

In method B, using 9 pitch-angle ranges (0.0 - 19.9, 20.0 - 39.9, etc.),
the steps are as follows:

B.I    A phase space density and a corresponding standard deviation are
       assigned to each matrix point that has been sampled, using the
       local average count rate, minus an average background count rate,
       and the number of samplings.

B.II   If only part of the pitch-angle range has been sampled, which is
       often the case (indicated by IPAMIN and IPAMAX), then the empty
       angular bins near 0 deg and 180 deg are assigned the same phase
       space density as the nearest sampled bin (closer to 90 deg) at
       the same energy.

B.III  A spherical coordinate system is envisioned with its polar axis
       along the magnetic field vector (arbitrary direction).  It is now
       assumed that the phase space density has azimuthal symmetry in this
       coordinate system (rotational symmetry around magnetic field vector),
       which is to say that the phase space densities in the 9 pitch-angle
       bins represent the entire unit sphere.  The number density and the
       parallel (axial) and perpendicular energy densities are calculated
       by summing over solid angle and energy in this system.  When summing
       over solid angle, the parallel and perpendicular energies are repre-
       sented by, respectively, the cosine square and the sine square of
       the pitch angle at the center of each bin.  The solid angle weighting
       factors in this case are 9 contiguous zones on a unit sphere, each
       defined by the boundaries of a 20 deg pitch-angle sector.  The two
       mean energies (EPAR8 and EPER8) are obtained by dividing the respec-
       tive energy densities by the number density (DENS8).  The correspond-
       ing standard deviations (ID9, ID8, and ID7) are derived from similar
       sums of variances, using partial derivatives as weights.  Only the
       standard energy range (0.1 - 16 keV/e) is included here.

EPER8 and EPAR8 should have a ratio of 2:1 if the velocity distribution is iso-
tropic (or if the count rates have been extrapolated from a single bin at 90 deg
pitch angle), since EPER8 represents two degrees of freedom and EPAR8 only one.
Due to rounding-off errors in the summation over angle, however, the isotropic
ratio is not exactly 2, but about 1.969.  More specifically, if statistical and
instrumental errors are neglected, EPER8 is very nearly exact (about 0.02% too
small), but EPAR8 is about 1.55% too large.  Naturally, neither energy will be
very meaningful if the magnetic field is in error (see above).

The "ion plasma beta" listed in the title line, BETA, is actually calculated
with method A.  The ion pressure used here is equal to 2/3 (two degrees of free-
dom) of the sum of "thermal" energy densities of the four ion species, that is
total energy densities minus the energy densities associated with the respec-
tive drift speed, as calculated assuming symmetry around the respective drift
velocity vector.  This pressure has been divided by a magnetic pressure based
on BTMD.  An alternative and more formally correct value may be calculated using
the "gyrotropic" density DENS8 and perpendicular energy EPER8, although those
quantities do not account for bulk flow (drift).  In case the magnetic field
is suspect, and other field measurements are available, the beta can only be
recalculated with method A (using DNS8, EMN8, and VDRFT for each ion).

The summation over energy treats each energy channel, except the first and
second ones, as a point measurement at the center energy, and takes the energy
bandwidth to be the distance between adjacent sampled channels in the trape-
zoidal fashion, ignoring intermediate channels with no samples.  At the second
channel an extra term is added to extend the standard energy integral from the
center of the channel downward to about 0.1 keV, assuming the flux to be a con-
stant.  This addition brings the mathematical energy range into better agreement
with the instrumental range of acceptance.  At the first energy channel, which
is treated separately, the energy summation has only one term that includes the
channel width (10 eV/e - 100 eV/e) as a factor (only DNS5 and ID0 calculated).

Since the summations are done after the completion of an energy/mass scan cycle,
the energy channels have normally been sampled in a contiguous fashion, but the
summation procedures are set up to accept gaps of as many as four channels (due
to noisy data), before declaring the data insufficient.

Depending on the scan mode, the lowest and highest energy channels sampled may
vary, and are sometimes different for different ions.  The summation procedure
uses the actual lower and upper channels, so the moments of different ions may
on occasion cover different energy ranges.  There are no flags to separate ions
in that regard in the MD-file (insufficient space), but the actual energy cov-
erage is shown for each ion in the MC-file (see Guide).  See also the explana-
tion of ENEMAX above.

The variable ACSEC is a sum of elementary time segments associated with each
commanded setting of the power supplies controlling energy and mass channels.
These elementary times are 1/4 sec during low bit rate operation (about 80% of
the time) and 1/16 sec during high bit rate operation.  These times include the
resetting of the power supplies, however, and are slightly longer than the times
associated with particle counting.  For simplicity, the particle counting is
interrupted for about 12% of the elementary time segments in both low and high
bit rate operation to allow for resetting.  The ACSEC therefore exceeds the ac-
tual particle counting time by about 14% in both cases.


                             4. THE PF-FILE

This file contains, in a certain sense, the three highest count rates (actually
counts per sampling) of the five ion species H+ (ion 1), He++ (ion 2), He+ (ion
3), O+ (ion 4), and O++ (ion 5) during each complete energy/mass scan cycle (a
few to about 20 minutes).  More specifically, it lists, separately for each
species, the maximum count rate from the three energy channels having the
first, second, and third highest count rates, respectively.  Following a title
line with date, time, ephemeris, and other information, the highest count rate
for each of the five species is listed on one line, along with auxiliary
information (see below), including the respective energy channel number (1-32),
the second highest on the next line, along with the same kind of information,
and the third highest on the following line.  As with the other data files, it 
is important to keep in mind that the various ion labels really only separate 
different M/Q values (M/Q= 1, 2, 4, 16, and 8, respectively).

Because the product of geometric factor and energy channel width is fairly
constant for this instrument (see a FORTRAN program listing below), the peak
count rates in most cases represent peak differential fluxes as well ("PF"
denotes "peak flux").  How a count rate is converted to differential flux or
phase space density is explained below.  This file has been derived from the
much larger MC-file, which has count rates from all 32 energy channels and
also has spin-averaged count rates and their standard deviations (see Guide). 


4.1 File Format

The PF-file has been written in groups of 4 lines (4 records), using formatted
sequential FORTRAN WRITE statements as follows: 

The first line in each group is a title:

      WRITE(13,120)
     * IYYDDD,JSTART,JSTOP,RX,RY,RZ,RT,RSEY,RSEZ,
     * DZ,IMLAT,TLOCL,BXMD,BYMD,BZMD,BTMD,BETA,IDBETA,BGND,IDBGND,
     * MAXES0,NSPLPS

  120 FORMAT(3I6,7F6.1,I4,F5.1,4F8.1,1PE10.2,I3,1PE9.2,I3,2I3)


The variable names represent the following quantities:

IYYDDD is the year (two digits) and day of year (three digits).

JSTART is the universal time in seconds (not minutes) at the beginning of
       the averaging interval, that is the time of the first good data in
       that interval.  This is normally at the start of an energy/mass scan
       cycle, unless some initial data in that cycle are bad.

JSTOP  is the universal time in seconds (not minutes) at the end of the
       averaging interval, that is the time of the last good data in that
       interval.  This is normally at the end of an energy/mass scan cycle,
       unless the last data in that cycle are bad.

RX, RY, RZ, and RT are, respectively, the GSM X, Y, Z, and radial distance
       at the midpoint of the averaging interval, all in units of "earth
       radii" ("Re").  RY and RZ are set to 999. if GSM coordinates not
       available (RX same in GSE).

RSEY and RSEZ are the GSE Y and Z (at midpoint of averaging interval) in units
       of "earth radii".

DZ     is the distance in "earth radii" (at midpoint) from the nominal neutral
       sheet in the geotail according to Fairfield and Ness [J.Geophys. Res.,
       75, 7032, 1970].  This is only displayed for GSM X < -11 Re, otherwise
       set to 999.  If no GSM coordinates available, it is set to 0.

IMLAT  is the geomagnetic latitude in degrees (at midpoint), rounded to the
       nearest integer.  This is set to 0, if no ephemeris tape available.

TLOCL  is the geographic local time in hours and 1/10 hours (at midpoint).
       This is set to 0.0, if no ephemeris tape available.

BXMD, BYMD, BZMD, and BTMD are the GSE components and absolute value, respec-
       tively, of the measured magnetic field, each averaged over the whole
       interval (for data quality check, see description of MD-file above).
       The unit is "nanotesla" ("nT"), or equivalently, "gamma".

BETA and IDBETA are a simplified representation of the ion plasma beta and its
       standard deviation (% of absolute value).  Its definition is explained
       in the description of the MD-file above.

BGND and IDBGND are the average background count rate in counts per sample
       (not per second) and standard deviation (%).

MAXES0 is the number of the highest energy channel sampled at any phase of
       the energy/mass scan cycle (1-32).

NSPLPS is the number of samples per second taken during the current energy/mass
       scan cycle, either 4 (low bit rate) or 16 (high bit rate).


The next three lines list, respectively, the highest (I=1), second highest
(I=2), and third highest (I=3) count rates and associated information for, from
left to right, H+ (J=1), He++ (J=2), He+ (J=3), O+ (J=4), and O++ (J=5).  The 
second and third highest count rates here are actually the maximum count rates 
in two energy channels other than the one with the absolute maximum:

      DO 140 I=1,3
      WRITE(13,130)
     * (IEPCNT(I,J),LOWSNS(I,J),
     * IPCTR(IEPCNT(I,J),J),IUTPC(IEPCNT(I,J),J),
     * IPDEG(IEPCNT(I,J),J),IWDEG(IEPCNT(I,J),J),J=1,5)

  130 FORMAT(I3,I2,I6,I5,I4,I4,4(I6,I2,I5,I5,I4,I4))
  140 CONTINUE


The variable names represent the following quantities:

IEPCNT is the number (1-32) of the energy channel having this count rate.

LOWSNS indicates whether the count rate was obtained in normal or low 
       sensitivity.  Normal is =0, low is =-9 (latter same as in MC-file).

IPCTR  is the maximum number of counts during any single sample (about 1/4:th
       or 1/16:th of a second) of the particular ion species at this energy.
       A value = -1 indicates that no data were available.  If LOWSNS = -9, 
       this count rate was obtained in low sensitivity (typical for H+ and 
       He++ in solar wind and for H+ in magnetosheath as well).  The number 
       listed here has been multiplied by a corrective factor but should none-
       theless be treated with great caution (see Guide).

IUTPC  is the (approximate) time of maximum count rate (IPCTR), expressed as
       integer number of seconds after the beginning of the current averaging
       interval.  That is, the universal time in seconds is = JSTART + IUTPC.

IPDEG  is the angle of motion in the s/c spin plane of those ions that cause
       the maximum count rate.  The angle refers to the midpoint of the samp-
       ling interval (and the midpoint of the instrument field of view), and
       is rounded to the nearest integer.  During each sampling interval the
       instrument sweeps (spins) through about 30 deg of angle in low bit rate
       (4 samplings/sec), and about 7.5 deg in high bit rate (16 samplings/sec).

IWDEG  is a measure of the angular width (nearest integer) of the ion flux dis-
       tribution around the maximum.  It is a sum of two angles, one being the
       closest spin angle from IPDEG with a count rate less than 1/3 of IPCTR,
       the other being the most distant spin angle from IPDEG with a count rate
       at least 1/3 of IPCTR.  That is, IWDEG is a crude measure of the full
       width at 1/3 of maximum.  It is measured after IUTPC if more than 1/2
       s/c spin remains, otherwise set to -1.  If IPCTR is more than 3 times
       greater than any subsequent counts, IWDEG is set to 30 deg in low bit
       rate and 8 deg in high bit rate (or -1 if too close to end of interval).


4.2 Relevant Instrument Parameters.

To convert counts per sample, or CTS, to counts per second, or CTRATE, use

       CTRATE = CTS *RATE /0.21865

where RATE = 1.0 in low bit rate, and RATE = 4.0 in high bit rate.

However, the count rates in the PF-file are raw counts and need to be adjusted
for detector degradation (including peak counts and background).  These count
rates have been obtained at the higher of two pulse hight triggering levels in
the MD particle detector, at the MDTCR = 2 level.  The lower level, MDTCR = 1,
provides a more nearly one to one detection level, that is one count for every
ion entering the detector, but it also admits more false counts due to penetrat-
ing radiation than does the higher level.  The reason for using the MDTCR = 2
level is to minimize the background.  The lower sensitivity to ions is not a
problem in itself as long as it is well known, since the count rate can be ad-
justed accordingly, but it has slowly declined over time, making it necessary
to do periodic in-flight calibrations.  These have consisted of intercomparing
the count rates at the MDTCR = 1 and = 2 levels, which are both part of the
instrument output, during times of extremely low background.  Fortunately, the
MDTCR = 1 level has shown no degradation, and can be used as a standard refer-
ence.  The following table shows the results of these intercomparisons in the
lowest and highest energy channels for the four principal ions (date refers to
beginning of month).  The intercomparisons for O++ (ION= 5) have been less ex-
tensive but suggest that the O+ (ION= 4) ratios can be used for the O++ as well.


c Ratios of MDTCR= 2 count rate to MDTCR= 1 count rate in flight;
c
c in lowest energy channel:
      DATA CMD01/
c  launch - Jan 78,    Jul 78,    Jan 79,    Jul 79,    Jan 80,    Jul 80
c ION= 1
     *       .90,       .81,       .60,       .48,       .36,       .24,
c ION= 2
     *       .95,       .90,       .80,       .70,       .60,       .50,
c ION= 3
     *       .95,       .85,       .70,       .60,       .50,       .40,
c ION= 4
     *       .95,       .89,       .75,       .65,       .55,       .45/
c
c in highest energy channel:
      DATA CMD32/
c  launch - Jan 78,    Jul 78,    Jan 79,    Jul 79,    Jan 80,    Jul 80
c ION= 1
     *       .94,       .93,       .82,       .72,       .61,       .50,
c ION= 2
     *       .97,       .95,       .90,       .85,       .80,       .75,
c ION= 3
     *       .97,       .95,       .90,       .85,       .80,       .75,
c ION= 4
     *       .97,       .95,       .90,       .85,       .80,       .75/


Intercomparisons have been made at many energies, and it appears that the ratios
vary about linearly with energy channel number (1 through 32).  That relation
has been used when converting count rates to velocity moments in the MD-file,
that is, the ratios have been interpolated linearly in energy channel number.
They have also been interpolated linearly in time between the dates above.  For
dates beyond July of 1980 this scheme has been abandoned, and MDTCR = 1 counts
have been used exclusively.  Given count rates from before July 1980, these are
thus to be adjusted by

       CTRATE = CTRATE /CMD(IE, date, ION)

where IE is the energy channel number, and CMD(...) is obtained by linear
interpolation in IE and date between the CMD01 and CMD32 in the table.  For
ION= 5 (O++) use the same numbers as for ION= 4 (O+). 

There is another potential deficiency in the peak count rates that depends on
the instrument mass scan mode and cannot be accurately adjusted for at this
stage.  That is, to have exactly one count for every ion entering the MD
detector, on average, requires that the power supplies controlling the M/Q
separation be tuned exactly to the peak response for a given ion at every
energy.  This is impractical, but with the exception of the rather infrequently
used "load mode", the single mass channel chosen to represent a given ion will
have let that ion through at about 90% of peak response, or higher.  In the
load mode, however, every mass channel has been sampled, and all counts at a
response of 40% or higher have been used (for the five ions listed), in order
to ensure reasonable total sampling time.  Although the peak count rate is
likely to have been obtained at 90% of peak response, or higher, even in load
mode, there is a possibility that it was obtained as low as the 40% level in
that mode, at least in cases where the ion flux may have been extremely
anisotropic. 

To determine whether load mode was being used at a particular time it is
necessary to compare the MC- and MS-files (see Guide).  Even if that has been
determined, the peak count rates (IPCTR) cannot be adjusted for this effect at
this stage, however, since the mass channel number is not listed either here or
in the MC-file (sacrificed because of formatting considerations).  By contrast,
all counts used when calculating moments for the MD-file were adjusted for
off-peak response on a sample by sample basis (after first summing over the
mass peak in load mode). 

Once adjusted (to the extent possible), the count rates in the PF-file can be
converted to differential flux "FLUX" and phase space density "F" with the
following subroutine. 


      SUBROUTINE AFLUX( ION, CTRATE, IE, FLUX, F )
c**** Input:  ION= 1 (H+), 2 (He++), 3 (He+), 4 (O+), or 5 (O++)
c****         CTRATE= counts per second (floating point), and
c****         IE= 1, 2, 3, ....., 32 (energy channel)
c****
c**** Output: "FLUX" in units of "/cm2/sec/ster/keV"
c****         "F" in units of "sec3/km6".
c**** _______________________________________________________________________
      DIMENSION AM(5),Q(5) ! ion mass and charge units
      DATA AM/1.,4.,4.,16.,16./, Q/1.,2.,1.,1.,2./
c**** instrument energies (center of channels):
      DIMENSION ENERGY(32) ! "keV/e"
      DATA ENERGY/
     *   .040,   .212,   .410,   .628,   .851,  1.095,  1.353,  1.633,
     *  1.929,  2.244,  2.580,  2.934,  3.317,  3.718,  4.146,  4.599,
     *  5.080,  5.592,  6.132,  6.713,  7.333,  7.998,  8.701,  9.446,
     * 10.235, 11.076, 11.969, 12.917, 13.927, 14.999, 16.144, 17.364/
c**** instrument geometric factors, including delta-E:
      DIMENSION G(32,5) ! "1.0E-4 cm2 keV"
      DATA G/
c**** ION= 1:
     * 3.60,6.00,6.00,6.00,6.01,6.01,6.01,6.01,6.01,6.01,6.02,6.02,6.02,
     * 6.48,6.94,7.40,7.85,8.31,8.77,9.23,9.69,10.3,10.9,11.5,12.1,12.8,
     * 13.4,14.0,14.6,15.2,15.8,16.4,
c**** ION= 2:
     * 4.50,7.37,7.20,7.04,6.87,6.70,6.54,6.37,6.21,6.04,5.87,5.71,5.54,
     * 5.85,6.17,6.48,6.80,7.11,7.43,7.74,8.06,8.39,8.71,9.04,9.37,9.69,
     * 10.0,10.4,10.8,11.2,11.6,12.0,
c**** ION= 3:
     * 7.20,11.9,11.3,10.7,10.0,9.41,8.79,8.16,7.54,6.92,6.30,5.67,5.05,
     * 5.37,5.69,6.01,6.32,6.64,6.96,7.28,7.60,7.99,8.38,8.77,9.16,9.54,
     * 9.93,10.3,10.7,11.1,11.5,11.9,
c**** ION= 4:
     * 3.10,5.28,5.23,5.17,5.12,5.07,5.01,4.96,4.91,4.86,4.80,4.75,4.70,
     * 4.85,4.99,5.14,5.29,5.44,5.59,5.73,5.88,6.26,6.63,7.02,7.42,7.82,
     * 8.23,8.61,9.02,9.42,9.82,10.2,
c**** ION= 5:
     * 4.71,7.83,7.55,7.28,7.01,6.74,6.47,6.19,5.92,5.65,5.38,5.10,4.83,
     * 5.05,5.26,5.47,5.69,5.90,6.12,6.33,6.54,6.92,7.30,7.68,8.06,8.52,
     * 8.96,9.34,9.72,10.2,10.6,11.0/
c**** normalize:
      GDE= G(IE,ION)*1.0E-4
c**** differential flux:
      FLUX= CTRATE/GDE/Q(ION) ! "/cm2/s/sr/keV)"
c**** phase space density:
      F= 0.5449208*FLUX*AM(ION)*AM(ION)/Q(ION)/ENERGY(IE) ! "s3/km6"
      RETURN
      END


The energy channel widths (in keV/e) and the angular fields of view in each
energy channel are inherent in the geometric factors listed in this subroutine
(G-delta-E), but it may be of interest to know them separately:

The external energy bandwidth is defined by the internal energy resolution of
the instrument, which is about a constant 5% at all energies, but the external
bandwidth is not a constant fraction of energy, because the ions are pre-accel-
erated by about 3.0 kV before they enter energy analysis (energy selection).
To obtain the absolute energy bandwidth to incoming ions, add 3.0 keV/e to the
center energies listed in the subroutine, except the lowest energy, and take 5%
of the sum.  The lowest energy channel is different, due to the applied RPA vol-
tage, and extends approximately between 10 eV/e and 100 eV/e (more precisely to
about 110 eV/e).

As described in the main Guide, the center of the instrument field of view (the
one used here) points 5 deg below the spin plane, that is about 5 deg below the
GSE X-Y plane (ion velocity vector pointing 5 deg above).  In this plane the
width is about 10 deg.  In the perpendicular (GSE Z) direction it varies with
energy (due to the pre-acceleration), from about 45 deg at 10 eV/e to 10 deg at
18 keV/e.  To be more specific, if the center energies of the 32 energy
channels are used as reference, the corresponding 32 angular widths are as
follows (full width at 25% of max; in deg): 

       40.0, 30.0, 26.0, 22.5, 20.0, 18.0, 16.5, 15.5,
       15.0, 14.0, 13.5, 13.0, 13.0, 12.5, 12.5, 12.0,
       12.0, 11.5, 11.5, 11.0, 11.0, 11.0, 11.0, 10.5,
       10.5, 10.5, 10.5, 10.5, 10.5, 10.0, 10.0, 10.0