The AE-8 Trapped Electron Model EnvironmentThe AE-8 Trapped Electron Model Environment James I....

NSSDC/WDC-A-R&S 91-24

The AE-8 Trapped ElectronModel Environment

James I. Vette

November 1991

National Space Science Data Center (NSSDC)World Data Center A for Rockets and Satellites (WDC-A-R&S)

National Aeronautics and Space Administration

Goddard Space Flight CenterGreenbelt, Maryland 20771

https://ntrs.nasa.gov/search.jsp?R=19920014985 2020-07-18T06:05:07+00:00Z

Contents

Chapter 1. Introduction .................................................................................................. 1-1

Chapter 2. Overview of the Model ................................................................................... 2-1

Inner Zone ..................................................................................................... 2-I

Transition Region ......................................................................................... 2-2Outer Zone ...................................................................................................... 2-2

Chapter 3. Data Processing/Analysis ............................................................................ 3-1

Azur Proton-Electron Detector .................................................................... 3-2

OV1-19 Electron Spectrometers ................................................................... 3-5OV3-3 Electron Spectrometer ............. : ........................................................ 3-7ATS 5 and 6 Omnidirectional Spectrometers ............................................. 3-8

Chapter 4. Comparison of the AE-8 Model with Data .................................................... 4-1

Chapter 5. Presentation of the Model ............................................................................. 5-1

Numerical ...................................................................................................... 5-1

Logical Organization ............................................................................... 5-2Physical Representation ......................................................................... 5-2

Analytical Forms .......................................................................................... 5-3

Magnetic Cutoffs Resulting from the Atmosphere ................................. 5-3Local Time Function ............................................................................... 5-4

Flux Variation Along the Field Line ....................................................... 5-4Statistical Function ................................................................................ 5-5

I

iii I_I{]!__) _ . I_TT_JT,nN_Ii V _IANK

PRECEDING IIAC_ BLANK NOT FILE#ED

GraphicalPresentation...........................................................................5-7

Orbital IntegrationResults.............................................................................5-8

AppendixA. lruncUon 'I'RARA2 ...................................................................................... A- 1

Method .............................................................................................................. A- I

Source Code Listing .......................................................................................... A-4

References ........................................................................................................................ R- 1

Tables ............................................................................................................................... T- 1

Figures ............................................................................................................................. F- 1

iv

List of Tables

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

Table 6A.

Table 6B.

Table 6(2.

Table 6D.

Table 7.

Table 8.

Table 9.

Table 10.

Table 1 1.

Table 12.

Table 13A.

Table 13B.

Table 14.

Azur Greater Than 1.5 MeV Normalized Local Time Distribution .............. T- 1

Characteristics of the OVl-19 Low and High Energy Electron

Spectrometers ................................................................................................ T-2

Ratio of (CR-BREM)/CR for OV1-19 Spectrometers ...................................... T-3

Flux Fraction d for OV1-19 HES Channels ................................................. T-3

Parameters for Conversion of OV1-19 Flux to Integral Energy

Spectrum ........................................................................................................ T-4

OV I-19 Equatorial Unidirectional Flux Uncorrected for Background(electrons/sq cm-ster-keV-s) ......................................................................... T- 5

OV1-19 Equatorial Unidirectional Flux Corrected for Backgroundand Using AE-8 (electrons/sq cm-ster-keV-s) .............................................. T-5

0V1-19 Equatorial Omnidirectional Integral Energy SpectrumCorrected for Background Using AE-8 (electrons/sq cm-s) .......................... T-6

OV1-19 Equatorial Omnidirectional Integral Energy SpectrumUncorrected for Background and Using AE-8(electrons/sq cm-s) ........................................................................................ T-6

Characteristics of the OV3-3 Magnetic Spectrometer .................................. T-7

Grid Points and Other Parameters for AE-8 Numerical

Representation .............................................................................................. T-8

AE-8MAX Header and Logical Data Record (partial) .................................... T-9

AE-8 Local Time Amplitude Function ........................................................ T-10

AE-8 Outer Zone Magnetic Field Line Parameter m (L) ............................. T-10

AE-8 Standard Deviation of the Z Function, O (> E, L) .......................... T-11

AE-8MAX Equatorial Omnidirectional Fluxes Above Energy E ................ T-12

AE-8MIN Equatorial Omnidirectional Fluxes Above Energy E ................. T-13

Four Circular Orbit Daily F1uence Summary Using AE-8MAX ................. T-14

v

List of Figures

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 1 1.

Figure 12.

Figure 13a.

Figure 13b.

Figu re 14a.

Figure 14b.

Figure 15a.

Figure 15b.

Figure 16a.

Figure 16b.

Figure 17a.

Figure 17b.

Figure 18.

Figure 19.

Figure 20.

Figure 21.

Figure 22.

Figure 23.

Local Time Variations for E > I. 5 MeV ....................................................... F- 1

Azur Data at L = 3.0 and the Determination of Atmospheric Cutoffs ....... F-2




Magnetic (Atmospheric) Cutoff Models ..................................................... F-6

Azur Data Greater Than 1.5 MeV Versus "I3me at L = 4.4 ........................... F-7

Azur Data Greater Than 4.5 MeV Versus Time at L = 3.0 ........................... F-7

OV1-19 Data at L = 3 .................................................................................... F-8

OVI-19 Data at L = 4.5 ................................................................................. F-9

OV1-19 Data at L = 6.0 ................................................................................. F-10

ATS Long-Term Electron Observations at L - 6.6 ..................................... F-11

Comparison of SOLMAX Models at L = 2.5 ................................................ F-12

Comparison of SOLMIN Models at L = 2.5 ................................................. F-12

Comparison of SOLMAX Models at L = 2.6 ................................................ F- 13

Comparison of SOLMIN Models at L -- 2.6 ................................................. F- 13

Comparison of SOLMAX Models at L = 2.7 ............................................... F- 14






Comparison of AE-8MAX with Outer Zone Data at L = 3.0 ....................... F- 17

Comparison of AE-8MAX with Outer Zone Data at L = 3.2 ........................ F- 18

Comparison of AE-8MAX with Outer Zone Data at L = 3.4 ........................ F-19




vi

Figure 24.

Figure 25.

Figure 26.

Figure 27.

Figure 28.

Figure 29.

Figure 30.

Figure 31.

Figure 32.

Figure 33a.

Figure 33b.

Figure 34.

Figure 35.

Figure 36.

Figure 37.

Figure 38.

Figure 39.

Figure 40.

Figure 41.

Figure 42.

Figure 43.

Figure 44.

Figure 45.









Comparison of AE-8 with Outer Zone Data at L = 6.0 ................................ F-31

Comparison of AE-8 with Some Outer Zone Data at L = 6.6 ...................... F-32

Comparison of AE-8 with Some Outer Zone Data at L = 6.6 ...................... F-33

Comparison of AE-8 and AE-4 at L = 7.0 .................................................... F-34




Comparison of AE-8 and AE-4 at L = 10.0 .................................................. F-38

Comparison of AE-8 and AE-4 at L = 11.0 .................................................. F-39

AE-8MAX Equatorial Radial Profile ......................................................... F-40

AE-8MAX/MIN Comparison at 0.04, 1.00, 3.50, and 5.50 MeV ................. F-41




AE-8MAX/MIN Comparison at 0.75 and 3.00 MeV ................................... F-45

v_

Chapter 1Introduction

The machine-sensible version of the AE-8 electron model environment was completed inDecember 1983. It has been sent to users on the model environment distribution list and ismade available to new users by the National Space Science Data Center (NSSDC). AE-8 is thelast in a series of terrestrial trapped radiation models that includes eight proton and eightelectron versions. With the exception of AE-8, all of these models were documented in formalreports as well as being available in a machlne-sensible form. The purpose of this report is tocomplete the documentation, finally, for AE-8 so that users can understand its constructionand see the comparison of the model with the new data used, as well as with the AE-4 model.

1-1

Chapter 2Ovendew of the Model

The model is comprised of three parts: (I) an inner zone that covers the L (McIlwainparameter) range 1.2 - 2.4, (2) an outer zone that covers the L range 3 - 11, and (3) a transitionregion for 2.4 < L < 3.0. For each part there are two versions: One depicts solar maximum(SOLMAX) conditions, and the other is for solar minimum (SOLMIN). An overview of each partfollows.

Inner Zone

The inner zone parts were produced and documented earlier as models in the overall series:AE-5 Projected (AE-5P) for SOLMIN (Teague and Vette, 1974) and AE-6 for SOLMAX (Teague etal., 1976). Both of these were based onAE-5 (Teague and Vette, 1972) and the revision of theOV3-3 flux levels used in AE-5. AE-5, with an epoch of October 1967, was developed in aunidirectional differential energy flux form and converted to omnidirectional integral energyflux for its final output form. Analytical functions for the pitch angle dependence, includingan atmospheric cutoff, and the energy spectrum were chosen based on the data. Three timeeffects were studied and modeled: magnetic substorms, Starfish decay, and solar cycle. Forelectrons below 0.7 MeV, the main temporal effect was a result of the solar cycle. Above thisenergy and at the L values above 2, substorm injections were large but infrequent. At epochthe Starfish residue was important for L < 1.7 mainly at intermediate energies. AE-5P wasobtained from AE-5 by using the Starfish decay model of Teague and Stassinopoulos (1972) toremove the Starfish residue and by adjusting the solar cycle dependent fluxes of AE-5 toSOLMIN. The AE-6 model consisted of the removal of the Starfish residue from AE-5; no solarcycle changes were needed, since the epoch of AE-5 was one of SOLMAX_ A later study of anumber of new inner zone electron data sets indicated that no changes to these models wereneeded (Teague et al., 1979).

2-1

Transition Region

This region is the most difficult to model since it is affected by infrequent but large substorminjections that result in greatly varying energy spectra. Long-term {~ yearly) averages do notprovide the quasi-steady picture found in the outer zone. Since the analysis of data to producemodels differs between the inner zone and outer zone, the decision was made to use a transition

region as an interpolation region between the two models. In pracUce this means prescribingthe flux at specified energies on the five L shells 2.5, 2.6, 2.7, 2.8, and 2.9. This was done aspart of the original AE-5P and AE-6 models to stitch them together with the AE-4 outer zonemodel. Naturally, the values for AE-8 in this region are different from these earlier models.These differences are mainly for energies above 1 MeV, as shown in Chapter 4. Both SOLMINand SOLMAX transition region versions exist, since the solar cycle effect is seen from L = 1.4out to L = 5.5.

Outer Zone

AE-8 in thls region was formulated by

Studying the data from Hovestadt's Proton-Electron Detector experiment flown on theGerman Research Satellite A (GRS-A); Vampola's Energy Spectra, Fluxes, and Pitch AngleDistribution of Electrons experiment flown on OV1-19; and Vampola's Magnetic ElectronSpectrometer experiment flown on OV3-3.

• Using the analyzed results of Paulikas and Blake (1979) of the energetic electron data fromtheir experiment on ATS 6 and McIlwain's experiment on ATS 5.

• Using the outer zone AE-4 model (Singley and Vette, 1972a and 1972b) to makemodifications dictated by the data above to arrive at the outer zone portion of AE-8.

The GRS-A satellite is commonly called Azur; this latter name will be used in this report.Using the Azur data, an empirical atmospheric cutoff was determined for AE-8 to replace theconservatively (pessimistically) chosen hmax = 200 km for AE-4. The local time variation wasextended down from L = 5 to L = 3, also using the Azur data. Based on the ATS 6 local timevariation obtained from Paulikas (1981), no solar cycle effect for this variation exists in AE-8,as opposed to AE-4. The energy spectrum above 2.5 MeV was enhanced at L = 6.6, using thegeostationary data and then using Azur and OV1-19 data, the spectra above 2.5 MeV werealtered from AE-4 throughout the outer zone. The flux variation along the field line has thesame dependence as AE-4, and the statistical variation given by the standard deviation of thelogarithm of the flux is also unchanged, except for the extension to higher energies.

2-2

Chapter 3Data Processing�Analysis

The framework for the outer zone portion of AE-8 will be discussed now so that the processingand analysis of the new data can be understood. The details of the inner zone formalism willbe reviewed in Chapter 5 (page 5-3 through 5-5). The formalism for AE-8 outer zone (OZ) is thesame as that used for AE-4, where the omnidirectional flux above an energy (E) is given as afunction of the position along a field line (b), the L shell (L), the local time (¢_), and theepoch (T). The variable b is

b = B/B o (3. I)

where Bo is the magnetic field strength at the geomagnetic equator based on an internal fieldonly. B is the magnetic field strength of the intemal field at the position in question; thus b isa coordinate along the field line that has the value I at the equator and _ at the dipole. Thelocal time variation is mainly the effect of the magnetic field generated by current sourcesexternal to the Earth's surface. Although this choice of variables for the model is not the bestfor studying the details of particle dynamics in the outer zone, it is much more convenient forthe user to apply the model to satellite orbits.

The AE-8OZ omnidirectional flux is written as

J(>E,b,L,(_,T) = NT(>E,L)(_(>E,L,_)G(b,L) (3.2)

where N T gives the equatorial integral spectrum, ¢_ gives the local time variation, and Gprovides the variation of flux along the field line. This simplification of three productfunctions is justified by the outer zone data. Specifically. the local time function has the form

_(¢-11)

_)(>E L,#) = K(>E,h) I0 [C(>E,L) cos ] (3 3)r 12 "

3-1

Data

The peak in this function at 4p= 11 hours is an approximation that is good down to 0.2 MeV,and it was felt, as in AE-4, that more detail was not necessary. The function K is merely one ofnormalization so that

2_

j_-_ - 10

(3.4)

The function C represents the amplitude of the local time variation as seen in the log of theflux. In AE-4 4) was dependent on epoch; this is no longer true for AE-8OZ as noted earlier anddiscussed further in the next section.

The G function has the value of unity at the geomagnetic equator and is

b-m (L)_bc-b_m (L) +0 •5

[bc_lj ; b < bc

G (b, L) = (3.5)

0 ; b > bc

The value for the exponent m is the same as AE-4, since this quantity can best be determined bydata covering the low and mid latitudes, not high latitudes. The cutoff given by bc can only beobtained from high latitude satellites such as Azur. It is useful to note that the form of the bdependence given by G for an omnidirectional flux has an analytical counterpart for theunidirectional flux perpendicular to the magnetic field line given by (Roberts, 1965)

b -m [bG-b_m_/ b c

2_(0.5,m+l)[bc_ij Wbc_ 1 ; b < bc

gp(b,L) = (3.6)

0 ; b > b c

where _(0.5,m+l) is the weU known _ function. Equation (3.6) was used in OVl-19 dataanalysis.

The processing of the Azur data will be described next. This will be followed by the OVl- 19processing, then that for OV3-3. Finally, the ATS 5 and 6 analyzed data will be discussed.

Azur Proton-Electron Detector

Azur was launched on November I0, 1969, into a 103" inclination orbit with perigee and apogeealtitudes of 387 km and 3150 km. The Proton-Electron Detector experiment consisted of twocubical silicon (lithium-drifted) detectors, each covered by hemispherical shielding. Therewere two pulse height discriminators associated with each detector. This instrument providedfour channels of information: (1) electrons greater than 1.5 MeV and protons greater than 20MeV, (2) protons 20-45 MeV, (3) electrons greater than - 4 MeV and protons greater than 40 MeV,and (4) protons greater than 72 MeV. This experiment provided data over the lifetime of themission and covered the time period November 25, 1969 - March 15, 1970. The original data setsupplied to NSSDC (ID# 69-097A-04A) contains count rates (CR) from the four channelsdescribed above along with all the position, time, and correlative data needed to analyze thedata. More details on the instrument can be found In Achtennann et al. (1970). Ebel (1972) hasgiven the details of the data processing of the raw data by the experimenters.

3-2

Data

For L > 3, channels (1) and (3) above were measuring only electron fluxes. The conversionfrom CR to flux was provided by the experimenter. The calibration curves were not provided, sothe usual threshold energy/average efficiency studies outlined by Singley and Vette (1972a)could not be done. However, comparison with other data showed that the threshold of 1.5 MeV

was good while the higher energy threshold was better suited to 4.5 MeV for analysis purposes.

The data were binned into selected L shells of + 0.05 width and tagged by the geographic localtime _ and the value of b. Plots were made of the flux versus b and, using equation (3.5) withm values from AE-4, avaluefor b c was determined. Having this, each CRat b = bi and L =L j was projected to the equator by using the G function. This procedure is given by

A = CR(bi,Lj) /G(bi,Lj,mj,bcj) (3.7)

and since G is unity at the equator (b = 1 ), one has

A = CR(b = I,Lj) (3.8)

Then these data projected to the equator were binned in one-hour ¢_ ceils to determine the localtime distribution. The empirical distribution is given in Table 1 with a normalization thesame as that given in equation (3.4). Any bins with no data were ignored, and the integral (orsum in this case) was divided by the number of occupied bins. The least squares fit to the log ofthe flux provides values of C, which are also given in Table 1. The 95% confidence intervalhalf width for C, which is quite small, is also given there. The value of K was also determinedin the fitting process, and, as expected, its value given in Table 1 is close to unity. In anysatellite orbit except geostationary (or near geostationary), it requires a long time to sample allthe local time bins. The coverage for Azur, which lived for about four months, can be seen inTable I. A highly elliptical satellite such as OGO 1, 3, or 5 takes one year to sample all localtimes; geostationary sateUites require only 24 hours. Consequently, there is "noise"introduced in the local time "signal" by enhancements (substorm injections) in the outer zone.One expects that the local time variation should cease around L = 3. The values of C atenergies above 1.5 MeV for various L values are plotted in Figure 1 for AE-4MAX and MIN, forAzur, and for ATS 6. The interval for ATS 6 data corresponds to SOLMIN conditions. Thecurve for AE-8 is shown; this applies to all solar cycle conditions. The AE-4MIN points arenow believed to be elevated because of "noise" in the elliptical satellite data. AE-4MAX had thebenefit of having the ATS 1 data of Paulikas and Blake incorporated. Below L = 6 the AE-8curve differs from the AE-4MAX model so as to conform to the Azur results. The fall of the

curve at high L values reflects the fact that as the flux goes to zero (literally to J = 1, which isabout the value of the cosmic-ray proton background), there is no local time variation.

After the AE-8 ¢_ function was determined, it was used to convert the Azur data base to thelocal time of ¢_ (L), which is defined by the equation

• (_) = 1 (3.9)

and explicitly is

_m = ii + 12COS-I(-c )71

(3.10)

If a measurement was made at bi, L j,procedure was used.

_)i, then to convert this to _mj

CR(bi, Lj, _mj) = CR(bi, Lj, _i)/(1)(Lj, _i)

the following

(3.11)

3-3

£1ata

For each L value this converts the measurement to that which would be observed for the localtime average at bl. The CRs were then converted to flux using the geometrical conversionfactor provided by the experimenter. Then the data were plotted with J versus b at various Lvalues. The results for L = 3.0, 4.0, 5.0, and 6.0 are shown in Figures 2 through 5. In this regionthe data provide good coverage where the cutoff effects occur. The curves that are drawn requiresome explanaUon. These have the form of equation (3.5) with a multiplicative factor insertedsuch that equatorial value of J is the time average of the Azur fluxes projected there, asdiscussed earlier. The two curves in each figure differ only in the value of bc that was chosen.The larger value was chosen so that pracUcally an the points have a b < bc2. The smallervalue was chosen to represent a boundary for "undisturbed" conditions. This is best seen inFigure 2 where there seems to be a boundary of some small width with a relatively smallnumber of points with larger b values. This curve was selected to pass through the center ofthe boundary, not its outer edge. As one looks at the higher L values, one sees a much higherpercentage of points with b values above bcl. Avertical dotted line at bcl is included to helpthe reader see the points beyond this undisturbed boundary. The figures also illustrate why theAzur data are not good for determining the rn value of equation (3.5). Satellites with 30" - 50"inclinations provide good coverage of the b region where cutoff effects are not present; all theavailable data of this type were analyzed in the construction of AE-4.

The bc2 cutoffs are the ones used in AE-8. The reason for this choice was to ensure that one isvery unlikely to experience fluxes beyond the AE-8 cutoff. Feedback from the users haveindicated this is preferable to them. The bcl cutoff is more useful in studying the particlepopulation. This is illustrated in Figure 6 where the cutoff values are plotted versus L. Theinner zone values are taken from the AE-5 document (Teague and Vette, 1972). Notice that theouter zone bet ±s virtually an extension of this inner zone boundary with nearly the same Lpower law dependence. In the outer zone bc2 is about a factor of 1.4 greater than bcl. Afterpassing through the transition region, there is no distinction between these two boundaries inthe inner zone.

The greater than 4.5 MeV channel was processed in the same manner as described earlier inthis section for the greater than 1.5 MeV data. The data from this channel showed the sameatmospheric cutoff (bc2) as the greater than 1.5 MeV data. The dynamic range for the greaterthan 4.5 MeV channel was not as large as that for the greater than 1.5 MeV, being about a factorof 50, and the intensity threshold corresponded to a flux of about 20 electrons/cm2-s. Becauseof these limitations the data did not reveal a consistent local time distribution. So the C (> 1.5MeV) was scaled using the AE-4 model energy dependence to obtain the local time distribution.

Returning to Figures 2 through 5, if one imagines moving the curve associated with bc2 so thatit passes through each plotted point in chronological order, then the projected equatorial fluxvalue as a function of time is obtained. The daffy averages of these projected equatorial fluxesfrom the two Azur channels are shown in Figures 7 and 8 for the L values corresponding to theouter zone peal_ The daily sample size varied from 5 to 18 and averaged about I0. Thestandard deviations of the logarithm of the flux (t_) for these plots are 0.51 and 0.12,respectively. The statistical function for AE-8, which uses t_ is discussed in Chapter 5 (pages 5-5 through 5-7). It was felt that the new data used in AE-8 could not add much to this statisticalfunction over that provided by the data used in AE-4. Both t_ values above from Azur are lowcompared to AE-4. Data sets that have a duration of less than six months often show lower (orhigher) ¢_s than longer lived ones. The use of daffy averages also reduces the t_ value. It isconcluded that Azur statistical behavior is similar to other outer zone data sets.

Thus, the Azur data have supplied the omnidirectional flux for E > 1.5 and > 4.5 MeV for Lvalues from 3.0 to 6.6. It is believed that the greater than 4.5 MeV data suffer from abremsstrahlung background that becomes important for L above 5.5. Another contributingfactor might be the intensity threshold for this channel; when flux levels fall more often belowthis threshold, the average value is distorted upwards. This effect would also reduce the valueof the ¢_ Just discussed.

3-4

Data

OV1-19 Electron Spectrometers

OVl-19 was launched on March 18, 1969, into a 105 ° inclination orbit with perigee and apogeealtitudes of 466 km and 5764 km. Thus, it was in a similar but higher orbit than that of Azur.Vampola had an experiment on board that was comprised of two magnetic electronspectrometers. These instruments provided data from March 18, 1969, to the end of spacecraftlife in March 1970. The data set deposited in NSSDC (ID# 69-025C-05A) terminates on January25, 1970; consequently, there is a data overlap period with Azur of about 61 days, neglecting

data gaps.

The initial results from this experiment were used to claim that the AE-4 model was in grosserror for electrons whose energies are above 1.5 MeV. Unfortunately, it was many years afterthese distorted (but not completely false) claims before the resolution of this matter wasobtained. This came about through the analysis described here, the result of which was theutilization of much of the data from this experiment in AE-8. However, the channels above 2MeV are rather useless in the outer zone as independent data, since a background correction isabsolutely necessary.

The description of the instrument was given by Vampola (1971) and will be summarized heresince an understanding of it is necessary to follow some of the analysis. The spacecraft wasspin stabilized at a rate of 8.4 rpm. Both spectrometers had their look direction perpendicularto the spin axis. A three-axis magnetometer was also on board. The low energy spectrometer(LES) had eight detectors for measuring electrons and one detector for background, all in ananalyzing field of 470 gauss. The background detector had two channels, one for measuringprotons greater than 55 MeV and one for measuring electron bremsstrahlung (BREM). TheBREM discriminator was set to the nominal energy loss level used by the eight detectors. Thehigh energy spectrometer (HES) contained 16 detectors plus a background detector with twochannels, one for protons greater than 130 MeV and one for electron BREM; this latterdiscriminator was set in the same manner as that for the LES. All detectors were lithium-drifted silicon I mm thick with an unshielded sensitive area of 0.95 cm x 1.37 cm. The energylevels and other information about this instrument are given in Table 2. Both spectrometerswere the 180 ° focusing type with internal baffling around the edges of the uniform field and onthe pole plates to provide a disk-loaded collimator. A tungsten collimator was used at theentrance of the magnet. Magnet pole pieces were made of Indox V, and an iron yoke enclosedthe whole assembly. From the threshold energy of protons arriving at the backgrounddetectors, one can infer that the HES had about five times as much shielding as the LES.

Data on magnetic tape (NSSDC ID# 69-025C-05A) contained the CRs for each detector alongwith all the ancillary data needed for analysis. A subset of these data was selected for AE-8analysis; only data with local pitch angles within 3 ° of the perpendicular to the measuredmagnetic field as determined by the on-board magnetometer were studied. Thus, one is dealingwith the unidirectional flux perpendicular to the field line, denoted here by j p. The CR meterswere sampled every second; however, only eight detectors plus two background channels wereread out at one time. LES was read and then two reads were required for the HES.

The big mystery for this experiment was the background. The proton channels had such smallcounting rates that they could be ignored in the outer zone. However, the HES BREM channelcounted much too high to be background for the HES detectors. In Table 3 the ratio (CR -BREM)/CR, averaged over the whole interval March 18, 1969, to January 25, 1970, is given.Negative ratios mean that the background exceeded the raw electron CRs, and from thesenumbers one can rule out the use of all channels above 1.7 MeV and the 53 keV channel over the

range of L values shown, unless appropriate backgrounds can be obtained for subtraction. Theratio of the two BREM channels has also been studied without shedding any light on the

problem. Ignoring the BREM channel, as Vampola did, one arrives at flux values that are muchtoo high (factor of 10-100) compared to other data, as shown in Chapter 4.

3-5

Data

The ATS 6 data of Paulikas and Blake (1979) showed clearly in the geostationary region forenergies above 2.5 MeV that AE-4 was too low and therefore needed revision in the high energyrange. Since the OV1-19 data was the only data set that covered the energy range between 2 and5 MeV at other outer zone L values, it was imperative to try to use these data to revise theouter zone.

The following technique was developed. In Figures 9 through 11 the OV1-19 data are shownprojected to the equator using the same techniques applied to Azur data except that equation(3.6) was used instead of (3.5). The open solid squares, labeled uncorrected, are the raw CRsconverted to flux using the conversion factors of Table 2. Notice that the spectrum is fiat aboveabout 3 MeV for all the L values. This raw directional flux, j r, consists of the true electronflux, jp, plus a background flux, Jb, resulting from BREM; i.e.,

Jr = Jp + Jb (3.12)

By taking the last three channels of the HES with the background (supposedly) removed andperforming the following operation

S = jp(5091 keY)[5243-4942] + jp(4783 keY)[4942-4633] +

jp(4476 keY) [4633-4500] (3.13)

the total electrons/cm2-ster-s in the energy interval 4500 to 5243 keV results. Now this can beconverted to an omnidirectional flux at the equator in electrons/cm2-s by multiplying by theratio of equation (3.5) to (3.6)

f = G/gp = 2_(0.5, m+l)(l-I/bc) 0-5 (3.14)

The product fS obtained from equations (3.13) and (3.14) is denoted here by Je3. Then

Je3 ----J(> 4500 keY) ---JA(> 4500 keY) (3.15)

where JA is the Azur data. This is approximately true since J (> 5243 keV) in the outer zone is

smaU relative to g (> 4500 keV). If j r is substituted for jp in equation (3.13), then Jr3replaces ge3 in equation (3.15). Jr3 is larger than ga, the amount depending on thebackground contamination. Taking the ratio

JAd - (3.16)

Jr3

the fraction of the uncorrected flux representing the real electron flux results. The empiricalresults for d are shown in Table 4. The data from both the Azur and OV1-19 experiments wereaveraged over the data overlap period November 25,1969 - January 25, 1970, to obtain thisratio. It is quite clear that in this energy range the OVI-19 experiment was highly contaminatedwith BREM from lower energy electrons. This quantity d has the same meaning as the ratiogiven in Table 3 except that the background is determined by using the Azur > 4500 keV data.The BREM channels had some 25 to 90 times more counts than expected. The most likely causeof this was that the HES BREM discriminator level in orbit was much lower than those for theHE1-16 detectors. In the case of the LES, the problem may have been that the LEI and LE2

discriminator levels were set high relative to the LES BREM discriminator. The considerablylower conversion factor in Table 2 suggests this was the case and is so noted in the remarkscolumn. This would mean that the background for these two channels would be less than thatindicated by the LES BREM channel. Noting that

3-6

Data

• The six highest channels of the HES showed nearly the same uncorrected flux for

the L interval 3.0 to 6.6,

• Most of the uncorrected flux was produced by BREM,

• The HF_,S BREM channel had much higher CRs than many of the HES detectors andcould not be used to properly subtract the background,

the following procedure was used to determine the average HES background. This is expressedas a directional background flux, Jb. This was obtained by averaging the six highest HESchannels and applying the factor ( 1 -d)

HE16

(l-d) Zjr(i) (3.17)Jb = 6i=HEII

Since Figures 9 through 11 show that these j rS are essentially independent of energy, it is

believed that Jb applies to all of the HES detectors. Then using equation (3.12) the value of jpcan be obtained from the uncorrected flux. In the few instances where this procedure resulted

in a negative jp, then the equation

jp(k) = djr(k) (3. 18)

was used. These results are plotted as the open squares, labeled corrected, in Figures 9 through11. It is apparent that the corrected and uncorrected data above 3 MeV differ by more than afactor of 10. The results also indicate that no correction is required for the LES detectors.

The first corrected integral spectrum for OV1-19 was then constructed by

Jv(> Ei)

17

= f Zjp(k)W(k)

k=i

+ JA(> 4500 keY)

+ 175dfjr(4476 keV) (3.19)

where W ( k ) is the energy channel width for the k th useful channel, and the factor 175 (keV) isthe width from 4325 to 4500 keV. The useful channel index and the Ws are identified in Table 5.

In the final results for OVI-19, JAE-8 (> 4500 keV) was used in equation (3.19) in place of JA (>4500 keV).

The numerical results of all these procedures of this section are given in Tables 6A through 6D.The comparisons of the final corrected data with other data are presented in Chapter 4.

OV3-3 Electron Spectrometer

The 0V3-3 satellite was launched into a 81.4 ° inclination orbit with perigee and apogeealtitudes of 360 km and 4492 km. Vampola had a magnetic electron spectrometer on boardvery ShTdlar to those on OVI-19. This one used nine detectors for measuring electrons, and oneof them had a discriminator channel for measuring penetrating protons greater than 105 MeV.

Since BREM was found not to be a problem in calibration, no BREM background channel wasprovided. The detectors, collimation, and baffling were nearly identical to those used later inOV1-19. Each detector had an independent set of electronics consisting of an amplifier, two-level pulse height analyzer and log(CR) to analog converters covering the CR ranges I- 103 and

3-7

300-2 = 105. More details have been given by Vampola (1969). The channel energy widths andgeometric factors are given in Table 7; also included are the threshold energies for integralspectrum calculations that are employed in the data processing done for AE-8. The geometricfactors are four times greater than those published by Vampola and are based on his revision(Vampola, 1972, as given in Teague and Vette, 1974).

The data were supplied as flux values versus time and included the pitch angle as inferred froma model geomagnetic field along with other parameters needed for analysis. The subset of thisdata used in the AE-8 analysis consisted of the data for pitch angles close to 90 ° for L < I0. TheNSSDC data set (ID# 66-070A-05C) covers the time period August 4, 1966, to September 9, 1967.

The main purpose in processing the OV3-3 data in the outer zone was to provide a comparisonwith the OV1-19 data in the energy ranges that overlapped. The 0V3-3 data had been used inproducing AE-5, and when Vampola changed the geometric factors of the instrument, it wasnecessary to produce AE-6 to replace AE-5. The processing for OV3-3 in the outer zone was donein an identical manner to that used for OV1-19 with one exception. The integral spectrum J(> 2.445 MeV) was estimated by extrapolating the OV3-3 differential spectrum to higherenergies. This procedure was not possible for OV1-19 because of the background problem. Theresults are shown and discussed in Chapter 4. The agreement between the OV3-3 and thecorrected OV1-19 data is good at certain L values. Time variations can explain thedisagreements at other L values.

ATS 5 and 6 Omnidirectional Spectrometers

On ATS 5 McIlwain flew an Omnidirectional High-Energy Particle Detector experimentcomprised of three plastic scintillator detectors with a 2_ field of view and hemisphericalshielding. The instrument measured electrons in the range 0.5 to 5 MeV in 12 channels andprotons greater than 12, 16, and 24 MeV. Paulikas flew an Omnidirectional Spectrometerexperiment on ATS 6 that consisted of four solid state instruments. One was a two-elementtelescope with a 30 ° full cone angle, and the other three were omnidirectional instrumentssimilar to the Azur detectors described earlier. Particles and energy ranges (in MeV) measuredwere

Electrons: 0.14-0.60, > 0.7, > 1.55, and > 3.9

Protons: 2.3-5.3, 3.4-5.3, 12-26, 20-52, and 40-90

Alphas: 9.4-21.2, 13.4-21.2, and 46-100

The lowest energy electron channel and the two lowest proton and alpha channels weredirectional (from the telescope); all the rest were omnidirectional. Only the electron channelsof these two experiments are of interest here.

Paulikas and Blake (1979) presented the data from McIlwain's ATS 5 experiment and their ATS6 data in the following manner, as shown in Figure 12. They produced from McIlwain's datathe omnidirectional fluxes to match their four channels on ATS 6. The ATS 5 data cover theapproximate period 1969.7-1972.3 while the ATS 6 data cover 1974.5-1978.3. The ATS 5 datawere normalized to the ATS 6 data during some simultaneous coverage in mid- 1974. TheZurich monthly sunspot number is also plotted in Figure 12 and shows that the combined datacover both SOLMIN and SOLMAX conditions. The ATS 1 data of Paulikas used in AE-4 also

appear in Figure 12. All of the electron data are plotted as 27-day running averages, and yearlyaverages are shown by the horizontal bars extending across each year or partial year. Theseyearly or partial year averages provide the pertinent parameters for AE-8. It can be seen inFigure 12 that there are no trends in these averages associated with the solar cycle. Thevariations are less than a factor of two except for the highest energy channel where variationsas large as a factor of 5 are seen; these are more stochastic in nature and possibly related to

3-8

Data

high speed solar wind streams according to Paulikas and Blake (1979). The three satelliteswere at slightly different coordinates, since they were operating at different longitudes. ATS Iwas right on the geomagnetic equator at L = 6.6 while ATS 5 and ATS 6 were slightly off theequator at L - 6.7 and 6.8, respectively. Paulikas and Blake ignored these differences since theywere unimportant to their study.

3-9

Chapter 4Comparison of the AFt8 Modelwith Data

This comparison is limited to the data discussed in Chapter 3 and to the AE-4 model. Thedocumentation for AE-4 and AE-5 gives the comparison of many data sets to the models, andthe work of Teague et al. (1979} shows comparison of other data sets with inner zone models.Therefore, this section is confined to outer zone electrons, whose phenomenology has beendiscussed for modeling purposes by Singley and Vette (1972b) and by Chan et al. (1979}. Thesecomparisons are shown in Figures 13 through 39. In all of these AE-8MAX (MIN) is representedby the large open squares (circles} and the other entries (except for Figure 33) by smallersymbols so that the reader can clearly see the data to which the new model conforms.

Figures 13 through 17 cover the transition region. Each is broken into two graphs: (a) SOLMAXand (b) SOLMIN. For SOLMAX, AE-8 and AE-6 agree up to energies of 0.75 MeV. Above thisenergy AE-8 becomes larger and extends to higher energies. For SOLMIN the agreementbetween AE-8 and AE-5P is good up to 3.5 MeV at which point AE-8 grows larger and extends tohigher energies. In Figures 17a and 17b AE-4MAX and MIN replace AE-6 and AE-5P,respectively. Here for SOLMAX the agreement extends up to energies of 3 MeV, then AE-4 fallsrapidly below AE-8. For SOLMIN the departure of AE-4 from AE-8 begins at 0.75 MeV, with AE-4 falling rapidly below AE-8; again AE-8 extends to higher energies.

The next set of figures that will be discussed involves Figures 18 through 32. In these thecomparisons of AE-8MAX with AE-4MAX and data from Azur, OV1-19 uncorrected (19U), OV1-19 corrected (19C), and OV3-3 are presented. OV3-3 is presented only for L values of 3.0, 3.5,4.0, 4.5, 5.5, and 6.0; thus, these data are only found in Figures 19, 20, 22, 23, 25, 26, 28, and 29.

Some remarks relative to this set of plots are appropriate. First, the focus will be on Figures 18through 21, which cover the L region 3.0 through 3.5. The electron fluxes above 0.5 MeV in thisregion are very volatile, even when one considers yearly averages. This is the same volatilityas that demonstrated in Figure 12 for the greater than 3.9 MeV fluxes. If one concentrates onthe energy region 0.75 through 2 MeV, one finds at L = 3.0 that 19C is low, Azur is in themiddle, and OV3-3 is hlgh with the ratio OV3-3/19C - 20. At L = 3.5 Azur is low, OV3-3 ismiddle, and 19C is high with the ratio 19C/Azur - 6. The reason for this behavior has been

4-1

discussedpreviously (Chan et al., 1979) and is related to injection events that penetrate deeplyInto the radiation belts. During the lifetimes of OV3-3 and OVI-19, there were two majorInjection events that penetrated to L = 3.5, but only one of those four events penetrated toL = 3.0. This latter event occurred during the OV3-3 lifetime. During the Azur lifetime onlyone of the OVI-19 events was present. Consequently, the observed behavior seen In Figures 18through 21 is understood. The position of AE-8MAX is consistent with AE-4MAX and lies nearthe geometric mean of OV3-3 and 19C at L = 3.0. The high energy extension above 2.5 MeV forAE-8MAX follows the Azur and 19C results. It is noted that there is forced agreement between19(] and AE-8MAX at 4.5 MeV, as explaIned In Chapter 3 (page 3-5 and subsequent pages). Below0.5 MeV there is relatively good agreement. The extreme of the 19U data above 2 MeV is obviousthroughout this L region.

A few remarks relative to errors are appropriate at this time. The general error assigned to themodels In this series has been stated as about a factor of 2. For AE-5 a more detailed statement

was made. What is meant by the factor of 2 error is that for a flux of Gm the reasonable upperlimit is Ju and the reasonable lower limit is Gt where

Ju Jm

Jm Jl- 2 (4.1)

Ju

Thus, the ratio _ = 4. Now the symbol for AE-8 in Figures 18 and 19 would have to have a

vertical extent about three times longer (linear not the log scale) to represent this error. Theactual dimension represents a factor of 1.25. Consequently, the symbol can be used to roughlygauge how weU the data and the model agree. Therefore, In the worst situation at L = 3 theerror is a factor of 4.5. Elsewhere in this region the factor of 2 is appropriate and, In somecases, is pessimistic. Only data lying outside the factor of 2 error will be noted for theremainder of the discussion of these figures.

In Figures 22 through 32 all is good save for a few spurious points until the Azur greater than4.5 MeV data gets too hlgh by L = 4.6 and continues thls trend at the higher L values. Thedisparity of the 19U data is obvious throughout this region. It should be noted in Figure 32 thatAE-8MAX and AE-4MAX are replaced by AE-8 and AE-4 since the solar cycle effect is no longerevident and the MAX and MIN models are the same at higher L values.

For L = 6.6, the nominal geostationary L shell, instead of plottIng AE-4, all of the satellitedata used In constructing both AE-4 and AE-8 are shown. This requires two figures because ofthe large number of satellites involved. In Figure 33a the ATS 5/6 data are plotted for both thehighest (U) and lowest (L) averages shown in Figure 12. It should be noted that the 4 MeV modelvalue conforms to ATS 5/6 U value and so is a pessimistic value. At least the neighboring 19Cpoints are In accordance. The Azur point at 4.5 MeV is clearly too high, as discussed In Chapter3 (page 3-2 and subsequent pages). The OGO 1 poInt around 2 MeV is hlgh, and the ATS 5/6 pointat 0.7 MeV is at the factor of 2 limit. The 19C points between 0.8, and 3 MeV are also errant. InFigure 33b the high energy poInts for Explorers 6 and 12 are low, but as ATS 5/6 data at highenergies have shown, fluctuations In long-term averages can be expected in this energy-Lregion. The high energy 19U points reach their ultimate departure from reality. For the latestideas on time variations of high energy electrons In this region, consult Baker et al. (1986,1989, and 1990) and Nagai (1988).

For the higher L values 7 through 11 there are no new data to compare with AE-8.Consequently, In Figures 34 through 39, the comparison of AE-8 and AE-4 is given.apparent that AE-8 possesses a high energy taft except for L = 11.

It is

4-2

Chapter 5Presentation of the Model

This model has several different forms of presentation. The most important for use is themachine-sensible or numerical form, which will be given first. Based on the analysesconducted to construct the model, there were certain analytical descriptions not incorporatedin the numerical model that might be useful to some recipients; these are summarized next.Graphics provide a good way of conveying the model. However, some of the standard formsused in previous model documents do not appear, such as the b-L and R-A flux contour plotsand the J versus b. The radial profile equatorial flux plots are included to illustrate the solar

cycle effect. Finally, the results of fluences obtained in the standard set of circular orbits aregiven in tabular form.

Numerical

The function

Z = log I0J

where

J (>E,b, L, T)

2_

J (>E, b, L, _),T) d_)0

is given at a fixed set of instances of the variables. This presentation consists of both thelogical and physical organization, since the physical format may vary depending on thestorage medium on which the model is conveyed.

(5.1)

(5.2)

5-1

Prasantaa_

Logical Organization

The logical organization for the numerical AE-8 was dictated by the desire to store theessential data in a minimum amount of storage space. This goes back to the early 1970s whenthe memory size of most computers was well under a megabyte. AE-4 and -5 were Just comingout and were larger than earlier models. Consequently, a BLOCK DATA statement approachwas taken using binary coded decimal (BCD) representation with six characters per storagecell. Also, the integer format made for easier interchange; this required the scaling of the databy differing scale factors.

The logical record chosen has been explained in Teague et al. (1972), but it will be described indetail here, since some updating is necessary. This logical record is variable in length with thefirst field giving the number of fields in the record. The second field is the scaled energy value.The rest of the fields are organized first by L value and then by a variable related to b. Inaddition, the variable Z of equation (5. I) is given at the equator and denoted Zl here. Thefirst field in the L substructure is the number of cells in the substructure, followed by thescaled L value and then the field for scaled Zl. The remainder of the cells in this substructurecontain scaled values of

8(b-l) = 8(x) = 8b = 8x(5.3)

where the change is defined by a fixed Z decrement, ZDEL, which for AE-8 has the value of0.25. Therefore, on the L shell to reach

Z2 -- Z1 - ZDEL

the b value must change from 1 to

bl = 1 + dbl

Thus, the value of _b i is variable,but given Zl the value of Zi+ 1 isknown from the cellindex of _bi. This patterncontinues foreach ofthe L valuesin the AE-8 grid,which can totalup to45 depending on the energy. (Thevariable x isconvenientforthe method ofinterpolationdescribedin Appendix A.) This logicalrecord then repeatsforthe other 17energies(18 total)ofthe AE-8 grid.As shown inTable 8 thisscheme utilizes13,548 cellsfor

AE-8MAX and 13,168 forAE-8MIN. What are not contained in the basicmodel map are thescalefactorsfor E, L, Z, and db as wellas the totalnumber ofcells,ZDEL, name, andepoch,the latterbeing redundant to the name. These are given in a header recordand are included inTable 8. The parameter ZDEL does not appear in the BLOCK DATA statement.

Physical Representation

Magnetic Tape. The data set NSSDC ID# MT- 2AB contains AE-8MAX with a BCD

representation and a physical record size of 80 bytes. The physical record is a card image; theheader record and first part of the model map are given in Table 9. There are 1692 physicalrecords in this data set. The first 28 physical records are header records, and there is one

trailer record containing the END statement. The format of the BLOCK DATA is given in Table9. The model is broken into 84 (sub) maps with the first 83 being of dimension 163 and the last19. By decoding MAP1, one can see that the first two L values are 0 and 1.1 with Zl = 0. Theseare guard values at the inner edge of the map. At certain energies the L value of I. 1 is replacedby one of the grid values in Table 9 that is Just prior to the L grid value for which Z has a non-zero value. The same two "empty" L sets occur at L values of 12.0 and 15.6 at the outer

boundary, with the L value of 12 being replaced by a lower value for certain energies. Thedetails of the L grid can be seen more clearly in Chapter 5 (page 5 - 7) where Table 13 is

5-2

Presentation

discussed. AE-8MIN differs only in its total length being 1646 physical records, containing 79(sub) maps of dimension 163, one of 159, and the last of 132. The data set ID# is MT-2A_ Asnoted above, the value of ZDEL is missing from the BLOCK DATA statement. This parameter

is contained in the software program MODEL sent with this data set and used to decode the map

to produce flux values.

Microfiche. These two data sets (AE-8MAX--#MT-52A and AE-8MIN_#MT-52B) provide

integral flux values from L = 1.2 to 11.0 at 0. I intervals for B values (magnetic fieldintensities) from the equator to the flux cutoff limit of 1 electron/cm2-s in 100 gamma steps

starting at the first multiple of 100 gammas. The energy levels covered are slightly differentthan the MAP energies being in MeV: 0.04, 0.10, then the range 0.25-4.00 in 0.25 steps, andfinally 4.00-7.00 in 0.50 steps.

Floppy Disk. In 1988 Bflitza completed the revision of Program MODEL (MODEL87) and wrotean interactive driver program RADBELT to handle the models in the BLOCK DATA format(Billtza, 1990). included as part of this package is AE-8. The whole package has a data set ID

number of PT-11B and Is available on two PC floppy disks. The parameter ZDEL is included inthe BLOCK DATA statement in this form.

Since the main element of decoding the BLOCK DATA format is contained in the FORTRANfunction TRARA2, this is described in Appendix A with some additional comments added to

the source listing to make it easier to follow the logic.

Analytical Forms

There are several analytical expressions that have been used in constructing the model, someof which are not incorporated in the numerical model. An example is the local time function

given by equation (3.3); this function also contains tabular functions. These analytical/tabular forms wlll be summarized in this section.

Magnetic Cutoffs Resulting from the Atmosphere

For AE-8 this takes the form

0.6572L 3"452 ; 1.2 < L < 2.4

bc2 = O. 196L4"878 ; 2.4 _< L _< 3.0 (5.4)

1.4567L 3"050 ; 3.0 < L

Results from equation (5.4) were incorporated into the numerical model. A more physicalcutoff was also obtained but not incorporated. This was given by

0.6572L 3"452 ; 1.2 < L < 3.23

bcl = (5.5)

1.0523L 3"050 ; 3.23 < L

5-3

Local Time Function

The function C (> E, L) is needed to use equation (3.3}; the function K (> E, L) can bederived once C is known. C is given as a tabular function in Table 10. As noted in Chapter 3(page 3-3), C has no dependence on epoch.

Flux Variation Along the Field Line

In the inner zone this was given as an equatorial pitch angle distribution, differential inenergy, in the form

j (E,_o,L,T) = a(ao, L, T) Eexp (-E/X (_o, L, T) (5.6)

where

sinP ((_o-(Xc)

a r (L, T) sinP ((xe-(Xc) ; _c < _o < (_e

a(_o,L,T) = (5.7)

ar (L,T)

Here the cutoff is expressed by

; (Xe < _o < 90 °

_c = Sin-I (b__icl ) (5.8)

The function X of equation (5.7) is given by

sinn_o

Xr(L,T) ; _c < _o < _esinn_e

X(ao, L,T) = (5.9)

Xr(L,T) ; _e _ ao _ 90 °

Now the functions at, P. (Xe, X r, and n were given as tabular functions for AE-5. However, inconstructing AE-5P and AE-6 these functions were not tabulated. The only tabular functionremaining for magnetic field line variation is in the outer zone and is the exponent m ofequation (3.5); this is given as a tabular function in Table 1 1.

It may be instructive to compare in more detail the differences between equations (3.5) and(5.6). Since there is no local time dependence in the inner zone. the _ function does not appearin equation (5.6). To show the comparison better, integrate equation (5.6) over energy to obtainthe integral spectrum

Ejiz( > E,_o,L,T) = aX2(_ + l)exp(- ) (5.10)

5-4

Presentation

Then by substituting

b = sin-2_o (5.11)

the perpendicular flux

Jpizbc-I

arXr2(b_) -p/2

-_bc-I

m

+ llxp

(5.12)

results. It is not possible to convert this analytically into an omnidirectional flux.Consequently, the best that can be done is to convert equation (3.2) into its jp form usingequation (3.6) to obtain

Jpoz = 2z_(0.5,m+l)[bc_lj _bc_ 1 NT(> E,L)(5.13)

In the case where X r << E and keeping only terms that convey functional dependence

(_¢b

JPiz-- b-i ]pbc-I Eexp [ (5.14)

-m m

Jpoz _ b (bc-b) NT(> E,L) (5.15)

A comparison of these two equations shows that the inner zone spectral function depends on bas well as E; both spectral functions also depend on L and T. All exponents depend on L andT. The main field line variation near the equator expressed by the first factor in each equationis the same; however, the behavior near cutoff is of a different form. In addition, the

exponential in equation (5.14) has a profound effect on the b variation. It is possible to use theform of the b variation given in equation (5.13) or (5.15) to fit the one given in equation (5.12)

or (5.14) at a given energy by adjusting the value of m, but then m is strongly E dependent.Since AE-4 and AE-5 were developed somewhat independently, a common form for the bvariation was not enforced.

This discussion shows where the character of the inner and outer zone portions of the model

are different and why a transition region is necessary.

Statistical Function

The statistical model associated with AE-8 is the same as that for AE-4 but extended to higher

energies. The time variations In the outer zone make the flux a random variable. All randomvariables in this section will be denoted with bold face symbols. The empirical cumulativedistribution function is obtained by

5-5

Presenm_n

Time that J > JsP (J > Js) =

Total time of sample(5.16)

where J is the random variable representing the local time averaged flux, which is stillsubject to large excursions resulting from injections. To a reasonable approximation thisfunction P can be represented by

oo

(Z-M) 2- " dZ) (5.17)P (Z > Zs) __ _-__ exp(- 2(;2

Zs

which is the well known normal distribution, and I is defined by equation (5.1). When Zs =]/. then P =0.5. ForAE-8, (; (> E,L) is a tabular function given ln Table 12. Thisfunctlonfollows the AE-4 function and is extended in energy. As the flux tends to zero. ¢_ also tends tozero. The value of }/ is obtained using (; and the long-term average value of the flux, as willnow be shown. The probability density function q is

i (Z-_) 2q(Z) - -- exp(- ) (5 18)

_2_ 2(;2

It is convenient to change variables from Z to ¥ to obtain a random variable with mean ofzero and standard deviation of 1. With

(z-g)¥ - (5.19)

(;

and J = 10_exp (k(;Y)

where k = ln(10) = 2.30259

one can compute the average value of J

J*

oo

= Jexp(-2 dY)

_OO

(DO

k2_2 I_2_10_exp (--_--) 1 exp (-

--OO

(Y+k_) 2

2 dY)

(5.2O)

(5.21)

(5.22)

5-6

Presentation

Since the integral is unity and the exponential can be written as a power of 10, the result is

k_ 2

logJ* = _ + 2 (5.23)

With AE-4 it was noticed that some users considered the relationship to be

logJ* =

which would result from treating the 50% probability of occurrence as being the average fluxvalue. Since ¢_ is typically equal to 0.5, this produces an error of about a factor of 2.

Although the statistical model for AE-8 is not directly incorporated into the machine-sensiblemodel, it can be done using Table 12 along with some suitable coding. This has been done at theEuropean Space Agency (ESA) European Space Technology Center (ESTEC), for example.

Graphical Presentation

In Figures 13 through 39 the integral spectral plots of equatorial omnidirectional flux versusenergy were used to demonstrate the comparison among AE-8, AE-4, and various data. Theequatorial omnidirectional flux versus the L value is now used to convey some features of themodel and to illustrate the solar cycle effect in some detail. The data base for these plots wasextracted from the BLOCK DATA statement and is printed as Table 13A (for AE-8MAX) andTable 13B (for AE-8MIN). An examination of these tables shows the position of the L valueswhere Z1 is equal to zero. Besides the special values of L (0, i. 1, 12, and 15.6) discussed earlier(page 5 - 2), the values 2.69, 2.79, and 2.89 also appear to handle the region near where the fluxminima occur in the slot region.

In Figure 40 the equatorial flux profile for all of the grid energies are shown for AE-8MAX. Noelectrons greater than about 4.5 MeV appear in the inner zone, while the outer zone containselectrons up to 7 MeV. When the energies are above about 0.75 MeV, the inner zone peak occursat an L value of 1.50, while at lower energies this peak is at 1.80. For energies above 2.0 MeVthe slot is very deep. In the outer zone the flux peak moves inward from about an L of 4.8 as theenergy increases to about an L of 3.1 for the highest energies.

Figures 41 through 45 show the equatorial profiles for AE-8MAX and AE-8MIN for the sameenergies, so that the solar cycle effect is clearly demonstrated. Large open symbols have beenchosen for AE-8MAX, while small solid symbols have been used for AE-8MIN. With this choiceit is easy to see when the fluxes are essentially the same value. From these figures it can beascertained

• For energies below 0.75 MeV the inner zone fluxes are higher at SOLMAX.

• For energies above 1.0 MeV the inner zone fluxes are independent of the solar cycle.

• For energies above 6.0 MeV the outer zone fluxes are independent of the solar cycle.

For energies below 6.0 MeV there is a region starting at the outer edge of the slot and

ending in the L range between 3.0 and 6.0 depending on energy where the SOLMINfluxes are less than SOLMAX fluxes. The ratio of these fluxes ranges up to 4 at the lowestenergies.

5-7

Prasoota_n

Orbital Integration Results

There is a standard set of circular orbits that are run with the models to demonstrate theamount of fluence in electrons/cm2-day accumulated in various energy windows and abovecertain threshold energies. The results are shown in Table 14 for AE-SMAX. The samplinginterval and the accumulation time vary with orbit altitude to take into account certainfactors and provide a reasonable average value. Thus, at low altitudes the sampling time is 30seconds because the satellite moves rapidly through the regions where flux gradients are large.The accumulation length is 36 hours to average out the South Atlantic Anomaly effects. Theseparameters are shown at the top of each page of the table. For orbits that traverse the innerzone the standard sampling interval is one minute and the accumulation time is 24 hours.Then the accumulation rises in discrete steps up to 4608 hours and the sampling intervalincreases up to 48 minutes. The table is organized with four orbits per page with the altitudeconstant and fixed inclination orbits of 0 °, 30 °, 60 °. and 90 °. The first column under each

inclination gives the daily fluence above the energy given in the first column of the page. Thesecond column under each inclination gives the daffy fluence in the energy band defined by thefirst two columns of the page.

5-8

Appendix AFunction T RA2

Within Program MODEL and now MODEL87 the subroutine TRARA1 handles the interpolationof Z in E, L, and b, and so serves as the gateway to the numerical AE-8 models. A FORTRANfunction, TRARA2, which is in TRARAI, handles the Z, L, and b interpolation linearly, butthe paths are not along constants of the variables. TRARA2 has been discussed briefly inTeague et al. (1972), but this and the source listing for the function leave some points unclearabout how TRARA2 really works. Because of this additional comments have been added to thesource listing, and the names of some variables have been changed to make it easier to followthe logic. The original code was written in the days when the GOTO command was in voguerather than structured programming. This has not been changed so that the function operatesin exactly the same manner as before. This makes the code harder to follow, but thedescription of the method and the newly commented listing presented in this appendix shouldmake everything clear to the user.

Method

The method can best be illustrated by using Figure A1. Here two Z versus x curves are shownfor adjacent L values, L1 and L2 (L2 > LI) at one of the model grid energies. Eachgridpoint in Z-x space for LI and L2 is shown in Figure A1. The grid energy is fed to TRARA2 inthe form of the starting address in the BLOCK DATA for that energy by the argument of MAP,which itself is an argument of TRARA2. Based on the input L value, TRARA2 determines L 1and L2. The general idea is to find the two radial lines passing from the Z-x origin throughany grid point that most closely brackets the input point. Since the Z coordinate of the inputis what is desired, then an iterative approach is needed. The coordinates of the grid points areknown; the equations of the two curves are known (these are straight lines connecting the gridpoints); the equations of the radial lines are known. Except for 0CB3 these radial lines areshown as line segments in Figure A1. The intersection of a radial line with the other curve canreadily be computed iteratively. On these two radial lines the L interpolation is done to findthe x values. Using this and the equation of the radial lines, the Z coordinates are obtained.Then the interpolation along the line defined by these two interpolated points provides the

output 7, value.

A-1

_etxlx A

The specificswillbe givenby consideringthreeinput pointsshown inFigureA1 as P I, P 2,and P3. On the basis of the equatorialvalues, Zl (LI) and Zl (L2), TRARA2 setsupthelarger one as the top (T) set of _x points and the other as the bottom (B) set. These sets areshown converted to x values in Figure A1 and are referred to as the T and B curves. Thus,initially the L1 curve is the T curve. The procedure to find the bracketing radial lines startsby stepping on the T curve from the equator to grid points until the grid point with an x valuegreater than the input value FNx is reached.

Consider the P1 case first. One can see that no grid point on L1 satisfies this condition. Thenthe code reverses the role of L1 and L2 so that L2 becomes the T curve. When the steppingreaches the grid point near P1 labeled BTI, then the following procedure is employed. The_ne OAT1 isconstructed(shown as ABI :AT1). Then the B curve (now LI)is stepped from theequator und] the g_d pointlabeled CB 1 isfound. The criterionused isto compute theintersectionpoint ABI between OAT1 and the B curve until

x(ABI) < x(Bi) (A.I)

where i is the index of the grid point. The formula for" x (AB 1 ) is given by

z(Bi)*(x(Bt)-x(Bi-1)) ]/x(ABI) = ZDEL + x(Bi) jl

Z (AT1) * (x (Bi) -x (Bi-l)) ]ZDEL*x (AT1) + 1 (A.2)

Thus, the straight line that represents the B curve changes with the value of i. For theexample being discussed, B21 = CB 1 and the equation of the line representing curve B areconsiderably different than for the segment AT3 : BT3. One can see by inspection that any gridpoint on L 1 closer to the equator would not satisfy the condition. The assumption is nowmade that the x values vary linearly in L along OAT i, so a linear interpolation in L is doneto obtain x (AT 1 ). The Z (AT 1 ) value is given by

Z (AT1) x (ABI)Z (AII) =

x (AT1) (A. 3)

These coordinates are then stored in the XPCM and ZPCM registers, which are used to hold thetrial coordinates for the nearest point with XPCM less than FNx. Next the slopes of OBTI andOCBI are compared, and the larger one (OCBI) is used first to produce the point labeled CII,whose coordinates are placed in the XPCP and ZPCP registers. Then the check is made ifx ( CI 1 ) is greater than or equal to x (P 1 ). Since it is not true in this case, the P CP registersare dumped into the PCM registers (OCT1 replaces OAT1), and the B curve is stepped andtested until the test slope is less than the OBT slope. In this case the next grid point testedwould be that of BTI. Since x (BII) is greater than FNx, the final interpolation in x canbedone. This final interpolation assumes that Z is linear in x. Knowing the coordinates of B I 1and CII, thevalueof Z (PI) is computed.

If one now considers P 2, which has the same x value as P I, things would proceed in the samefashion as for P1 up to the test x (BII) is greater than x (PI). However, the position of P2implies L(P2) islessthan L(PI), so all the interpolated points AII, BII, and CII wouldbe closer to the origin than shown in Figure A1. Thus, the new BII would fail the test x (BII)is greater than x (P2). This would result in testing the next grid point radial line that had thelarger slope, and the ping-ponging between the L1 and L2 curve would continue until the lines

A-2

Appendix A

3

L1

AB1CBIBBI

AB2

BB2[

CB3

AllAT1

L2 > L1

CT1BT1

L2

AT2

BT2

0

0 100 2O0 30O

AI. Illustration of TRARA2 Method of Calculation

A-3

_pandxA

OAT2 and OBT2 would be reached. The finalsolutionwould be done in the same manner asdescribed above.

What has been described above is the most straightforward way for the program to proceed.However, there is a conservative approach in the logic that produces a path that leads to thecorrect answer but apparently is not the most direct path. Things actually proceed as describedabove up to the place where AT1 and BTI are identified. Because there has been a reversal ofthe curves, the logic now forces a path through the code that has been devised to handle the casewhere FNx is near the equator. This procedure makes OAT (the numeric suffix is dropped atthis point) the Z axis so that the determination of AI does not involve any interpolationusing x. Then BT is the first step on the T curve and CB is the first step on the B curve. Thelarger slope point is tested for the solution as described above, and the ping-pong procedure isstarted. In the case of FNx near O, either this first step BT or CB provides the XPCP. In theP1 example the failure of the first step to provide an XPCP starts the ping-pong procedure thatresults in the same solution as described previously.

Now consider P 3 because it illustrates another aspect of the logic employed in the code. Noreversal is needed because the point BT3 satisfies the condition. In this case the L1 curveremains the T curve. Thus, AT3 and BT3 are identified as shown in Figure AI. However, thefact that now x (AB3) is greater than x (AT3) causes the logic to force the computation topass through the FNx near 0 procedure described above. Here again the ping-pong procedureproduces the proper answer, which in this case uses the lines OAB3 and OBB3 shown near P3.If in Figure A1 Z 1 (L2 ) is greater than Z 1 (L 1 ), then for all cases considered above theprocedure would progress as Initiany described above, except no reversal would be needed forany of the cases considered.

There are several other cases handled in the code, but these are quite transparent. It is believedthe code is now commented well enough that users can understand in detail exactly what isbeing done.

Source Code Listing

C***

C***

C***

C***C***

C***

C***C-W*

C***

C***

C***C***

C***

FUNCTION TRARA2 (MAP, IL, IX)

TRARA2 INTERPOLATES LINEARLY IN L-B/B0-MAP TO OBTAIN

THE LOGARITHM OF INTEGRAL FLUX AT GIVEN L AND B/B0. ***

INPUTS: MAP(..) IS SUB-MAP FOR SPECIFIC GRID ENERGY ***

OF TRAPPED RADIATION MODEL MAP ***

IL SCALED-L VALUE ***

IX SCALED-(B/B0 - I)=X VALUE ***

OUTPUTS: TRARA2 SCALED-LOGARITHM OF PARTICLE FLUX=Z ***

MOST WORKING VARIABLES, I.E., THOSE THAT CHANGE MEANING

IN COURSE OF THE PROGRAM ARE DENOTED WITH THE SUFFIX

LETTER, W. THIS DOES NOT APPLY TO INDEXES.**************************************************************

SEE MAIN PROGRAM 'MODEL' OR 'RADBELT' FOR EXPLANATION ***

OF MAP FORMAT SCALING FACTORS ***

THE PARAMETER THAT DEFINES THE FIXED CHANGE OF Z BE- ***

TWEEN X GRID POINTS IS OBTAINED FROM 'COMMON/TRA2/' *********************************************************************

A-4

Appendix A

DIMENSION MAP (i)

COMMON/TRA2/FISTEP

C

C CHANGE INTEGER INPUTS TO FLOATING POINT, RENAME FISTEP, AND

C INITIALIZE.

C

FNL= I L

FNX=IX

ZDEL=FI STEP

ITIME=0

IT=0

C

C FIND CONSECUTIVE SUB-SUB MAPS FOR SCALED-L VALUES, LSB & LST,

C WITH LSB.LT.IL AND IL.LE.LST . LB & LT ARE LENGTHS OF THE

C SUB-SUB MAPS. IB+I & IT+I ARE THE INDEX VALUES IN MAP

C WHERE THE VALUES OF LB & LT ARE STORED. IB+2 & IT+2 ARE

C THE INDEX VALUES WHERE LSB AND LST ARE STORED. IB+3 & IT+3

C ARE THE INDEX VALUES WHERE THE EQUATORIAL Z VALUES, ZIB AND

C ZIT ARE STORED.

1 LT=MAP (IT+l)

IF(MAP(IT+2) .GT.IL) GOTO 2 !PROPER LST HAS BEEN FOUND

IB=IT

LB=LT

IT=IT+LT !CHECKING ON NEXT L VALUE

GOTO 1

2 CONTINUE

C

C IF A SUB-SUB MAP IS EMPTY, I.E., LENGTH LESS THAN 4, THEN

C TRARA2=0; DOUBLE EMPTY SETS OCCUR AT THE INNER AND OUTER

C BOUNDARIES OF THE MODELS.

CIF((LB.LT.4).AND. (LT.LT.4)) GOTO 50 !THIS SETS THARA2=0.

C

C IF ZIT IS LESS THAN ZIB INTERCHANGE VARIABLES AND INDEXES SO

C THAT THE SUFFIX LETTER T IS ASSOCIATED WITH THE L VALUE THAT

C HAS THE LARGER ZI. THIS MAKES IT EASIER TO FOLLOW THE LOGIC OF

C THE CODE.

C

IF (MAP(IT+3) .GT.MAP(IB+3)) GOTO i0 !NO INTERCHANGE NEEDED

5 KT=IB

IB=IT

IT=KT

KT=LB

LB=LT

LT=KT

C

C DETERMINE THE INTERPOLATION FACTOR IN SCALED-L VALUE

C

i0 FLLB=MAP (IB+2)

FLLT=MAP (IT+2)

DFL = (FNL-FLLB/ (FLLT-FLLB)

Z IB=MAP (IB+3)

ZlT=MAP (IT+3)

XBW= 0.

XTW=0.

ZBW=ZIB

ZTW=ZIT

IF(LB.LT.4) GOTO 32

!SET WORKING VARIABLES

!CASE WHERE ZIB=0.

A-5

_A

cc THE X LOOPING IS BASED ON FINDING, FOR A GRID ENERGY AND THE

C TWO SELECTED SCALED-L VALUES, IN X-Z SPACE TWO POINTS, PCM AND

C PCP, WHERE X(PCM) AND X(PCP) BRACKET THE INPUT X VALUE, FNX.

C EACH SUB-SUB MAP CONTAINS THE INFORMATION TO CONSTRUCT A PLOT

C OF POINTS GIVING Z VERSUS X SO WILL BE REFERRED TO AS A CURVE.

C FOR THE LINEAR INTERPOLATION USED THESE GRID POINTS ARE CONNECTED

C BY STRAIGHT LINES. THERE ARE SEVERAL SPECIAL CASES BUT THE GENERAL

C APPROACH IS TO START AT THE EQUATOR (X=0) FOR THE TOP CURVE AND

C STEP FROM GRID POINT TO GRID POINT UNTIL FNX IS

C BRACKETED. TAKING THE SMALLER XT GRID POINT, AT, ONE DRAWS A

C RADIAL LINE, OAT, TO THE X-Z ORIGIN. THE INTERSECTION OF OAT

C AND THE LOWER CURVE IS POINT AB. IT CAN BE DETERMINED DIRECTLY

C SINCE THE EQUATIONS OF BOTH LINES ARE KNOWN. THE SECOND XT GRID

C POINT IS BT AND THE INTERSECTION OF LINE OBT WITH B CURVE IS BB.

C A GRID POINT ON THE B CURVE IS CB AND THE INTERSCTION OF LINE OCB

C WITH THE CURVE IS CT. USING COMPUTED X(AB) AND X(CT)

C AN L-INTERPOLATED X (PCM) IS FOUND. THEN ONE ITERATES BY STEPPING

C IN X FIRST ON THE B CURVE AND THEN IF NEEDED ON THE T CURVE IN A

C PING PONG FASHION TO GET THE BRACKETING. THEN AN X, Z

C INTERPOLATION USING PCM AND PCP IS MADE. FINALLY THE INTERPOLATED

C Z VALUE IS RETURNED.

C

DO 17 J2=4,LT

XTINCR=MAP(IT+J2)

IF(XTW+XTINCR.GT.FNX) GOTO 23 !USUAL CASE, SELECTED POINT,ATXTW=XTW+XTINCR

17 ZTW=ZTW-ZDEL

ITIME=ITIME+I !SETS FLAG THAT NO SUCH POINT FOUND ON CURVE.

C

C IN THIS CASE FNX LIES IN THE RANGE BETWEEN CUTOFFS OF THE TWO

C L VALUES AND REVERSAL OF CURVES IS REQUIRED.

C

IF(ITIME.EQ.I) GOTO 5 !LEADS TO REVERSAL OF T AND B CURVES

GOTO 50 !SET TRARA2=0. REVERSAL FAILED.

23 IF(ITIME.EQ.I) GOTO 30

C

C THE GOTO 30 OCCURS FOR THE CASE WHERE THERE IS A REVERSAL AND THE

C POINT, AT, HAS BEEN FOUND. IT IS NOT CLEAR WHY THE CODE IS WRITTEN

C THE WAY IT IS. PROCEEDING AT 30 RESETS THE LINE OAT TO BE THE Z

C AXIS(X=0) AND THINGS PROCEED LIKE FNX IS NEAR THE EQUATOR. THE

C TEST IN 15 THROWS THIS OUT AS A SOLUTION AND THE PING PONG BETWEEN

C 15 AND 20 EXPLAINED BELOW RESULT IN STEPPING OUT ON BOTH CURVES

C UNTIL THE PROPER TWO BRACKETING LINES ARE FOUND. THUS THE RIGHT

C ANSWER IS OBTAINED BUT THE LOGIC IS CONFUSING.

C

IF(J2.EQ.4) GOTO 28 !THIS IS CASE WHERE FNX IS NEAR 0.

SLTW=ZTW/XTW !SLOPE OF RADIAL LINE, OAT

C

C THE GRID POINT, AT, HAS BEEN FOUND. NOW THE B CURVE IS STEPPED

C AND THE X(AB)=XABW BELOW IS COMPUTED UNTIL ITS VALUE IS LESS THAN

C THE VALUE OF X(CB)=XBW BELOW.

C

DO 27 JI=4,LB

XBINCR=MAP(IB+JI)

XBW=XBW+XBINCR

ZBW=ZBW-ZDEL

A-6

Appendix A

XABW=((ZBW/ZDEL)*XBINCR+XBW)/((XBINCR/ZDEL)*SLTW+I.)

IF(XABW.LE.XBW) GOTO 31

27 CONTINUE

IF(XABW.LE.XTW) GOTO 50 !TRARA2=0.

31 IF(XABW.LE.XTW) GOTO 29 !USUAL CASE.ONLY FALSE FOR REVERSAL

C

C 31 WILL NOT BE REACHED IF THERE IS A REVERSAL OR FNX IS NEAR 0.

C FAILURE OF TEST IN 31 OCCURS ONLY WHEN T CURVE LIES BELOW B CURVE

C IN THE REGION OF THE INPUT VALUE FNX. IT IS NOT CLEAR

C WHY SUCH CASES ARE ROUTED THIS WAY. HOWEVER, THE

C CORRECT ANSWER IS OBTAINED. CODE BELOW TREATS PROPERLY THE CASE

C WHERE FNX IS NEAR 0. THUS OAT = Z AXIS AND ZPCM IS COMPUTED USING

C ONLY L INTERPOLATION. THE SLOPES OF OBT AND OCB ARE EXAMINED TO

C SELECT THE LARGER ONE AT 15. THEN XPCP AND ZPCP ARE COMPUTED IN 15

C OR 20. IF THIS IS A SOLUTION, I.E. XPCP.GE.FNX, THE FINAL ANSWER

C IS COMPUTED. IF NOT IT STEPS THE CURVE AND TESTS UNTIL THE TEST

C SLOPE IS LESS THAN THE OTHER CURVE'S SLOPE.

C

XBW=0. !SETTING TO EQUATOR

30 XTW=0. !AT FOUND AFTER A REVERSAL

32 J2=4 !CASE FOR ZlB=0

XTINCR=MAP(IT+J2)

ZBW=ZIB

ZTW=ZIT

28 ZPCM=ZIB+(ZTW-ZBW)*DFL !Z VALUE AT X=0;CASE FOR FNX NEAR 0

XPCM=0. !X VALUE FOR ZPCM

XTW=XTW+XTINCR !IST STEP ON T CURVE, BUT IS BT NOW

ZTW=ZTW-ZDEL

SLTW=ZTW/XTW !OBT SLOPE

IF(LB.LT.4) GOTO 35 !LB IS AN EMPTY L SET SO XBINCR=0.

Jl=4

XBINCR=MAP(IB+JI)

XBW=XBW+XBINCR !IST STEP ON B CURVE, CB

ZBW=ZBW-ZDEL

SLBW=ZBW/XBW

GOTO 15

C

C THIS GENERATES PARAMETERS FOR THE NON-NEAR EQUATORIAL CASES

C

29 XPCM=XABW+(XTW-XABW) *DFL !L INTERPOLATION BETWEEN AT & AB

ZPCM=XPCM*SLTW

ZTW=ZTW-ZDEL !NOW THE T CURVE IS STEPPED.

XTW=XTW+XTINCR

SLTW=ZTW/XTW !SLOPE OF OBT

SLBW=ZBW/XBW !SLOPE OF OCB

C

C THE CODE IN 20 COMPUTES INTERSECTION POINTS ON THE B CURVE AND

C STEPS ALONG THE T CURVE UNTIL THE SLOPE OF THE RADIAL LINE TO THE

C GRID POINT IS LESS THAN THE SLOPE OF THE RADIAL LINE THROUGH THE

C LAST SELECTED POINT ON THE B CURVE. THE CODE IN 15 HANDLES THE

C SAME FUNCTIONS WITH THE B AND T CURVES REVERSED. IF THE PATH TO

C 60 IS FROM 15 CODE THEN XPCP COMES FROM A T GRID RADIAL LINE. A

C B GRID RADIAL LINE COMES FROM 20 CODE. THE SELECTION AT 15 ALWAYS

C MAKES THE LARGER SLOPE RADIAL LINE THE FIRST TO BE TESTED. IF

C THAT FAILS THAT CURVE IS STEPPED AND TESTED UNTIL THE PCP POINT

C IS FOUND OR THE TEST SLOPE BECOMES SMALLER THAN THE SLOPE OF THE

C LINE THROUGH THE GRID POINT WAITING TO BE TESTED ON THE OTHER

C CURVE. THIS IS THE PING PONG.

A-7

J_pex_A

C

15 IF(SLBW.LT.SLTW) GOTO 20

XCTW=((ZTW/ZDEL)*XTINCR+XTW)/((XTINCR/ZDEL)*SLBW+I.)

XPCP=XBW+(XCTW-XBW)*DFL !L INTERPOLATION

ZPCP=XPCP*SLBW

IF(XPCP.GE.FNX) GOTO 60 !READY FOR FINAL X INTERPOLATION

C

C MUST BEGIN ITERATION TO GET POINTS PCM AND PCP BRACKETING INPUT

C SO PCP REPLACES PCM AND NEXT POINT ON B CURVE IS EXAMINED TO FIND

C A PCP.

C

XPCMmXPCP

ZPCMsZPCP

IF(JI.GE.LB) GOTO 50 !LB GRID IS EXHAUSTED, SET TRARA2=0.Jl=Jl+l

XBINCR=MAP(LB+JI)

ZBW=ZBW-ZDEL

XBW=XBW+XBINCR

SLBW=ZBW/XBW

GOTO 15 !NOW RETURN TO SEE IF 20 OR 60 EXIT IS OPEN

C

C THE BB OR SUBSEQUENT INTERSECTION POINTS ARE COMPUTED AND TESTED

C

20 XBBWz((ZBW/ZDEL)*XBINCR*+XBW)/((XBINCR/ZDEL)*SLTW+I.)

XPCP=XBBW+(XTW-XBBW)*DFL

ZPCP-XPCP*SLTW

IF(XPCP.GE.FNX) GOTO 60 !USUAL CASE

C

C NOW THE TOP CURVE MUST BE STEPPED TO THE NEXT POINT AND THE

C PCP VALUES MUST BE TRANSFERRED TO THE PCM CELLS

C

XPCM=XPCP

ZPCM=ZPCP

IF(J2.GE.LT) GOTO 50 !END OF TOP CURVE, SET TRARA2=0.

J2=J2+l

XTINCR=MAP(I2+J2)

ZTW=ZTW-ZDEL

XTW=XTW-XTINCR

SLTW=ZTW/XTW

GOTO 15

35 XBINCR=0.

SLBW=-900000. !T CURVE WILL ALWAYS BE TESTED AT 15 BRANCH

GOTO 20 !ENTERS 20 WITH XBW=0.

60 IF(XPCP.LT.XPCM+I.E-20) GOTO 50

TRATRA2=ZPCM+ (ZPCP-ZPCM) * ((FNX-XPCM) / (XPCP-XPCM))

TRARA2=AMAXl (TRARA2, 0. )

RETURN

50 TRARA2_0.

RETURN

END

A-8

References

Achtermann, E., B. Hausler, D. Hovestadt, G. Paschmann, and P. Laeverenz, Exper/ments E188and E1 93 for the Measurement of High-Energy Electrons, Protons, and Alpha Particles in theAzur Satellite--Physical Properties and Test Measurements, Max-Planck-lnstitute forExtraterrestrial Physics, BMBW-FB 70-67, December 1970.

Baker, D. N., J. B. Blake, 1% W. Klebesadel, and P. 1% Higble, "Highly Relativistic Electrons in the

Earth's Outer Magnetosphere I, Lifetimes and Temporal History 1979-1984," J. Geophys. Res.91, 4265, 1986.

Baker, D. N., J. B. Blake, L. B. Callis, 1% D. Belian, and T. E. Cayton, 'IRelativistic Electrons NearGeostationary Orbit: Evidence for Internal Magnetospheric Acceleration," Geophys. Res. Lett.

16, 559, 1989.

Baker, D. N., 1% L. McPherron, T. E. Cayton, and 1% W. Klebesadel, "Linear Prediction FilterAnalysis of Relativistic Electron Properties at 6.6 RE," J. Geophys. Res. 95, 15133, 1990.

Bilitza, D., Solar-Terrestrial Models and Applications Software, National Space Science DataCenter, NSSDC/WDC-A-R&S 90-19, July 1990.

Chan, K. W., M. J. Teague, N. J. Schofield, and J. I. Vette, '3Vlodeling of Electron Time Variationsin the Radiation Belts," Quantitative Modeling of Magnetospheric Processes, ed. W. P. Olson,

Amer. Geophys. Union, Washington, D.C., 121, 1979.

Ebel, B., Processing Raw Data from Experiments E188 and E1 93 on the Satellite Azur, Max-Planck-Institute for Extraterrestrial Physics, MPI-PAE/Extraterrestrial 76, March 1972.

Nagai, T., " 'Space Weather Forecast:' Prediction of Relativistic Electron Intensity ofSynchronous Orbit," Geophys. Res. Leth 15, 425, 1988.

Paulikas, G. A., and J. B. Blake, '1_ffects of the Solar Wind on Magnetospheric Dynamics:

Energetic Electrons at the Synchronous Orbit," Quantitative Modeling of MagnetosphericProcesses, ed. W. P. Olson, Amer. Geophys. Union, Washington, D.C., 180, 1979.

Paulikas, G. A., private communication, 1981.

R-1

Re_m_s

Roberts,C. S., "On the RelationshipBetweenthe Unidirectionaland OmnidirectionalFlux ofTrappedParticlesona MagneticLineof Force,"J. Geophys. Res. 70, 2517, 1965.

Singley, G. W., and J. I. Vette, The AE-4 Model of the Outer Radiation Zone Electrc_nEnvironment, C72-06, August 1972a.

Singley, G. W., and J. I. Vette, A Model Environment for Outer Zone Electrons, National SpaceScience Data Center, NSSDC 72-13, December 1972b.

Teague, M. J., and J. I. Vette, The Inner Zone Electron Model AE-5, National Space Science DataCenter, NSSDC 72-10, November 1972.

Teague, M. J., J. Stein, and J. I. Vette, The Use of the Inner Zone Electron Model AE-5 and

Associated Computer Programs, National Space Science Data Center, NSSDC 72-11, November1972.

Teague, M. J., and E. G. Stassinopoulos, A Model of the Starfish Flux in the Inner RadiationZone, Goddard Space Flight Center, X-601-72-487, December 1972.

Teague, M. J., and J. I. Vette, A Model of the Trapped Electron Population for Solar Minimum,National Space Science Data Center, NSSDC 74-03, April 1974.

Teague, M. J., K. W. Chan, and J. I. Vette, AE-6: A Model Environment for Trapped Electrons forSolar Max/mum, National Space Science Data Center, NSSDC/WDC-A-R&S 76-04, May 1976.

Teague, M. J., N. J. Schofield, K. W. Chan, and J. I. Vette, A Study oflnner Zone Electron Dataand Their Comparison with Trapped Radiation Models, National Space Science Data Center,NSSDC/WDC-A-R&S 79-06, August 1979.

Vampola, A. L., "Energetic Electrons at LaUtudes Above the Outer-Zone Cutoff," J. Geophys. Res.74, 1254, 1969.

Vampola, A. L., "Access of Solar Electrons to Closed Field Lines," J. Geophys. Res. 76, 36, 1971.

Vampola, ,_ L., private communication, 1972.

R-2

Tables

Table 1. Azur Greater Than 1.5 MeW Normalized Local Time Distribution

Ix}c.sJT_ae L = 3 L = 4 L = 5 L = 5.5 L = 6

(Hrs.) _/K _/K _/K _/K _/K

i .....

2 - - 0.767 0.672 0.6983 - 0.700 0.894 0.810 0.5944 1.038 0. 795 0.853 0. 992 1.0815 1.122 0.849 1.024 0.960 0.8616 0.968 0.973 0.951 0. 885 0. 7967 0.953 0.996 1.026 1.034 0.9518 0.820 1.039 1.087 1.064 1.2579 - 1.130 1.127 1.254 1.203

10 - - - 1.151 1.38511 .....12 .....13 - - - 1.024 1.43414 - - 1.099 1.160 1.17015 - 1.055 1.057 1.065 1.19916 0.952 1.0,33 1.096 1.231 1.04817 0.929 0.992 1.051 1.045 1.04018 1.079 1.057 1.047 0.987 0.96119 1.014 1.063 1.075 1.071 1.03120 0.968 0.997 1.008 0.940 1.00221 - 0.889 0.811 0.904 0.91622 - - - 0.629 0.859

3 .....

24 .....

C -0.04995% ConfidenceInterval Half 0.003WidthK 0.981

0.053 0.063 0.0_ 0.1_

0.004 0.003 0.005 0._7

0.9_ 0.992 0.970 0.991

T-1

I

i

J

lJ

o._,2

_8

oo_

"_ "_ _. ¢_ .- 0

"0 "C_

oo _

__o_°.000..0

_g__

,_C)_I_ I

o _o

o.

_ _.. _-_

LOGO0 LO_O'_r-._oDo4,--_OO_O_flO

00_00'_0') 04C",I _ t

,'_,"_,'-_C'4C'4C'4

T-2

Table 3. Ratio of (CR-BRE]_/CR for 0VI-19 Spectrometers

Detector _ LID _e_ 3 3_ 4 4_ 5 5.5 6 6.6

LEI 53 -0.83 -3.56 -4.42 -1.86 -1.30 -0.63LE2 52 0.92 -0.55 -0.51 0.63 0.69 0.83tMA 192 0.99 0.87 0.92 0.98 0.99 1.00LE5 250 0.99 0.90 0.91 0.97 0.99 0.99

LE6 312 0.97 0.79 0.77 0.93 0.96 0.98LE7 376 0.95 0.71 0.67 0.89 0.95 0.97LE8 444 0.92 0.56 0.53 0.85 0.92 0.95HE1 537 0.97 0.96 0.98 0.98 0.98 0.99HE2 822 0.51 0.57 0.76 0.83 0.86 0.90HE5 1711 -2.12 0.79 0.80 0.61 0.34 0.06HE6 2018 -0.86 0.73 0.70 0.48 0.14 -0.06HE7 2321 -6.62 0.27 0.10 - 1.29 -3.75 -6.24HE8 2632 -2.69 0.50 0.24 -1.03 -2.80 -4.53HE9 2932 -7.55 0.16 -0.70 -3.55 -7.49 -9.49HEll 3557 -8.09 -1.76 -4.40 -11.40 -14.79 -12.77

HEI2 3863 -9.82 -1.12 -3.56 -9.15 -14.67 -16.70HE13 4169 - 13.97 -3.08 -8.00 -17.57 -22.13 -20.16HE14 4476 -9.13 -2.04 -5.15 -10.62 -13.60 -12.51HE15 4783 -11.46 -3.61 -8.63 -16.49 -19.33 -16.22HE16 5091 -12.36 -3.33 -8.80 -16.30 -18.61 -18.77

-0.390.881.000.990.980.970.950.970.85

- 1.09-1.54

- 14.03-7.72-7.50-6.22-9.35-6.87-5.68-6.42-7.41

-0.750.800.990.990.970.950.900.980.41

-0.53-0.24-3.69- 1.90-3.06-2.20-3.76-3.532.46

-3.16-3.18

Table 4. Flux Fraction d for OV1-19 HES Channels

L d Remarks

3.0 0.14503.2 0.10403.4 0.07443.5 0.07203.6 0.05493.8 0.04444.0 0.04864.2 0.04964.4 0.05034.5 0.04404.6 0.05414.8 0.05515.0 0.0547

5.5 0.04786.0 0.0322

6.6 0.0145

DeterminedDeterminedDeterminedDeterminedDeterminedDeterminedDeterminedDeterminedDeterminedDetermined

using AZUR > 4500 keV data.using AZUR > 4500 keY data.using AZUR > 4500 keY data.using AZUR > 4500 keV data.using AZUR > 4500 keV data.using AZUR > 4500 keV data.using AZUR > 4500 keV data.using AZUR > 4500 keV data.using AZUR > 4500 keV data.using AZUR > 4500 keV data.

Determined using AZUR > 4500 keV data.Determined using AZUR > 4500 keV data.Determined using AZUR > 4500 keV data.Determined using AZUR > 4500 keV data.

Determined by Interpolation between L = 5.5 and 6.6; d AZUR = .0527.

Determined using ATS 6 > 3900 keV data; d AZU = .0592.

T-3

Table 5. Parameters for C4mversion of OV1-19 Flux to Integral Energy Spectrum

Electron Energy (keV)Useful Channel

Channel Detector Upper Effective Lower Width

Index-k ID Limit Midpoint Limit W ( k )

1 LE 1 71 55 39 322 LE2 140 106 71 693 _ 220 180 140 804 LE5 281 251 220 615 I.F_,6 344 313 281 636 LE7 409 377 344 657 /.F_,8 448 429 409 398 HE1 677 563 448 2299 HE2 1266 972 677 589

I0 HE5 1866 1566 1266 60011 HE6 2172 2019 1866 30612 HE7 2478 2325 2172 30613 HE8 2785 2632 2478 30714 HE9 3237 3011 2785 45215 HE11 3708 3473 3237 47116 HE12 4016 3862 3708 30817 HE13 4325 4171 4016 309

T-4

i!

!

0A

O

,gIt

II

o

I-1

qp

II

qlp

II

II

N

p.=

N

II

o

q

N

?,,-1

I

t.l

u_

M

i.l

l|

,-1

n

(-1

o

l

1.1

iiiiiiiiii?iiiiiiiiii?iiiiiiiiiii;iiiiiiiiiiiiiiiiiiiiiiiiiiii?iiiiiiiiiiii;iiiiii;;iiiiiii;iiiii;;;

iiiiiiii?iiiii?ii;iii?;iii;iiii;iiiiii;

_MM_NNM_MM_MNN4MNNN

_mm _NNNNN_N_8

i

T-5

i+

i-I

o

II

i-1

,4II

1-4

o

,,4II

14

_0

II

',IF

|I

*4%

qlP

II

,IF

o

II

7,

,4n

i-1

,4II

o

||

iiiiiiiiiiiiiiiiiii...... _ . ._ .........

iiiiiiiiiiiiiiiiiiiiii;i;iiiiiiiiiiiii

_M_M_MMMM_M_MMM_

_iiii!+!!!ii!!!!!i!M_MMM_M

M_NN_MNNMM_MNN_N

!!ii!!_!!!!!!i+!i!!

iiii!!!!!!!!!i!!!!i_NMM_M_NNM_M_MNM

°#

°MU

II

+ +||

o

m

1 :II

,4

||

0

"I'-6

!!

t_

I:1¢_

I__¢J

>j• LO

0

0 A

0

0 I-,_o

0

o _"

ddddddddd

od6d6dddd

_4M44dddd o

0000__0 ____0_0____444dddd

000000000

LOOOO,_Cxlt'-_"¢qO0

_._ . . ._._._0,1__0000

N_,.4,4MMddd

T-7

Table 8. Grid Points and Other Parameters for AE-8 Numerical Representation

Energy Value Other Values o_ Other(MeV} L Value L Value Parameters Parameters NoteslRemarks

0.04 0.00 3.200.10 1.10 3.400.25 1.20 3.500.50 1.25 3.60O.75 1.30 3.8O1.00 1.35 4.001.50 1.40 4.202.00 1.45 4.402.50 1.50 4.503.00 1.60 4.603.50 1.70 4.804.00 1.80 5.OO4.50 1.90 5.505.00 2.00 6.005.50 2.20 6.606.00 2.40 7.006.50 2.50 7.507.00 2.60 8.00

2.69- 2.70 9.00

2.79- 2.80 10.00

2.89- 2.90 11.00- 3.00 12.00- - 15.60

Model Names AE-8MINAE-8MAX

Total Storage 1316813548

Scale Factors

Energy 6400L 2100b Increments 1024Z1 1024

Cells for AE-8MIN.Cells for AE-8MAX.Stored Value/Scale Factor = True Value.

Occurs when Z has dropped by 0.25.This parameter ZDEL ffi 0.25 does notappear in BI.L)CK DATA statement butis in Program MODEL87 that handlesBLOCK DATA statement.

T-8

Table 9. AE-SMAX Header and Logical Data Record (partial)

C******* AE8MAXBIX_K DATADOUBLE PRECISION NAMECOMMON/AE8MAX /NAME,EPOCH,SCAE,SCAL, SCAB,SCAF,LENGTH

X,MAP 1(163),MAP 2(163),MAP 3(163),MAP 4(163),MAP 5(163)X,MAP 6(163).MAP 7(163).MAP 8(163).MAP 9(163),MAP 10(163)X,MAP 11(163),MAP 12(163),MAP 13(163),MAP 14(163),MAP 15(163)X,MAP 16(163),MAP 17(163),MAP 18(163),MAP 19(163),MAP 20(163)X.MAP 21(163).MAP 22(163),MAP 23(163).MAP 24 163),MAP 25(163)X.MAP 26(163),MAP 27(163),MAP 28(163),MAP 29X,MAP 31(163),MAP 32(163),MAP 33(163),MAP 34X.MAP 36(163),MAP 37(163),MAP 38(163),MAP 39X,MAP 41(163),MAP 42(163),MAP 43(163),MAP 44qX.MAP 46(163).MAP 47(163).MAP 48(163),MAP 49qX,MAP 51(163).MAP 52(163),MAP 53(163),MAP 541X.MAP 56(163),MAP 57(163),MAP 58(163),MAP 59_X,MAP 61(163).MAP 62(163),MAP 63(163),MAP 64'X,MAP 66(163),MAP 67(163),MAP 68(163),MAP 69'X,MAP 71(163),MAP 72(163),MAP 73(163).MAP 74X.MAP 76(163),MAP 77(163).MAP 78(163),MAP 79X.MAP 81(163),MAP 82(163),MAP 83(163).MAP 84

DATA NAME /8HAE8-MAX /

163),MAP 30(163)163),MAP 35(163)163),MAP 40(163)163),MAP 45(163)163),MAP 50(163)

163).MAP 55(163)163),MAP 60(163)163),MAP 65(163)163),MAP 70(163)163).MAP 75(163)163),MAP 80(163)19)

DATA EPOCH / 1990.000/DATA SCAE / 6400.000/DATA SCAL / 2100.000/DATA SCAB / 1024.000/DATA SCAF / I024.000/DATA LENGTH/ 13548/DATA MAP 1/

X 1442, 256. 3. 0. 0, 3, 23 I0, 0. 27,X 2520, 5907, 37, 19, 19, 19. 18. 17, 16.X 15, 13, 12, 1 I, I0, 9, 8, 7, 6.X 6, 5, 4, 4, 3, 3, 3, 2, 32,X 2625, 7393, 72, 33, 33, 32. 30, 28, 26,X 24, 22, 19, 17, 16, 14, 12, 1 I. 9,x 8, 7, 6, 6, 5, 4, 4, 3, 2,X 3, 2, 2, 2, 34, 2730, 7926, 171, 55,X 49, 46, 42, 38, 34, 30, 27, 23. 20,X 18, 15, 13. II. I0, 8. 7. 6. 5.x 4, 4, 2, 3. 2, i, 2, 2, 1,X 1, 0, 35, 2835, 8153, 279, 85, 72, 65.X 58, 51, 44. 37, 32, 26, 22, 18. 15.X 12, 10, 8, 6, 6, 4, 4, 2. 3,x 3. 2, I, o, o, o, o, o. o.X 0, 36, 2940, 8339, 389, 123, 105, 93, 80,X 67, 55, 45, 36, 29, 23, 18, 14. 11,X 9, 7, 5, 4, 4, 2, 1, 1, 0,

Y 0/

00000010

0000002000000030OOOOOO4OOOOOOO5OOOOOOO6O00000070OOOOOO8OOOOOOO9O00000100000001 i00000012000000130OOOOO14000000150000001600000017000000180

00000190

00000200

000002100000022000000230000002400000025000000260000002700000028000000290

0OOOO3OO0000031000000320OOOOO3300000034000000350OOOOO36OOOOOO370OOOOO38000000390OOOOO4OOOOOOO410OOOOO420OOOOO430OOOOO44OOOOOO450OOOOO46OOOOOO470OOOOO480

T-9

A

o

U

A

U

o

U

el,a

q_

u

{J

u

11

000000000000000000

ddddoood_d_oddddd

dNdNdddddo_N_od

__ ..........000000000000000000

odddoooooooddddddd

ooooooooooooodoodd

....... __. ooooooooooooooodddd

oooooooooooooodo_

ddddddddddddddoddd

oooooddddddddddddd

dddddddddddddodddd

......... o_oooooooooooooooodoodddddd

000000000000000000

dddddddddddddddddo

oddddddddddddddddd

ddddddddddddoddddd

oooddddddddd6ddddd

dddddddddddddddddd

dddddddddddddddd_d

0 __

dddddddddddddddddd

88888oooo_oo_ggddddddddoooodddddd

000000000000000000

000000000000000000

ddddddddddo

_8888888888

_8888858554dddddddddd

T-IO

A

A

0

i@

D

_0

_0

_._..o.o.o. .............000000000000000000

dddddddddddddddddo

ddddddddddddddoddd

..... _0_ . ._ ......000000000000000000

_,0_.._.. ..........000000000000000000

000000000000000000

000000000000000000

000000000000000000

000000000000000000

dddddddddddddddddd

dddddddddodooooooo

dddddddddddddddddd

000000000000000000

ddddddddddddddddod

000000000000000000

000000000000000000

000000000000000000

ddddddddddoooooooo

_0 _ ,'-'_0_0_

dddddddooooooooooo

000000000000000000

oodddddddooooooooo

000000000000000000

T-II

X

_6

_6

,6

>.

d

_E

d

_E

od

c_

T-12

i]

8

8

8

8

8

T-13

t

"00 O00UO00 O0000000 O00C3 O00

WW_JWt_J_wtJJUJt_J '_IJJ_w_uj_j_jt_jUj_

_0000000000000000000000000

J_J_JJJ_JJ_J_jj_jjjjjjj

_000000000000000000000000

_0000000000000000000000000

000000000000000

__°J__'O_O0000000000000

jjj_jjjj_jjjj_jj,.. oooJJJojjjj_

0000000000000000+++ +_÷÷++÷+÷÷÷+÷

JJ_JJJ_JJJJ_j_jjj_jj_jjjjj

[-*-]000 O000000 O0000000 O0 O00000000

_.ooooooooooooooooooooo_ooo_00000000000000000000000000000

_10 _ ° _lr 0 if') 0 tO 0 t/) 0 t/3 o U') o U) 0 _ 0 g3,_ t[) 0 U) 0 _ 0

e • • • • • • • • • • • • • • • • • •

_o_o_o_o_o_o_o_o_o_o,,o_o_o_o_._9_o_o_o_o_99_oe_o°ee$°oeeo eeeo oeo

T-14

_g=

i

o0{a o

m_

i

•_,.., 0 0 O0 0 0 0 0 0 0 _J 0 0 0 0 0 _,,_0 0 0 0 0 0

_T_ LU W W_J LU_J _.JLU _U_J t_JLU _ILU LU W _U _ _J

_000000000000000000000000

_ _0_00_0_0_0__

eoeeeeoeeeeeeeeeoelltoseolellOOQOOQOOOOOOQQOOOOOOQO0000000

-.,,.400000000000000000000000

÷÷ ÷'I. _.÷ +-), ÷,i,+ "l. + +'i. _' ++_+ +l_j'l'' ÷LU bJ LU_ UJ UJ _ UJ LLI_U _ LLILU Ld _ LLI LULd LUUJ UJ UJ LW

_;dgogog333oogg_;gggddgggdggggg

_OOOOOOoOOOOOOOoOOOOooOOo

_OOOOOOOOOOOOOO

_O_O__

leleolleleleeleeeseeeoeeOeeeeoooOooooOOOOOOOOOOOOOOOOOOOOO

_ OOOOOOOOOOOOOOO

÷÷++÷++++++++++++

__00___O_O__

Seole_eloeoe$_$$$eel$loeeelelOOO000OO000000000000000000000

OOOOOOOOOOOOOOO

ggg;;g;gggggggggggggggggggggg

OOOOOOOOOOOOOOOO

÷+÷÷+_÷÷÷÷÷++÷+÷

__O__

0000000000000000

°°°°9°_°°°°lee eOll0000000000000

kO 0 _} 0 _I]0 _00 %30 _] 0 iO 0 iO 0

...... _....... _.O O O -- -- -- .-.{W _ {W 04 _")M _'_t'_4'

_0_0_0eeeeeeeee

T-15

litilifi_gllillf_li_91tllll_l

00000000000000000000000000000

_O_____N_000000000000000000000000

___0___

_U_N_____O 0eeeeeoeeoeoeeeeeeeeoe_eoooee

0000000000000o0000000000000oo

_oo_m_____ooooooooooooooo0000oooo

__O0__O_O_Ow____0_0_00_0_

00000000000_00000000000000000

_O__m_____000000000000000000000000

___00____00_0_0___

I_eelol_e_OO_eoge_ooooeoee

00000000000000000000000000000

_000000000000000• ÷+ ÷÷_÷÷+ +++÷+_+ ÷

i _0___0_0

____000000000000eeoqoOeeoeoOeeeooooo_eoooo_eo

00000000000000000000000000000

_0000000000000000+÷+÷÷++÷÷÷÷÷+÷+_÷÷

_0____0________00000000000

oooeeoeeoeeee_oeeeee_eeeoe_ee

00000000000000000000000000000

000000000000000• ÷+ ÷÷+++÷÷+_+++

___W_O0000000000000_eeeee_e_eeo_o_eeoeee_eoeee

00000000000000000000000000000

0000000000000000÷++++÷÷÷+ ÷÷÷÷++÷

O0_O__Nq_

00000000000000000000000000000

eeeeeeeeee_Oeeeeee_eeeoee

T-16

I¢1

I

_O00000000000000OO000000

llltllil_ttlll$ lie//t/t/ /Itlt

00000000000000000000000000000

_._00000000000000000000000

÷+÷+++÷++÷+++÷+÷÷+ +÷÷ _ ÷÷÷÷

It11115 119t tlitllOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

_00000000000000000000000

÷÷÷÷ ÷÷÷+÷÷+÷_+÷÷÷÷÷÷+÷+÷÷+

___N___OOO

gggdgggdgggggggggg;g;;;g_;ggg

_OOOOOOOOOOOOOOOOOOOOOO

+_++_+ ++_++++÷÷÷÷_++÷+÷_÷++

OOOOOOOOOOOOOOOOOOOOOOOOOOOOO

_OOOOOOOOOOOOOOO

_N_NN__O00000000000

ggg;ggggggggggggggggggdgggg;J

_000000000000000÷÷+÷ ÷÷ ÷÷++÷÷ _+÷ ÷÷÷

__N_N__O0000000000

gggggggg;gggggggggg;_gggggggg

_00000000000000

_ ÷+÷÷÷÷ +÷÷÷÷++÷÷ ÷

tl itl tlt00000000000000000000000000000

_00000000000000÷÷÷÷ +++_÷+÷+÷÷++ ÷

_=9999_=_9=99_999_9999_9

_O_O_O_O_O_O_O_O_O_O_O_O_O_O

oOSeeooooooeo$ol eeoeO

T-17

i

Ii

J

• '1 t_ _ 000 _,'_0_ O_ O_ O_ ¢0 ¢j ¢0 f,,. p,. p,,, p,. ,04,1 _0 _0 Lt) ur) u_,q'"I "'q "d "_ "q "d C) 00000 ¢.P00000 Oo 000000

_.j_j't'4.,4. 4.4. 4.4,4.÷4.÷.4..t.÷ 4.4. ÷_j_÷÷.W W _111J _JJ UJ UJ W IIJ _ UJ LLIUJ IIJ W 1211,,UI/J _IWUd

0000000000000000 O0 O0000000000

__0000000000000000000

00000000000000000000000000000

__000000000000000000000

d;gg;ggggggg_ggg;g;ggggg;dggg

__00000000000000000000

00000000000000000000000000000

__000000000000_+++÷÷++÷++÷÷÷+÷÷÷÷

gggggggggdggggggggggdggggggg;

÷÷÷÷÷÷_÷÷÷÷÷÷÷+÷÷_÷

ggggggggggggggggdggddgggggdgg

__00000000000

00000000000000000000000000000

÷++++++÷÷++++÷+++÷+

00000000000000000000000000000

_0_0_0_0_)0_0_0_0_0_0_0_0_0_0

_9__°9_9o_o_999_9h99_9_.,.,,.....0000______

T-18

g

a

i

w-4

I

C,]

I

'_'_ _ '_0 _0 O00¢_Q 0000 OQ 00000000

_J_J _JLUW W _J_J

00000000000000000000000000000

oggogoo

00000000000000000000

gggggggggggggddggggg_g

_000

_++÷+++

g_dg_dg

0000000000000000000

gggg;gggggg_dggggg;ggg

__00000000000

_0_0_00_ _

000000000

÷÷÷÷_÷+÷+

_0___0_0

_--_00000000000000

÷÷+++÷+++÷++÷÷÷÷++

gggdgggggggggggggg00000000000

ggggg;ggggg

C,i

!

_00000000000000

++++++++++÷++ +++÷+

_-_-_ _o_ooooo_eIee@ee_eeI@eo e_@ _eee

00000000000000000000000000000

_000_

+++÷+++

_0__0_

000000000000

+++++÷+÷++++

_==__°_°°°_... ... ...0000000000000000000000

Ou;O_ 0_0_0_0_0_0_0_0_0_0_0

eee Oeeoee@ee _ee

_0

000

_0_0 _o_o_o_o_o_o_o_o_o_o_oeleo e01 eee ei_

T-19

Ii

I

e

88

OOOOQO00000.(..I. 1.4. ÷÷ ÷_.÷_.÷_ _ U,J LLI_ID _J UJ _J _ _J

• 1_ u_uJUJ

_1_. _ _

ggdog

_000000000000000000

____0__

;gdgggggdddggdddggggdgdg

_OOOO___OO

, __

d_gggg_gg

ooooooooooooooooo___O_

ON_N_=___N____O0

_N_OOOOO__

__m_oOOOOO

_ O_OO__

$$$e I$$ei$

0000000000000000

OOOoOOOOOOoo

_O____O_N_N_O

OOoOoOOOoooOO

ggggg

_OOOOOOOO

_gg_ggggg;

OOO÷_

_OOOOOOOOOO

UJUJ

_0.'_

o_

_ ÷.q- 4.+÷, _0'_ _ _

_0_0_0

elee_OOOOO

_oOOO__

_M_OOOOOOOOo+÷++++÷_+÷++_÷÷

__W_W_O_

leeleeeo_oe_ee_e

OOOOOOOOOOOOOOOOOOOOOOOO

_O_O_

OOO_

_O_O_O_ON_O_9_O$eeese_ieselloseele

_O_O

O_O

_;ggg2

_O_O_o_Do_O_O_O_O_O_OO_O_OO

"1"-20

i

.g

t

i °°0I==m

, _ _ O__PP _6)__

iiiiiiiiiiiiit111tlltlt1111tl

O0000000000000000000000QO0000

___0_000000000000000

gg_gggggggggggggg;gggdggg_ggg

__0000000000000000000

lee _e_ t_eee

00000000000000000000000000000

00000000000000000000000000000

+÷+÷÷_÷÷÷÷÷_÷÷÷÷÷_÷+

g;ggg;;g;ggggg;ggggg;gggggggg

÷÷÷÷++++÷+++÷÷+++÷÷

00000000000000000000000000000

__0000__

÷÷+.÷÷+.*+_÷÷÷'+÷+÷÷

00000000000000000000000000000

t130 U')':,,.) u_ 0 _r3 o u3 o_)o _} o _3 o MlO t_ otl') o tn 0 tf) 0 t_3 0

T-21

i

J

j

!

J

i °°0

t_

-/

UJW _1W W W LU U.Ii£1ill U,JUJ UJUJUJ LUIjJ Ijj I/d*,M _ _ _ _ _ _ _

_--__000000000000000000

.... ....9_........, o..000000000000000000.00000000000

__00000000000000

0000000000000000000000

00000

_NO_

0000000

___00000000000000000

O0000000OO0000000000000000000

_ __00000000000000

___0000000000000

00000000000000000000000000000

..._-_9__°°°°°°oooo• 0$eee _o_e_

00000000000000000000000000000

00000000000000000000000000000

_0_0_0_0_0_0_0_0_0_0_0_0_0_0

_99_°_°_9999 _o

T-22

|

J

_.* ,._ *.* ,_* ,_ .-* ._*'* 0 Q Q 4.; 0 0 0 0 0 ¢_Q 0 0 0 0 0 0 0 0

tUW_ UJ_J

_O__O__'O__N

ggggggggggggggggggg;ggggggdgg

__000000000000000000

ddggggggggg;ggg;;_dgggd_g;dgg

!

__o_ooooooooo+÷+_+_++÷_÷÷÷÷_+÷÷÷+

gggggggdgggdgggggggg;gggggggg

÷+++ + +_÷+÷_÷ +÷ • ÷ ÷÷ ÷_÷

e.eooeeeoeeoo_oeeooeoeeoee_ee

+_+++++÷+++÷+÷+_÷÷+

___0_

eo_eeeeo_eo_ooee#eeee_eeeeoee

___00000000

_0_)0_0_0_0_0_0_0_0_0_0_0_0_0

eeese_e*oeoeeeeeoeeeeeeeeeee

T-23

!ij

I_s

i

,_.m ,,.*..*-.I ,_ '_000 r*J 0 'J 0000 q,._00000 O000

_g;doooog_ogc;;_;;oo;;gggg;g_

___000000000000000000

_0000000000000000000000000000

!

__0000000000000000000

_____0_0

@@@@_geo @oe@@@@@@oee@@@ @_0000000000000000000000000000

"___00000000000000000

__0000000000000000000

ddgggddgdggggg;gggggggggggdgg

__m_O00000000000000000

@_$@@@ @@@@o@@@@@@@@@_@@00000000000000000000000000000

__"'_=_°°9__....... ......00000000000000000000000000000

*') 0 _r) 0 U; 0 _; 0 UI 0 _) 0 _r) o _/[3o _3 o_o_o_o_o_o

_o_0_o_o_0_0_o_o _0_0_0_0_0_0

T-24

_8

i

ttlllllliittittllttllStitllllO0000000000000OO0000000000000

__0000000000000000000

iiiiiiiiiiiiiiiiiiiiii:::::i NNNNN

Illtlli@fl$11)lllliiltilllt91

00000000000000000000000000000

___000000000000000000

00000000000000000000000000000

__00000000000000000000

_ _0_____

eooe_ooeoeeoeeeeeOoeooooeee_

00000000000000000000000000000

_N_O000_______0000000000000000000

@÷ +÷ ÷ ÷÷+ ÷_ ÷÷÷÷÷ ÷ ÷÷ ÷÷÷ _ ++_ ÷÷

_______0oeeeeooeeeeeoeeeeeeeoeeeeeeee

0000000000000000000000_000000

_N_O000__

P)____--_O0000000000ooseseeeoseeeseeseooeeseseoeo

00000000000000000000000000000

_m__O00000000

÷÷÷÷÷÷_÷÷÷÷÷_÷÷÷÷+

ggggggggg;gggg;ggg_g;;d;;g_gg

_0_0_0_0_0_)0_0_0_)0 _0_0_0_0_0

_0_0_0_0_0_0_0_0_0_0_0_0_0_0

T-25

e

g

__O_V_OOO_QO0000000000

_ _ _1_ _ _0_ _ _0 _0 _ _

00000000000000000000000000000

__mO000000000000000000

__000000000000000000000

_000000________000000000000000000

_O000_@_W______000000000000000000000

.... ... _...__-_

__00000000000

......... . ..... . , ,0000000000

OOOO0000000000000000000000000

__00000000000÷÷÷++_÷÷++÷÷÷+÷÷++÷

_-_-_-__ _............ __ _00000000000000000000000000000

eeoooeeoeeoeee oe_ o_e

_o_o_o_o_o_o_o_o_o_o_o_o_o_oooo _oeoeooeeoee_e ° o_eo_

0000______

T-26

-.g

e a

J

!r-.I

i

0,1

i

C_

@tleelttllgleell_ll_illl_@_ee00000000000000000000000000000

gggggggdgggggd

000000

ggggd;

_--_--000000000000

ggggggdgdgggggggg_g_

000000000

;ggggg;gg

__0000000000

gggggggggggggggg;ggg

000000000

gggg;ggg;

__0000000000000

gdggggggdgggggdggggg

00_000000

ggggdgg_d

+_÷÷++÷+++÷÷++÷÷++

eleoeeoeel,leeeeet000000000000000000

0000000

ggggggg_;

_0000___

eleeeeteetleeetttt

000000000000000000

0000000000

__0ettlteeeeet

00000000000

000000000000000000

00000000000ttetet,t_e

00000000000

eleettl tett

0

+

00000000000

_0_0_0_0_0

_o_o_eteele

' oleleeeo oleo

0_0_0_0_0_0

tee eee

T-27

i

I

.8

...oa

• _j

@lli@ii@llltt@llt_illllllli@t

00000000000000000000000000000

--_'_0000_0000000000000

__00000000000000000000

looege@ee_oeeeleoooo@eseeeee e00000000000000000000000000000

_N_OOOOOO____R___0000000 00__

0__0_0_0_00_._.• :__-o_-__©_o._

_._;_;;_-_-_-___@OOOOOI00@O$II

00000000000000000000000000000

W_O000_____

__000000000000000000000

* _ __

_11 it@ltlllllltllltlttllltllOOOo0000000000000000000000000

_N_O00000____

___000000000000_0_

IllOl@@@Ol@l@@lttl

_00000000000000

+++_+_+++++_++_++++

e°@eeol°le@oooo@eoel@eeelolel

_9_:_ 9 _ -_... :.,.: ...:_9°°°_• los00000000000000000000000000000

I/lOuJO_lO

000,-,--,.,°05 cole BoO

_0_0_0_0_0_0_0_0_0_0_0_0_0_0

___°_°_°_99 _9_eel _lle@e_ee$ol 9

T-28

i

"iI

_000000000000

I_ Lid UJ t_d tIJ tIJ tU tl_ t_ t_ I_ _JJ _J

t'_,#..,,' r,..,_") {%1-- _ ,L'_B,,_ _ r,, ,-...,• • • • • e • o • •O00OO000000OO

__00000_______m_O000000000000000000

ggggggggggggggggggggggggggggg

_00000_____

_--_00000000000000000000

eoeeeoooOOOoOOeeO_oeooo_oeeeo

00000000000000000000000000000

_N_m_O0000_

lllielltlll$

000000000000

00000000000000000

_O_m__

ooeeeeoeeeeeeeeee

gdggggg_dggggggggggggg;;g;;g;

_00_

e*oll_|e_

0o0000000

_ _0000000000ooeooee_eeeeeeeeoeo

0000000000000000000

_w_O000000000

gggggggggggggggg

0000

_000000000

gg_dggggggggg

_OY)O _0 _0_0_)0 _0 _0_0_0_0_0_0 _0

__o_o_o_o_o_eeeeeoeeeeeeoe_oee_eee

T-29

0_

,,g

I_8

I

i °°ca oa_

i

;;;;;;;--° .,o_oo_oooooooooooo

i _W____W___ _

e_eegeoeeeeoeeeo_eeelettet_o

O0000000000OO0000000000000000

m___O0000000000000000

_w__O00000000000OO 000__ 00______

O°e_e°eeeoBogoo_B_eo_e_e_e_

0000000000000000000_000000000

__00000____

__mm_O0000000000000000

..... ,....... .., ... _00000000000000000000000000000

!

W_O00000_____

--'__0000000000000000000

__00000____

_m__O0000000000000000

_O_O____NO_ 0

_ uJ__,__ul__ _" " ' "_ " ' . • • • . • . . . , . . . . . . . , .

O0000OO0000000000000000000000

!___0__

_0_____

eeo eeoeeeeee _oe ,

00000000000000000000000000000

÷÷÷÷÷+÷_+÷+_+÷+÷÷÷++

__...____00000000000000000000000000000

_0_;)_0_0_0_0_0_ 0

_o_o_o_o_o_o_o_o_o_o_o_o_o_oo_o__o__o__eeeee_ee eeoeoe e_ee

T-30

Jt

-8

+!i

J

tv)_ ,-, .q O O O O O O O_t.,t _._ O_ O_ _ _ _ _ p,. p,. p,, p. _O _O _O _ qt) i_

,.., ,.,i " -, ."o .'_"t ,"l .'I ,,.e s,,_ _.10 O O O Q O O O _ O O O O O O O Ot._l| .k + 4-,4. +.b + + ++ 4,,,I.+ +++ 4.,(.++++++++ ++ +

M.IUJ f¢l ILl tIJ tU LLIIM UJ t/J IM ID lU ID W t/J _lJ ID tlJ _J _ _ _ _ _ _ _ _ _

lib tltllt llllttitllll

OOOOOOoOOooOOOOOooOOOOOOOOOOO

_NN_O00000@____--___OOOOooOOOOoOOOOOOo

;ggggg;ddgggdgggggggggg;gg;gd

C4 •p,P ++ +

0..., 4' P" _

OOOOOO____--_--_OOoOOOOooOOOOOOOOO

ggg;g;ggg;ggggddggggdgdd

___OOOOOOOOOOOOOOOo

ee_e_eee_eeee_ooeeooeeoeeeeo@

i

__000000000000

+++++++++++++++++++

ooeeeeeeeeeoeoeee_eeelooeo_ee

_OOOO

++++++++

_0_

--00000000000

++++++++_+++

_0__OO_O_

000000000000000000000

_o_o eBIool

OOO_

_0_0_0_

0000_

0_0_0_0_0_0_0_0_0_0_0

ltll9_9tllO_|tll

T-31

I

i|

I=

ml

4.

,.._ cO

o

..i

4.UJ

N

O

!

i

v-.i

ml.a_

ID tU _J

_;gg

_uJ Wwww WuJUJW _u

oooggc:goooo

O04JOOOQO000000

W _J _ UJ _J _ _J _J UJW W _J _J UJ

g_gog;;og;odgo

_JLD0_0 __0__0__0_

0000000000000000000000000

__W__NO_N_O_O__

00000000000000000000000000000

_O____O__O____O____

00000000000000000000000000000

_NN__OOOOO

ggggg_ggggg_ggg

OOOOOOOOOOOOOO

__O__

gg_g_ggggdgggg

___OOOO

__O_O_

llieeliililitll

000000000000000

OOOOOOOOOOOOOO

__N__

eeee_eeeoeee

oOOOoOOOOOOOOO

___0000000000000000

_0_0__0__

........... _ __

_o_o_o_o_

_o_o_eoeeo_

OOO__

O_O_O_O_O_O_O_O_o_O

_O_O_O_O_Oooze eoe_o4 eeeoo

_o_o_)o_o

ogog22:'/__O_O_O_O_O_O_O_O_O_O_O_ON_ON_O_O

T-32

.i

iI

Pl CM ,.., -.* ,..* ..., 0 0 0 0

LU LU _J _ _J _J tLJL_ UJ

ggoogo;gg;

_O00000000000OO0000

ggdggggggg_;g;gdggg

tlllllelle II!_

00000000000000000000000000000

I

0000000000000000000000

0000000

oooeooo

0000000

;ggggggggg gg_gggg;gggg

0000000÷÷+÷÷÷9

ggddggg

|

_NN--OO000_

ololeelelo

_000_00000

0000000

÷_÷+÷÷÷

• • • O • • •

00000_0

000000÷÷÷÷_÷

0_0

000_00_0000

0000O000O0

_000000+÷÷+÷÷÷

*ooo

0000000

0000000

-_-_oo_eleeeooeo

000000000000

000__o*ooooo

_0_0_0_0_0_0

T-33

i

!j!

I ,,g

c_ 0

OOO00000000000000000000000000

____000000000000000

g_gggdggdgdggddgggggggggdgggg

_NN_O0000

O_Om_O00_0_0_

eooeeooooloo000000000000

0_____0000000000000000

_0_0_0_O_O_N__

oeeee_et_teeeee00000000000000000

__--_000000000000000

_ __O_O0__O_WO_O_

ggg;gg;gggdgggdgggggggg;gdggg

___0000

_0___

gggggggggggdggg

_0000000000000

ggg_gggg_ddggg

eooloeeee_ooo_oooeeeoe_oe_o_e

O0000000OO0000000000000000000

oee_e_o_oogoo_eo_o@eeoooooeol

00000000000000000000000000000

_o_o_o_o_ee_ _$oe_eool

000___

0_0_0_0_0_0

_O_O_O_eo_eo_eo

_o_o_o_o_o_o_o_;o_o_o_o_o_o_o

ojeeeo$oo ooeeeeoo o*o

T-34

o

0

!

i° °_ 0

oeeee$4e$$oeeseeeeeeweeSeeoee

O000000OO000OO000000000000000

--_--___00000000000000

ggggg;g;ggdgdggggggdggggdd;gg

o

_N__O0000________00000000000000

00000000000000000000000000000

÷÷+÷++÷+÷÷÷+÷÷÷÷÷÷+÷_÷÷_÷÷_+÷

gg_gggggggggggggggggggggggggg

,'4

oeeeeeeooe_ooeoooeoeoeoee_oe

00000000000000000000000000000

i

_--__000000___

ggggggggggg;ggggggggggggggggg

_o_o_o_o_o_o_o_o_o_o_o_oo_o_o_o_9_o_o

ooeeo_ooeeeeeeee oOoOeo

T-35

Ii

U

OOOO000000000QOQOOOQOQOQQO000

g_ggggg;_ggg;ggggg;;gg;gg;ggg

!÷+'÷+÷+÷+÷" ÷÷''÷÷**+'÷++_

00000000000000000000000000000

_NNNN_

00000000

I_lltl_f_t_91titiltll

000000000000000000000

!


00000000000000000000000000000

!+÷÷÷÷+++÷÷÷÷÷÷_÷_÷÷_÷_÷÷÷÷÷÷

00000000000000000000000000000

_0_0 _)O_OUl 0_0_0 _0_0_ 0_0_0_0 _0

Iltltlltll411ttllilllltllllft

T-36

P

i

t)

•.* -.a -_ 0000 r.300 (.) 000 ,.300

÷ + ÷ 4" 4. + + ÷ + "O".k '@ ÷ ÷ _. _" <._ UJ UJ _ _; UJ tU UJ _J UJ UJ U.I U.I _ UJ _ bJ

+÷÷÷÷

o@$ee

00000

_00000___

__0000000000000

++++÷+÷÷+÷÷_++÷÷_++

__0__0_

tooetotoeome_eelolle000000000000000000000

000

000

__00000___

_m___O00000000000

+++_ ÷_++_÷÷++÷+÷_+÷+÷_++÷++

___ _0__0_

eeelooee_ee_eeeeeeeleeeeeeelel00000000000000000000000000000

__00000___

÷_++ ÷+÷+÷ ÷÷++÷++÷÷+÷÷+÷÷+

;ggg;gggggggg;gggggdggggggdg;

_leeeele_o_oeeeoee_leellOelll

00000000000000000000000000000

__m_O0000000000

+_÷+ +_÷+÷+_÷÷÷++÷+÷÷+÷÷÷+

Ioeoeleeeoeltoet_eooeeeeoeoee00000000000000000000000000000

_0_0_

_0000_____00000000000

÷÷+÷_+÷_÷÷÷+÷÷÷÷÷+

_ i_'_ 00_ _ _ 0 _

0_10_0_0_0_0_0_0_0_0

lee oeo Oelll

_0_0_0_0_0_0_0_0_0_0_0_0_0

e_eoelle eeeeee eeelsDll

T-37

I

i!

g

,.i ,., ,_ ,.d ,-, ,_ ,I -, ,-6 ._ ,.o _ _ 0 0 0 ,_ M 0 r_ 0 ¢.j 0 _ 0

_ UJWJ_U WJW.JW LUUJUJ W ul UJW u./U.JU./U./UJUJ_ _ _ _ W W

• • • • $ • $ • • i • • • i I • i • i $ • I $ • $ • $ • •

00000000000000000000000000000

gggggggggdggggggggggggggggggg

___mO000000000000

ggggggggg;gggggdgggggg;gggggg

_÷++÷÷+*÷÷*÷÷÷+*+÷÷÷÷÷÷++*

gg;gggdggggggggggg_gggggddggg

**++÷÷+÷+*+÷÷+++++.+÷++÷++

gggggggggggggggggdggggggggggg

_O__O___

_ _--_O_--O_O_O_O_

gggggggggggggggggggggggggggg;

___OOOO______OOoOOOOOOO÷÷_+÷_+÷÷÷÷+÷++÷÷_÷+++_÷+÷

_O_O_O_O___O_

oo ooe oee

_0_0_0_0_0_0_0_0_0_0_0_0_0_0

_O_O_O_O_O_O_9_O$$eo_eeooseeeooeoeoooe

_O_o_o_o_O_O_O_O_O_o_O_O_O_O

O_0_O_90_O_O_O_

T-38

00000000000000000000000000000

___O000OO000000

___==_q__°_... ..,..,,..O000000000000OO000000000000OO

_-_:__'_'__... .....00000000000000000000000000000

_.+÷÷÷.÷.+÷,÷*+÷_+÷÷++÷+÷_w_wwwww_w_w_wwww_w_w_

ggg;gggggggggggggggggggg;;dg;

÷+÷÷÷+÷÷÷÷+÷_÷+÷++÷+÷÷÷÷÷

gggggggggggdggggggggggggggggg

÷÷_÷++++÷+÷÷++÷÷_+++÷+÷_

_ _____00000

ggggg;ggggggggggggggggggggggg

++++÷÷+++_+÷÷÷+÷++÷÷÷+_÷+

_0_0_0_0_)0_)0_0_0_0_0_0_0_0_0

_o_o_o_o_o_o_o000______

_0_0_0_0_0_0_0_0_0_0_0_0_0_0

_ O_O_O_O_O_O_ON_O

T-39

IiI

,j

,I I1

1

1i!

I

-.i _ _ ,.,i ,.i ,,..i .-I _.i ..,i _O000_O0_ 000_ 0

elletleDDtlll_eiBl$1_ll$ooooooooooooooooooooooooog;_;

÷÷÷ ÷÷ _÷_÷ +÷ ÷÷÷÷+_+÷++ ÷÷

_O_O0_ON_O_N_

N_N_N_¢__N_N_N_OOO00

g;gg;ggggg;gg;gggg_ggggg_;dgg

__0000000000000++÷++÷+÷÷+÷++÷_÷÷++÷+÷+

OOOOffllOOOeBOOlOOOfOOotillOOQ

O0000OOOOOOOOO00OO00000000000

___O00000000000_+÷++÷++÷+÷÷÷_++_÷÷++_+÷

ttllOllllltllllllttltltllitll

000OOOOOOOoooo00OOOO00OOOOOOO

+ +÷+++÷+÷+÷÷_+÷÷÷÷÷+++÷

tlllllltllttltllitlltlt

0OOO00OOOOO00000OO00000000000

_,RNNN_OOOO_¢_h_

++++÷÷+++÷+÷÷++÷÷÷÷+++++

IIIIttIOItOtOOllOtIItlIOIIIOI

O000000000o00000OOOOOOOOOOOOO

O0 O0

÷÷÷÷_++÷÷÷÷÷++ +÷÷÷+_÷÷

ltOItltllllllllOOlOOllllOl$11

00000000000000000000000000000

++÷÷++÷++++++++÷+++÷÷÷++

ggggggggggggggggggggggggg;gg;

tllolltelltOoltoolltoeoiooiI

_0_0_0_0_0_0_0_0_0_0_0_0_0_0

toll111 tllOllllttlt

T-40

i

J

UJ u_ _J _J I_ LU _J _J uJ _J _J uJ _1 _lJ uJ W L_ILU _ _J uJ U_J_

0000000000000<3000000000000000

_.__000000000000

;gggggggggggggggggdgggggdgggg

___000000000000÷÷_÷_÷÷_÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷

le_oeeeeeeoo_oeelee_

_e_o_oo o_0 iio00000000000000000000000000000

o_eeee oee_oe eeoe

÷÷÷÷÷÷÷÷÷÷÷_÷÷÷÷÷+÷÷÷÷÷÷


eooooeltoe_eoeeee_loeoooOeooe

00000000000000000000000000000

+ +,1,4, ÷'_ ÷ 4" ar +÷ +÷ *4.* 4.4-4"4.4. 4-4" 4"LIJ tLJ U.J_.1 t_J LLI tLI LL_UJ I_J UJ tU Ia.JUJ t_ LU LU U.JUJ W t_J U.I U.I U.I

_._.._...:._,,._..:_ _..:=.,_._®_.o.ooo.o..... .... .00000000000000000000000000000

T-41

IJ!aj

!I_ _J _J LLJLU UJ UJ U_ILkl I_J I_ U,JUJ U,J _ LL,Itl_ U_ _ tU _

!

..... . ..,..._00000000000000000000000000000

___000000000000

__00000000000

ee_e_e ee_eeeee

00000000000000000000000000000

_NN_O000___

___0000000000

_ r_O_O___O_O_

wee_e#_ we_

00000000000000000000000000000

__0000__

__M_O00000000

÷÷+÷+÷+_+÷_ +÷÷÷÷ ÷_÷+÷+

00000000000000000000000000000

tf) 0 _rl 0 U30 _30 _ 0 _) 0 _r_ o _) o I_rlo _ o u30 _3 o _r_ r_ u) o

| • • • e e • • • • o • • o • • • • • • • • • • •

_0_0_0_0_0_0_0_0_0_0_0_0_0_0

_.o_oN_o_o_o_o_o_o

T-42

0

|

2,

i

•_ ,,_. 4. +.,k',_ "$'._ ÷ ÷.1.,,_,4..,k.I- ÷ -p4. ,,_-p _ _

_÷+_÷÷÷++÷÷

gggggggggJg

000000000000-I,'÷ _÷ ÷._÷..l..k 4,,÷.,kLU ',.;JLU LU _J LLIg.I t_l _ LU LU _1

ooogggogdggoogdgoo

+_++_+++÷÷÷÷÷÷÷_

_--__0_0

jggggggggggggggg

000000÷÷+÷÷÷

__0000000

g;ggggg;.ggggg

+_÷÷÷÷+÷÷÷÷÷÷÷_÷

__0__

0000000÷+÷÷÷÷÷

JjggggggggggJ

___00000000000

_0__0_0_0_

g;gJgJggJjJgJJJjgjgJJ;JJgJJJg

__0000___

___00000000000

÷ ÷÷÷÷_++÷÷÷÷+÷÷÷÷÷÷÷÷_÷

ooeeeeeeeee@eeeoeo@#ooemoooee00000000000000000000000000000

++++÷÷÷÷÷+_++÷+÷÷+_+÷++

eeeeeeoeeeeoeeeeeeeeeeeeeoeea00000000000000000000000000000

_0_0_

000_.__

o_o_o_o_o_o_o_o_oo_o_o_o_oeeeeoeoeoe_oeoe

_0_0_0_0_0_0_0_0_0_0_0_0_0_0

0_0_0_0_0_0_0_0

T-43

Ii

I

ii

eeeoeeeeege_eeoeeeeeoeeeee

00000000000000000000000000

_0000___

__o__u__N'__N__N_OOOOOOO

g;ggggg_;_gg_gggggdg_gg_ggg

__mO0000OOoOOOO0

NN_N_N_N___OOOOO000

OOOOOOOOOOOOOOOOOOOOOOOOOOOOO

_N_OOO_____OOOOOOOOOOOOO

_OO_O_O____--____N_OOOOOOO

eeoeeoeeeeeeeeeee_oeesee_oee

oOOOoOoOOOoOOOOOOooOOOOOOOOOO

_N_OOOO____m__OOOOOOOOOOOO

__W___OOOOOOOOeeoeoeoeooeseeeeeoeoeeooooooooooooooooooooooggggggg

__OOOo______OOOOOOOOOOO÷ ÷÷÷÷÷÷ ÷÷÷ ÷÷ ÷_ ÷÷ ÷_÷÷

_t_O_OO_O_O_____OOOOOOO

oeOoeoe_o_oe_eeeeoeeeeooooooooooooooooooooooggdgggd

_N_OOOO_____OOOOOOOOOOo

__O__O_OO______OOOOOOOOeoeee_eeee_eeeeeeoeeeeoooooooooooooooooooooogggggg_

__OOOO_W____OOOOOOoOOO÷÷÷4÷÷_ ÷÷_÷÷÷_÷÷÷÷÷÷÷÷

____O_O_____OO______NOOOOOOO

g;ggggggg;ggggggg;gg;;;gggg;;

li'10 ID O I/}O I_ O UI O It10 IN O I_ O It1Oil10 li10 I11O ID O tll O

_o_o_o_o_o_o_o_o_o_o_o_o_o_o9_°_°_9_°_°_9 _°

"1-44

l@

_g

iI

lj!

,_ _* _, *,.* _.* _.,r-.I 4.14.P g _1Q 0 Q g Q O00 Q 0

lilli@Si@@tilil@lilillililili

00000000000000000000000000000

00000000000000000000000000000

I

__00000000000000

÷÷÷÷ ÷÷÷÷÷÷÷÷÷÷_÷_÷÷÷ ÷

_0_0___0_

gggg_g;ggggg;ggg_dggg_gg;gg_;

__0000000000000

__0'0_0__

00000000000000000000000000000

__000000000000

+++÷_÷÷÷÷ ÷+_+ ÷÷+ _÷÷÷÷

___0_0___0__0_000

eee@@@i@ee@ee@eeele@e@i@@eei@

00000000000000000000000000000

__O000_WW__

__000000000000

+÷++÷÷÷÷+÷÷+÷÷_÷_÷÷++÷

____00_

W_____O000000eeeooeoeooeeeeoee@oeeeeooeeO@

0000000000_000000000000000000

__O000_W_m_

__00000000000

++÷÷÷÷++÷÷÷÷+ ÷÷_ +÷ _÷÷

_0_0______O__MO_

___ff)__WO0000000eeeeeeeeooeeoeeooeoeeeeeeoooo

00000000000000000000000000000

__0000_____m_O0000000000

wwwwwwwwww wwwwwwwww_

;;ggggggg;gggggggggg;gggggg;g

_o_o_o_o_,o_o_o_o_o_o_o_o_o_o_o_o_o_o_o_o_

@e_OO@@@@@@@e@@@@@@@@@@9@

_o_o_o_o_o_o_o_o_o_o_o_o_o_o9999°_°_99_°_99 °_°_°O000___4W___

T-45

Figures

0.6

r_ 0.4

0.2

I I).0

-0.2

•E_I I

&

I I ! I

4 6 8 10

L

Figure I. Local Time Variations for E • 1.5 MeV

2

AE-8

• AE-4MIN

[] ATS6

A Azur

• AE-4MAX

F-1

O

Omnidirectional Flux > 1.5 MeV (e/sq cm-s)

F-2

r_

p_

0

I I I I


F-3


F-4

I I I !

.Q

o

0

n

a


F-5

10000 .

iL

|

IOO0

10(3

10

bc2

L

bc2. AE-8 model

bcl, a more physical model

bcl

I0

Figure 6. Magnetic (Atmospheric) Cutoff Models

F-6

107

1_ 10 6

i 105

i 104 3OOI " I I I l " I

320 340 360 380 400 420 440

DOY 1969

Figure 7. Azur Data Greater Than 1.5 MeV Versus Time at L = 4.4

106

4; 1051

10 4

I IlO31 . . .

Ik_ 300 " 320 3;0 360 3;0 4;0 4'_0440

DOY 1969

Figure 8. Azur Data Greater Than 4.5 MeV Versus Time at L = 3.0

F-7

10000

1000

6 lOO

t

@

.1

n

,'I

[]

[] 0 []

• • •

I I i I l

1 2 3 4 5 6

o Corrected

• Uncorrected

E(MeV)

Figure 9. OVl-19 Data at L = 3

F-8

i

@a.

10000

1000

IO0

10

.1

B

• [][]

D

[] n

D

• •

I I m I I

1 2 3 4 5

E(MeV)

[] []

6

[] Corrected

• Uncorrected

Figure 10. 0VI-19 Data at L = 4.5

F-9

11

10000

1000

IO0

10

[] []

ra

0 rl

O O D

i i i

2 3 4

• • •

[][]

D

D Corrected

• Uncorrected

E(MeV}

Figure 11. OVl-19 Data at L = 6.0

F-IO

107

I0B

A

"T05

i

Ee_

w

104

_o3Z

=E

B

102

10I'[

1967

:_ Ee>

--E e >I.05

"-- LI

ATS-5

0.14<E<0.60

Ee>0.7i I

Ee > 1.55

1969 1971 1973 1975

YEAR

"1150

1

J 100F I

,

5O

o

r_

r_

:E

Z

CDO-ciOZ

c_

c_O0

C_C_

Figure 12. ATS Long-Term Electron Observations at L ~ 6.6

F-1I

108

107

A

106

105,104 ,

[] AE-8MAX

103,

102

10 1

a_' 10 0

• AE-6

• []

[]I " I " | " ! | !

1 2 3 4 5 6

E(MeV)

13L Comparison of SOLMAX Models at L = 2,5

10 9

107" I_

0 AE-8MIN

A 10 6 ,

105,

-jo 104

i 103102

10 110 o

0

• AE-5P

@

@

@

Q

@! " I " I " 0 "

1 2 3 4! • !

5 6

E(MeV)

Figure 13b. Comparison of SOLMIN Models at L = 2.5

F-12

109 .

108_

107 .._[._

r_ 1o 6.

o 103 ,@

i 102,

101

10 0

%

• [][]

• []

[] AE-8MAX

& AE-6

&

[]I l " I I " I " I

1 2 3 4 5 6

ElMer)

Figure 14a. Comparison of SOLMAX Models at L = 2.6

109

108

107@

fd^ 10 6

10 5

104o

103

102

101

100

C) AE-8MIN

®®

• AE-5P

®®

®Q

®

90

1 2 3 4 5 6

]_(Mev)


F-13

lO9]_

! 108 '_l AE-8MAX

i 104']],_ A[_] A[_

,DD100/ , ..... ,

0 1 2 3 4 5 6

E(MeV)

Figure 158. Comparison of SOLMAX Models at L = 2.7

7

109

108_107

C) AE-8MIN

_" 1% • AE-5P_' 106

lO2_ Q

!o100/ O .

0 1 2 3 4 " 5 " 6

E(MeV_

7


F-14

10 91 AE-8MAX

,°_5 _} ,o,f_ _-o. lO,t%_

,o,l ?o

i Oooi loOl . , . . , . ; ; E:]--

1 2 3 4

E(MeV]


lo9]

lo e._ O AE-SMIN

107 "_ • AE-5P

"11;1%

io21 O

1011 " O O, O,O°o' ; _ __ _-9.E(MeV)


F-15

10 9 ,

_ /_E-4NAX

i ,oS_ [] []

lo21] [] I-'1

lOll ] 17 []

'°°o' _ " _ " " 4 ; _ "E(MeV}


109

I07_ _) • AE-4MIN

=_ 1051 _)_

i 1°"I o o,o_ ° 0 0

i ,o,_ 0 01°11] 0

E(MeV)

Figure lTo. Comparison of SOLMIN Models at L = 2.9

F-16

10 9 ,

10 8

107 _x

_XX X

==t

105 'Jl:! [_] I:_g mm

"÷

10 4 []

101

100

0 1 2 3 4 5

E(MeV)

[]

[]

[]

6 7 8

[] AE-8MAX

e, AE-4MAX

_- _zur

• OVI-19U

[] OVl- 19C

X 0V3-3

Figure 18. Comparison of AE-8MAX with Outer Zone Data at L = 3.0

F-17

109

108 t

107

'_ 10 6

MA 10 5

10 4

i 10 3

10 2

101

10 0

_)a • •

_m_o _mm

[]

[]

[]

[]

• m " u • i - u - m - u • m •

0 1 2 3 4 5 6 7 8

E(MeV)

[] AE-8MA.X

• _-4MAX

-J-

• OVI-19U

n OVI-19C

Figure 19. Comparison of AE-SMAX with Outer Zone Data at L = 3.2

F-18

'°°1lO8-J

13 •lO 6- [_ •

°"÷J_o • ,A 105.

i 104,

103

i 10 2

101

[]

[]

[]@

[]

[]

10 0 • l • , • i • , • , • i • , -

0 1 2 3 4 5 6 7 8

[] AE-8MAX

@ AE-4MAX

"1- Azur

• OVI-19U

,'I OVI-19C

Figure 20. Comparison of AF,-8MAX with Outer Zone Data at L = 3.4

F-19

1°'1lO8J

107

106,

A 10 5

104,

i 10 3

10 2

,ol]10 0 1

0

x [] •

*l-a

°

[]

[]

° []

[]

° []I " I " I " I • I 0 I " I "

1 2 3 4 5 6 7

-t- Azur

• OVI-I9U

D OVl- 19C

)¢ 0V3-3

E(MeV]


F-20

109

108 1

...A

_ _o_ _o ",

i 104

0

_ 10 3

I_' 102 .

101

100 • i • i , •

0 1 2 3

[]

D@

[]

[]@

I " I _ I "

4 5 6 7 8

E(MeV)

[] AE-SMAX

• AE-4MAX

-I- Azur

• OVI-19U

a OVl- 19C

Figure 22. Comparison of AE-8MAX with Outer Zene Data at L = 3.6

F-21

109

108_

107t__ I

,o+; _:::,M

105

i 104,

103,

102

101

[][r-_-]m,,• •

m

'_;p-

K!

[]

r-i

r'!

100 • - m - m - m - m • , - m -

0 1 2 3 4 5 6 7

]r4Me_

[] AE-SMAX

• AE-4MAX

"F Azur

• OVI-19U

O OVI-19C

F-22

1°91

10 8 _]_i_]

10 3

10 2 ,

10 1

10 0

[]

[]

[]@

• I " I " I " I I _ I 3 I

0 1 2 3 4 5 6 7 8

l¢(MeV)

[] AE-8MAX

@ AE-4MAX

-I- Azur

• OVI-19U

OVI-19C

X 0V3-3


F-23

°°I

108__]

107 .

106

105

i 104,

_ 103,j102

10 1

100

,,

r,q°[_g, •

[]

• []

[]

I I I " I I " I I "

0 1 2 3 4 5 6 7 8

E(MeV)

[] AE-8MAX

@ _J_-4MAX

"J- Azm"

• OVI-19U

a OVl- 19C


F-24

109

108_

105

i 104

103

102

101

100

I_D II ii

[]

[]

[]

I I " I " I " I " I " I

0 1 2 3 4 5 6 7 8

_(x®v)

[] AE-8MAX

• AE-4MAX

-!- Azur

• OV1-19U

OVI-19C

l_gure 26. Comparison of AE-8MAX with Outer Zone Data at L = 4.4

F-25

10 9 ,

10 8

10 7

10 1

[]

[]10 0I ' " ' I u • u • I •

0 1 2 3 4 5 6 7 8

E(MeV)

[] AE-8_LA_

"l-_

• OVI-19U

0 0VI-19C

X 0V3-3


F-26

6

i 10 5

10 4

I 10 3

10 2

I0 1

10 0

,', ]m

[]

[]

[]

@

• I | • | " I " | " O " g

0 1 2 3 4 5 6 7 8

E(=®v)

[] AE-8MAX

@ AE-4MAX

+ Azur

• OV1-19U

[] OVl- 19C

Figu_ 28. Comparison of AE-8MAX with Outer Zone Data at L = 4.6

F-27

109

108_]_

{. ,o+.lo5, Ula'l •

10 4

i °+103 []

j102

101

100

[]

O

I " l I " I " I " I " I

0 1 2 3 4 5 6 7 8

E(MeV)

_ E-8MAX

AE-4MAX

4- Azur

• OVl- 19U

[] OVI-19C


F-28

10 9

108 t

10 7

O

10 6

J4

i 10 5

10 4

10 3

10 2

10 1

10 0

11;

X

i,I"1"

[]

[]

[]

I " I " I " I " I " I l

0 1 2 3 4 5 6 7 8

E(MeV)

[] AE-8MAX

• AE-4MAX

-i- Azur

• OVI- 19U

13 OVl- 19C

X 0V3-3


F-29

1

108_

106

i 105

104,

i 103,

102

10 1

x llqm •

llm"_" m m

x 2 •

=D

° r'l-'ol ,I+

°1-1

[]

100I " I " I " I I " I " I "

0 1 2 3 4 5 6 7 8

E(MeV)

[] AE-8MAX

• AE-4MAX

-I- Azur

• OVI-19U

o OVI-19C

X 0V3-3


F-30

10 7

105,

I 104

103

|10 2

101

100

[]

• I " I " I " I " i " I " l "

0 1 2 3 4 5 6 7 8

[] _-8

• /_-4

• OVI-I9U

O 0VI-19C

x 0V3-3

E(MeV)

Figure 32. Comptflson of AE-8 with Outer Zone Data st L = 6.0

F-31

109

108 1

107

_' 106

i 105

i 10 4

10 3

10 2

101

100

x

13

"?° [] =[_1-1 -I-

AD

[]

• I " I " I I I I I

0 1 2 3 4 5 6 7 8

E(MeV)

[] AE-8

AATS1

• ATS 5/6U

ATS 5/6L

_Azur

OO(301

OOGO3

o OVl-19c

X OV3-3

Figure 33a. Comparison of AE-8 with Some Outer Zone Data at L = 6.6

F-32

1°°1108-1

6

_ lO

105

i 104

103,

i 102

10 1

10 0

=D

IDI IIi • •

° 0 D D

[]

[]0

[]

[]

• I " I " I " I I " I " I

0 1 2 3 4 5 6 7 8

E(MeV)

[] AE-8

0 ERSI3

• ERS17

O Explorer 6

0 Explorer 12

0 Explorer 14

• IMP1

• OVI- 19U

Figure 33b. Comparison of AE-8 with Some Outer Zone Data at L = 6.6

F-33

10 7 []

106

105,

i 10 4

]103

j102

101

10 o

0

r'l

%r'l

[]

[]

[]

-I-1

[]

° []

[]I " I l " I " I " I " I

1 2 3 4 5 6 7

E(MeV)

[] AE-8

• AE-4

Figure 34. Comparison of AE-8 and AE-4 at L = 7.0

F-34

,091108 t

107. _

1°6 []

A

105

lO4

10 3

i102

101

100

%[]

[]

[]

i " I • I " l • I " I • I " I

0 1 2 3 4 5 6 7

E(MeV)

8

[] AE-8

• AE-4


F-35

10 9 ,,

10 8

10 7

_' 10 6 ,

M

10 5

i 104,

10 3 .

10 2

10 1

10 0

0

r_

%[]

@

[]D

[]

1 2 3 4 5 6 7

E{MeV)

8

D AE-8

• AE-4


F-36

109 ,

108_

107!

106

i 105,

104

I 103

Ir

101

10 o

[]

[]

[]

?

• I

0 1

[]

[][]

[][]

[]

I I I " I I " I

2 3 4 5 6 7

E(MeV)

[] AE-8

• AE-4


F-37

109

108

107

"_ 106

105

! ,o,_1_

103,

.lo2 []

101

100

0

[]

[]

I " I " I " I " I " I I

1 2 3 4 5 6 7

E(MeV)

[] AE-8

• AE-4

Figure 38. Comparison of AE-8 and AE-4 at L = 10,0

F-38

10 9

10 8 ,

10 7

10 6

i 10 5

10 4

i 10 3

10 2 ,

10 1

10 0 • I " I " I " I I " l " I

0 1 2 3 4 5 6 7

Z(MeV)

8

[] AE-8

• AE-4


F-39

10 9

10 8 E • 0.04 MeV

i

10 7

10 6

10 5

10 4

10 3

10 2

10 1

4.5O

5.00

0.50

0.I0

10 0

2 3 4 5 6 7 8 9 10 11

L

12

Figure 40. AE-8 MAX Equatorial Radial Profile

F-40

10 9

10 8 ,

_ "'_._..._ [_ [] m c_ [] gg

i_1 -_m10 7

2.o<<.-[ 1.. oO:i ,o_4--.o

®_ "FiFil A

AA A % A

[]10 1 •

[]

A []A

10 0 , • , , , • , • , •1 2 3 4 5 6 7 8

L

[]

®

A

[]

®

[]

I I " I

9 10 11 12

[] O.04Max

0 1.OOMax

A 3.50Max

[] 5.50Max

• O.04Min

• l.OOMin

• 3.50Min

• 5.50Min

Figure 41. AE-8MAX/MIN Comparison at 0.04, 1.00, 3.50, and 5.50 MeV

F-41

10 9

10 8

10 7

_ 10 6

10 5

i 10 4

10 3

04,1

I_ 10 2.

10 1

10 0

0

.,,. []

. []

[] ®

0

• 0

• ¢ %

[]

A

& A0

N "

A• []

& A_ 12 [][] •[]

='_" I I I I I

2 4 6 8 10

L

[]

la

[] O. 10Max

0 1.50Max

A 4.00Max

[] 6.00Max

• O.lOMln

• 1.50Mln

• 4.00Min

• 6.00Mln

12

Figure 42. AE-8MAX/MIN Comparison at 0. I0, 1.50, 4.00, and 6.00 MeV

F-42

10 9

10 8 ,

10 7 .

'_ 10 6 ,

i 105.

104.

I 10 3

i 10 2

10 1

10 0

0

[]

_ BB B B BB

O

®

@

®

®

®

&

&

• & A

• &

%

• Bin I I

2 4

[]

®

[]

[]

I I I

6 8 10 12

L

[] 0.25Max

0 2.00Max

• 4.50Max

[] 6.50Max

• 0.25Min

• 2.00Min

• 4.50Mln

• 6.50Min


F-43

108

107 ,

106 .

i 105.

'_ 10 4 .

10 3

10 2 ,

101

100 ,

0

&&

&

[]

®

[]

[]&

2 4 6 8 10 12

L

I-I 0.50Max

0 2.50Max

A 5.00Max

[] 7.00Max

• 0.50Mln

• 2.50Mln

• 5.00Min

• 7.00Mln


F-44

107

10 6

"_ 105

i 104

i 10 2

10 1

,_," =1

o _./ []

0

0 O. ®

% o.

• ..0

e eq

0

® •

®

@

@

B

®

[]

10 o I I I I I

0 2 4 6 8 10

L

2

[] 0.75Max

0 3.00Max

• 0.75Min

• 3.00Min

Figure 45. AE-8MAX/MIN Comparison at 0.75 and 3.00 MeV

F-45

Date post:	29-Jun-2020
Category:	Documents
Upload:	others
View:	3 times
Download:	0 times

The AE-8 Trapped Electron Model EnvironmentThe AE-8 Trapped Electron Model Environment James I....

Documents