Empirical Solar Proton Model for Orbiting Spacecraft Applications

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I ntroductionEmpirical Solar ProtonModel for OrbitingSpacecraft ApplicationsE.G. STASSINOPOULOSJ. H. KINGNASA-Goddard Space Flight CenterGreenbelt, Md. 20771AbstractAn empirical model for energetic solar proton fluxes is presented.With this model the effects of such protons on geocentric spacemissions, to be flown during the next solar active period(1977-1983), and with orbits involving partial magnetosphericshielding, may be estimated.A synoptic background review is given, followed by a detaileddiscussion of the model's use, errors, uncertainties, and limitations,including sample calculations which demonstrate the application ofspecific or general project missions. Finally, for circular trajectories,percentage exposure maps are presented, depicting fractionalmission times spent outside particular L shells as functions of orbitaltitude and inclination.The distinguishing assumptions of this analysis are: 1) that thesolar proton flux in the 10-100 MeV energy range, as accumulatedover solar cycle 20 due to several discrete events, will beaccumulated at a uniform rate for the seven active years of solarcycle 21; and 2) that all protons in the energy range of interest havea common geomagnetic latitude cutoff.The purpose of this paper is to describe theinterplanetary proton fluxes of solar origin observed at 1A.U. (astronomical unit) between the years 1964 and 1972for integral threshold energies at 10, 30, and 60 MeV, andto introduce a method for obtaining practicalapproximations to these fluxes as a function of energy andtime.In the past, workers in applied study areas, such assatelite design, component development, or missionplanning, often used either estimates of expected energeticsolar proton fluxes derived from cycle 19 groundobservations or used approximations based on fractionalcycle 20 data, usually obtained from a single independentsource without comprehensive temporal or spectralcoverage.The present study proposes a more representativeempirical solar proton model for the energy range10-100 MeV, derived entirely from cycle 20 experimentalmeasurements and based on a uniform, coherent, andhomogeneous treatment of several available data sets. Adescription of its development, from an analysis andevaluation of the data, is given in the following sections.Throughout this work, one overriding considerationprevailed: to produce a versatile, simple, and practicalmodel that would be easy to use while yielding resultswithin acceptable error limits. In view of this scope, somesimplifying assumptions were made along the way to reducethe complexity of the problem.Crude confidence levels, that is, the probability of actualcycle 21 fluxes exceeding the predicted intensities, areincluded in this effort. A formal statistical treatment will befound in [5], where the probability of exceeding givenmission fluence levels is calculated as a function of missionduration and energy.Physical BackgroundA. The MediaManuscript received October 2, 1973.Due to the inability of the solar gravitational field tocontain its extremely hot corona, the coronal plasmaexpands radially away from the sun and draws out thecoronal magnetic field in the process. The resultanttransonic flow is referred to as the solar wind and extendspast the Earth to a distance of several tens of astronomicalunits (1 A.U. = earth-sun separation distance).As the result of diamagnetic effects, the geomagneticfield causes a cavity to be formed in the solar wind.Conversely, the geomagnetic field, which would extend toinfinity in the absence of current systems external to theEarth, is confined to a finite region of space by the solarwind. The geomagnetic cavity in the solar wind, called themagnetosphere, is approximately hemispherical on the dayside of the Earth, with a boundary at about 10 to 12 Earthradii geocentric distance. On the night side, the sweepingaction of the solar wind results in the formation of theIEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL AES-10, NO. 4 JULY 1974442geomagnetic tail, which is approximately cylindrical inshape, antisolar in direction, several hundred Earth radii inlength, and about 40 Earth radii in diameter.The regions of space occupied by the solar wind and bythe Earth's magnetosphere are referred to as interplanetaryand magnetospheric. Cislunar interplanetary space is thatregion of interplanetary space in the immediate vicinity ofthe Earth-moon system.B. The ParticlesInterplanetary energetic particle populations are of twosources, galactic and solar. Galactic particles (as observed incislunar space) have spectra which are peaked in the 0.5 to1.0 GeV range and which vary with an eleven-yearperiodicity corresponding to different levels of modulationby the interplanetary extension of solar magnetic fields. Inthe energy (10-100 MeV) and time (1977-1983) range ofinterest in this paper, yearly averaged galactic fluxes aresmall relative to yearly averaged solar particle fluxes.Galactic particle fluxes are not considered further here, butare discussed in detail by Burrell and Wright [2].Solar particles in the energy regime of interest resultfrom acceleration in solar flares by a process not yet wellunderstood. Particles accelerated in flares include electrons,protons, alpha particles, and heavier nuclei. Fluxes ofheavier nuclei are very small relative to proton fluxes andprobably pose no hazard to space systems. Electrons, dueto their very small masses, likewise cause little damage.Alpha particle fluxes typically amount to 2 to 10 percentof the proton fluxes for similar energies and could, onoccasion, be troublesome. However, due to the diminishedabundance and importance of alpha-particle data relative tothe available proton data, this discussion will be restrictedto solar proton fluxes only.Because propagation of solar protons is controlled bythe plasma and the magnetic fields in the lower corona andin interplanetary space, particle flux profiles observed byinterplanetary spacecraft are often very complex. Typically,particle onset begins several tens of minutes to several hoursafter the parent flare; peak flux usually occurs between twohours and one day after the flare; fluxes usually decay tobackground within a few days to one week after the flare.There is a tendency for particle-producing flares to occur ingroups, so that very often flare-associated fluxenhancements may occur well before the particle flux of aprevious flare has decayed to background, even thoughappreciable time intervals (weeks-months) may occurduring which no solar event is observed.Solar particle fluxes in the magnetosphere are morecomplex than interplanetary fluxes, because the Earth'smagnetic field prevents low-energy solar particles frompenetrating deeply into the magnetosphere, except near themagnetic poles. Thus, protons with energies below a givenvalue are excluded from a shell of dipolar magnetic fieldlines intersecting the northern and southern hemispheresalong a corresponding constant geomagnetic "cutoff'latitude. Only protons with increasingly higher energies areable to penetrate deeper into the magnetosphere and reachcorrespondingly lower magnetic latitudes. To describe theaccess of solar protons to the magnetosphere, thespecification of this cutoff latitude versus proton energy isthen required.For the particles considered in this study, that is,protons in the energy range 10-100 MeV, the cutofflatitudes lie between 60 and 70 degrees. A diurnal variationof 2 to 4 degrees has been observed, presumably associatedwith geomagnetic tail effects and apparently affecting allenergies. Variations of similar or somewhat largeramplitudes also occur in association with geomagneticstorms. The magnitude of such storm-induced changes incutoff latitude varies with each event.Due to these variations and due to the fact that thisanalysis is intended to be used for temporal extrapolationsinto the next solar cycle, which extrapolations have asignificant intrinsic uncertainty, we have chosen to describesolar proton entry into the magnetosphere in terms of ahighly simplified picture. It was assumed that protons of allenergies above 10 MeV have free access to allmagnetospheric regions external to a shell characterized bydipole field lines intersecting the globe at a geomagneticlatitude of 63 degrees, and have no access to the remainderof the magnetosphere. In the magnetic equatorial plane,this corresponds to free access to 5 Earth radii geocentricdistance. Note that this assumption results in a somewhatsofter orbit-integrated spectrum than would be obtainedfrom a' rigidity-dependent cutoff analysis.A good review of magnetospheric cosmic ray cutoffs andtheir variations is given by Lanzerotti [7], while Fanselowand Stone [3], and references therein, present more currentobservational data.C. The ObservationsThe most continuous set of data covering solar protonfluxes during the 20th solar cycle (1964-1975) is thatavailable from the IMP series of spacecraft launched intohighly elliptical geocentric trajectories. These interplanetaryobservations are used to generate a list of peak andevent-integrated fluxes for the major recorded protonevents. From that list, yearly solar proton fluxes are thenobtained, which in turn are used in the ensuing analysis.Events considered include:1) the only significant cycle 20 event that occurredprior to the launch of IMP 32) all events that occurred during the life of IMP 3 (May1965 to May 1967), in which the peak flux ofprotons above 20 MeV was greater than 1(cm2 * sterad * s)-1, according to the Goddard SpaceFlight Center data (as taken from Kinsey [6] )3) all events that occurred during the lives of IMP 4 and5 (May 1967 to December 1972), in which the peakflux of protons above 10 MeV was greater than 25(cm2 - sterad - s)-', according to the data of C.O.Bostrom (Johns Hopkins University, Applied PhysicsSTASSINOPOULOUS/KING: SPACECRAFT PROTON MODEL 443TABLE IIntegrated Proton Fluxes For Large Solar Events, February 1965 Through March 1967TIME PERIODFeb. 5-8, 1965Mar. 23-26, 1966Jul. 7-9, 1966Aug. 28-31, 1966Sep, 2-6, 1966Jan. 28 - Feb. 8, 1967Mar. 12-15, 1967TIME INTEGRATED THRESHOLDFLUX (cm2-ster)lI' ENERGY (WeV)20 x6.1 x3,2 x3,7- x1.4 x3.0 x9.0 x5.5 x4.3 xt - -I10610l1061o51,3 x 1082.0 x 1066.4 x 10'7.6 x 1062,4 x 1072,8 x 1054.1 x 1051015401020102010201020SOURCElvebber, 1966[Lo7OO'Gallagher, 1970 [8]Webber, 1966 [10]Yucker, 1970 [.11]Kinsey, 1969 [61Yucker, 1970 fu.1Kinsey, 1969 f61Yucker, 1970 u117Kinsey, 1969 [67Yucker, 1970 A)7Kinsey, 1969 [6110 Yucker, 1970 [U7120 Kinsey, 196!6720 Paulikas 6 Blake, 1968! ~~~[9]20 iKinsey, 1969 [6720 Paulikas 6 Blake, 1968W~nLaboratory) published monthly by the U.S. NationalOceanic and Atmospheric Administration in Solar-Geophysical Data.Note that the criteria used for selecting events in 2) and3) are mutually consistent for an integral power-law energyspectrum characterized by the exponent -4.65.All fluxes were taken to be isotropic in obtaining this listand in the subsequent analysis. On an event-integratedbasis, departures from isotropy are typically only a fewpercent or less. This applies to the interplanetary mediumand to much of the magnetosphere, but may not apply atlow altitudes where anisotropy should result fromatmospheric loss mechanisms.Table I contains the data for the events that occurredbefore the launch of IMP 4. Table II contains data forevents that occurred after launch of IMP 4. Peak fluxes(Jpk) are taken directly from the Bostrom data published inSolar Geophysical Data (with subtraction of galacticbackground). For the period May 1967 to April 1969,integral fluxes (J) are computed from the best-fitdifferential spectra obtained from Goddard Space FlightCenter (GSFC) (McDonald), University of Chicago(Simpson), Bell Laboratories (Lanzerotti), and JohnsHopkins University, Applied Physics Laboratory(JHU/APL) (Bostrom) data. The fits, themselves, are givenin Table 3 of King's 1972 report [4]. For the period fromNovember 1969 to November 1970, the integral fluxes areas computed from the estimated curves that best fit GSFCand JHU/APL data. For the 1971 to 1972 time period, theintegral fluxes represent JHU/APL data only.From the data in Tables I and II, Fig. 1 was generated. Itillustrates the annual integrated fluxes of protons above 10,30, and 60 MeV for the 1964-1972 time period. It isimmediately apparent that, except for 1970, the annualfluxes were approximately constant over the six-yearinterval 1966-1971. For earlier years, the fluxes arenegligible relative to the active years (and also to thegalactic fluxes). For 1972, owing to the August events, theannual fluxes are significantly larger than those for earlieryears. In fact, the 1972 annual flux of protons above 10MeV is greater by a factor of 2 than the corresponding flux,as summed over 1964 through 1971. At 30 and 60 MeV,this factor is more nearly 4. That such a large portion of thecycle 20 flux should have occurred during only one week ofthe eleven-year cycle dramatically illustrates the difficultyof predicting solar particle fluxes to be encountered duringa planned future mission. This point will subsequently beraised again.Finally, Fig. 1 shows the total proton fluxes above thethree energies, summed over the entire 20th solar cycle, forall major recorded events. It is assumed that contributionsto these fluxes from the remaining years of decliningactivity of this cycle will be negligible.The ModelA. DevelopmentHaving presented the cycle 20 solar proton data in termsof 1) event-integrated fluxes for all major events, 2) yearlyintegrated fluxes, and 3) cycle-integrated fluxes, it remainsto set forth a model which may be used in predicting fluxesto be encountered by space missions of specified durationand trajectory characteristics, to be flown at specifiedphases of the next solar cycle.IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS JULY 1974444TABLE IIPeok and Integrated Proton Fluxes For Large Solar Events, May 1967 Through August 1972TIME>10 MeVP Ji (>10 MeV) c(>30MeV MeV) i Jpk(>60 MeV) Ji(>60 MeV)TIME PERIOD (cm -ster-sec) (cm2-ster)-' (cm -ster-sec)-' (cm2-ster)-l (cm -ster-secV1 (cm2-ster)-1May 25-26, 1967May 28-30, 1967Dec. 3-6, 1967Jun. 9-11, 1968Sep. 28 (hr 12) -Oct. 2, 1968Oct. 4-6, 1968Oct. 31 - Nov. 3, 1968Nov. 18-21, 1968Dec. 4-9. 1968Feb. 25 - Mar, 1, 1969Mar. 30 - Apr. 10, 1969Apr. 12-17, 1969Nov. 2-6, 196931 - Feb. 2, 19706-9, 197029-31, 197023-25, 197014-17, 19705-8, 1970Jan. 24-29, 1971Apr. 6-8, 1971Sep. 1-5, 1971May 28 - June 1, 1972Aug. 4-7 (hr 12), 1972Agu. 7 (hr 12)-9, 1972X 107x 106x 106322710.53.3 x 107 12.4x 10X 107X 107X 1075S0 x 1063.5 x 1061.2 x 1086.9 x 1072. 2 x 1068.0 x 1064.7 x 10'6,5 x 1062.1 x 1077.7 x 1061.2 x 1082,3 x 1063.0 x 1075.5 x 1061.64 x 1091.9 x 108196.310.0 (10/31)11, 7 (11/1)4043141,5 (2/25)9. 3 (2/27)131237376.20.920.20.82.71.74085.01622, 7210003841.7 x 1061.3 x 1064.6 x 1058.9 x 1056.9 x 1052,6 x 1051.2 x 1061.7 x 1073.2 x 1062.1 x 1061.3 x 1061,6 x 1072.1 x 1072.7 x 1051.0 x 10l1,7 x 1065.8 x 1043.9 x 1052.8 x 1052.7 x 1072.0 x 1051.3 x 1075.3 x 1056,2 x 1083.0 x 1072.39,43.85a410.31.11. 4 (10/31)1.1 (11/1)96.05.224,3 (2/25)3. 7 (2/27)8a 716,0201.01.8(NO INCREASE)6,5(NO INCREASE)0.30.489.41.166.51.26400702. 5 x 1044.3 x 1052.5 x 1059.0 x 10143.4 x 1055,0 x 1042,0 x 1056.2 x 1065.6 x 1051, 3 x 1068.1 x 1054,6 x 1069,6 x 1067.3 x 1046.2 x 1039.3 x 1052,9 x 1033, 2 x 1043.5 x 1044.7 x 1062. 7 x 10144.4 x 1061,2 x 1051.9 x 1084. 7 x 106Fig. 1. Annual and cumulative solar cycle 20 proton fluxescliz00trYEARSTASSINOPOULOUS/KING: SPACECRAFT PROTON MODEL4,67.12.23.33,62o 19,02.2101511531,53543236133 (10/31)152 (11/2)84915288 (2/25)28 (2/27)261375131724.293662061834211715135239860003500Jan.Mar.Mar.Jul.Aug.Nov.-.- - -- - . - --445f -V-A7 -~Js(>E09L10'H1l -0 20 40 60 80 100 120 140E ( MevjFig. 2. Cumulative energetic solar proton fluxes for the active phaseof solar cycle 20.In attempting to construct such a model, two importantitems have to be kept in mind. First, there is no assurancethat the overall flux levels observed during the 20th solarcycle will occur during the 21st cycle. Second, there is noreliable way of predicting the distribution of individualsolar events in time, in flux level, and in spectra through the21st cycle.With due consideration to these uncertainties, the solarcycle integrated fluxes in Fig. 1 were then examined to findthe best spectral representation. This turned out to be anexponential in rigidity' representation, specifically:J(>R)= 1.5 X 10 le-RI88 (1)with J in cm 2 and R in Mv. For the convenience of thosereaders who may be more accustomed to energy thanrigidity, the energy-rigidity relationship was used to expressthe solar cycle integrated fluxes asJ(> E)= 1.5 X 101 1 exp [- (E/4)s] (2)where J is in units of cm 2 and E is in MeV. This expressionfor J(> E) is illustrated in Fig. 2, along with the data points.1 Rigidity may be thought of as a measure of the resistance of acharged particle to the bending of its trajectory by a magnetic field.For subrelativistic protons, rigidity R may be related to kineticenergy E by the expression R = 43.3E1 /2, with R in Mv (millionvolts) andE in MeV.Mission Duration (years)Fig. 3. Probability of exceeding solar proton fluxes predicted bythis analysis.This expression is valid over the energy range of thedata, that is, 10-60 MeV; but in the remainder of theanalysis, it will be used with the assumption that its validityextends out to be subrelativistic energy of 100 MeV. It isnot advisable to extrapolate (2) beyond the 10-100 MeVthreshold energy range.For simplicity, it will be assumed that the total 20thcycle fluxes were evenly accumulated over a seven-yearperiod, forming a plateau of constant amplitude extendingfrom 1966 to 1972, henceforth called the "active" years ofthe cycle, without any contributions deriving from theremaining years of decreased activity.Accordingly, one-seventh of the cycle integrated fluxesmay be regarded as an annual mean for its active years. Thisaverage annual intensity may be used to estimate theexpected solar proton fluxes on Earth-orbiting satellitesduring the active years of the next solar cycle.Subsequently, the term "model" or "model flux" shallrefer to this annual mean.As a crude estimate of the confidence one may place insuch a model, note that if the cycle 20 integrated fluxconsisted of 6 arbitrary fluence units contributed by 6equal-amplitude events occurring during a six-yearsolar-active period, this model would predict that futureextramagnetospheric solar-active period missions of 1, 2,and 6 years would encounter 1, 2, and 6 flux units,respectively. However, the statistical analysis of Burrell [11indicates that the probability of exceeding 1, 2, and 6 fluxunits on these missions is 33, 42, and 50 percent,respectively. Thus, one may be more confident in thepresent analysis for shorter missions. Fig. 3 shows theIEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS JULY 1974446.535%1.31 .230%5% 10% 15% 20% 25%10 1I0 30 60 90Inclination (degrees)Fig. 4. Percentage exposure map for circular orbits for particlecutoff latitude of A = 63.40, L = 5 (Earth radii).probability as a continuous function of mission duration. Amore probabilistic analysis of solar cycle 20 fluxes isavailable elsewhere (King [5]).B. ApplicationThe approximate number of solar particles encounteredby a satellite during a given mission depends on the amountof time spent by the spacecraft outside the geomagneticcavity, in cislunar space, plus the amount of time spentwithin the accessible (to these particles) regions of themagnetosphere. The sum of these times determines the trueexposure time, which is a characteristic of that particularmission.The flux encountered by a satellite over its entiremission is then simply the true exposure time, in years,times the model flux given in terms of annual intensity.For most near-Earth space missions, however, it is notnecessary to perform lengthy computer calculationscovering the entire operational lifetime of a satellite toevaluate the exposure factor. Very good approximationscan be obtained from relatively short flight simulations (orreal-flight data considerations). Thus, for circulartrajectories, depending on their altitude and/or inclination,about 15 to 30 revolutions (periods) are sufficient todetermine a fractional exposure time for the mission. Theratio of this time to its interval of evaluation, times themission duration in (years), approximates the true exposure103100% 1%900 30 60Inclination (degrees)90C)2 X1.51.31.2 '1.1Fig. 5. Percentage exposure map for circular orbits for particlecutoff latitude of A = 65.90, L = 6 (Earth radii).time, and the total mission encountered flux is then theproduct of model flux and true exposure time. Ellipticaltrajectories require longer flight time intervals, frequentlyup to several days or weeks, depending on eccentricity,perigee and apogee altitude, and inclination.Since all solar protons in the energy range of interestwere assumed to have one common cutoff latitude, thecharacteristic exposure time of a given trajectory mustconsequently be the same for all energies considered.Hence, the calculated exposure factor may beindiscriminately applied to the entire model spectrum.C. DiscussionExposure MapsFor geocentric missions with circular trajectories,percentage exposure maps were constructed asfunctions of orbit altitude and inclination. These mapsdepict "isopercentage exposure contours," representing as apercentage rate the amount of mission time spent by asatellite in regions of space that are external to given dipolecutoff shells. Figs. 4 through 6 are such geomagneticexposure maps, where the contours were calculated fordipole cutoff shells determined by values of the Mcllwainparameter L equal to 5, 6, and 7 Earth radii; in terms ofinvariant magnetic latitude, these cutoff values correspondto A = 63.4, A = 65.9, and A = 67.8 degrees, respectively.In each case, the region under the zero percent curveencompasses those orbits which are completely inaccessibleSTASSINOPOULOUS/KING: SPACECRAFT PROTON MODEL80X70%60%55%0% 50%45040035030050 20%110% 1 X% 25X1 11 [I ~ ~ ~ ~~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~r10.5.0%3447T-T-V-90Gp0I-9t0 30 60 90Inclination (degrees)Fig. 6. Percentage exposure map for circular orbits for particlecutoff latitude of A = 67.80, L = 7 (Earth radii).to solar particles. On the other hand, the region above thehundred percent contours encompasses those orbits whichexperience no geomagnetic shielding, and for whichunaltered interplanetary conditions prevail. The regionbetween the zero and the hundred percent curvesencompasses the orbits that experience partial geomagneticshielding.As would be expected, the outer boundary lines displayno altitude dependence. Their position, in terms ofgeocentric distance, is determined solely by the associateddipole cutoff shell, and it is equivalent to the correspondingvalue of L.All maps indicate an almost linear dependence ofexposure on inclination at the very low altitudes(h < 1000 km), while, due to the nearly vertical nature ofthe magnetic field lines, exposure is very weakly dependenton height in that domain. Specifically, on the mappertaining to the dipole cutoff shell of L = 5 (Fig. 4), theinaccessible region below 1000 km reaches up to an orbitinclination of about 50 degrees, and thereafter exposureincreases by an average of about 0.75 percent per degree.Consequently, only orbits with tilts greater than 50degrees will encounter solar protons, and only for about 0to 32 percent of their lifetime. Towards polar inclinations,some altitude dependence is evident, with the greatestvariation occurring at i = 90 degrees, where the exposurerises from approximately 26 percent at h = 200 km toapproximately 32 percent at h = 1000 km.L (earth radii)Fig. 7. Cutoff dependence of percent exposure.At very high altitudes (h > 10000 km), the exposurecurves, contained in the envelope formed by the twoboundary contours, converge rapidly towards a focal pointat the equatorial inclinations. The incomplete focusing, thatis, the apparent separation between the boundary contoursat the equator, is a geomagnetic geometry effect resultingfrom the asymmetry of the magnetic field models used andfrom the tilt of the dipole axis to the axis of the Earth'srotation.For h > 1000 km, exposure appears to depend stronglyon both variables, altitude and inclination. Between 10 000km and the outer boundary, the exposure in the range ofi> 60 degrees shows a progressively weaker inclinationdependence, while the contours indicate an almost lineardependence on altitude.The accuracy of the contours is affected by the fieldmodel used in the B - L computation, the orbit-generatingmethod employed, the flight time duration considered, andthe integration step size applied. The uncertainty due to allthese factors is less than 10 percent, which is small relativeto the uncertainty involved in applying this model to futurespace missions.CutoffDependence ofPercent ExposureWhen the orbital parameters of inclination and altitudeare fixed for a circular trajectory, the exposure timebecomes a function of cutoff latitude only. Fig. 7 Indicates,IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS JULY 197444810'Js(>E)(protons)bCM2 )1081 model intensities0 50 100E(Mev)Fig. 8. Annual satellite encountered energetic solar proton fluxes.for specific missions, the percentage of time spent outside agiven L shell. Such curves may be constructed for anydesired mission from the percent exposure maps of Figs. 4through 6.The low-altitude exposure contours for both inclinationsshown display only a very small variability over the range4 < L < 7, that is, about 10 percent or less in the exposurefactor.Through the assignment of cutoff L values to eachparticle energy, one readily determines the percentageexposure time for particles of any given energy. Recall thatthe present model is based upon the assumption that allparticles in the 10 to 100 MeV energy range have acommon L cutoff. However, the reader may use anotherassumption and, with the figures, estimate the (varying)exposure times to particles of differing energies. For furtherdiscussions of the relation between energy and cutoff Lvalue, see Lanzerotti [7] and Fanselow and Stone [3].ResultsTo demonstrate the use of the model, some specificmissions with circular and elliptical trajectories wereselected for solar proton evaluation. The missions relate toactual NASA projects, but calculations are based onprelaunch nominal trajectories. The percent exposure timein each case was obtained by integrating the flight path over24 or 48 hours, for circular or elliptical orbits, respectively.TIhe product for the percent exposure time with themean annual model fluxes represents, then, the "annualencountered solar proton fluence" for these missions. Fig. 8shows the resulting spectral curves for three IUE (SAS-D)trajectories, one SSS, one ANS, two AE (C and D), oneERTS, and one NIMBUS trajectories.No change is expected to appear in the structure of thedifferent spectra because of the energy independent cutoffassumption made in the model for this energy range. Theonly effect of varying percent exposure times is, therefore,a vertical displacement of the curves, without altering theirshapes.References1 ] M.O. Burrell, "The risk of solar proton events to spacemissions," NASA Tech. Note D-6379, June 1971.[2] M.O. Burrell and J.J. Wright, "The estimation of galacticcosmic ray penetration and dose rates," NASA Tech. NoteD-6600, March 1972.[3] J.L. Fanselow and E.C. Stone, J. Geophys. Research, vol. 77,pp. 3999-4009, 1972.STASSINOPOULOUS/KING: SPACECRAFT PROTON MODELSAS-D (IUE) (29 27952-43615 k100%44ERTS (81'/869 km)- 28. 96%NIMBUS(88/llll km)-28.58%AE-C(65/150-4000 km)9.34%I10"lE, 7449[4] J.H. King, "Study of mutual consistency of IMP 4 solarproton data," National Space Science Data Center, Greenbelt,Md., Rept. NSSDC 72-14, October 1972.[51 J.H. King, "Solar proton fluences for 1977-1983 spacemissions," J. Spacecraft and Rockets, vol. 11, pp. 401408,1974.[61 J.H. Kinsey, "A study of low energy cosmic rays at 1 A.U.,"NASA-Goddard SFC, Greenbelt Md., Rept. X-61 1-69-39t,September 1969; also Ph.D. thesis, University of Maryland.[7] L.J. Lanzerotti, Rev. Geophys., vol. 10, pp. 379-392, 1972.[8] J.J. O'Gallagher, "The heliocentric longitude-intensity profileof 15 MeV protons from the 5 February 1965 solar flare," J.Geophyss. Research, vol. 75, p. 1163, 1970.[9] G.A. Paulikas and J.B. Blake,, "Solar proton observations atsynchronous altitude (ATS-1) during 1967," AerospaceCorporation, Rept. TR-0200(4260-20), September 1968.[101 W.R. Webber, "An evaluation of solar cosmic rays eventsduring solar minimum," Boeing Rept. D2-84274-1, June1966.[111 W.R. Yucker, "Statistical analysis of solar cosmic ray protonfluence," McDonnell-Douglas MDAC, Paper WD-1320, June1970.E.G. Stassinopoulos was born in Bonn, Germany, in 1921. He graduated from theExperimental College of Athens University, Athens, Greece, in 1942, where hesubsequently studied law and economics, from 1951 to 1954. He received the B.A. degreein mathematics from American University, Washington D.C., in 1961. He has alsocompleted graduate studies in physics at American and Catholic Universities, washington,D.C.From 1946 to 1950 he served in the Royal Hellenic Army Signal Corps, where histraining included electrical engineering, communication theory, and cryptography. He hasalso been a Graduate Research Assistant for Computer Science at the Electronic DataProcessing Laboratory, Center of Technology and Administration, American University.Since 1961 he has been with NASA-Goddard Space Flight Center, Greenbelt, Md., wherehe has worked on application-oriented problems in the areas of magnetospheric physics,geomagnetism, and space radiation. Since 1971 he has been with the Goddard SFCNational Space Science Data Center as an Acquisition Scientist for the Field and ParticlesGroup of the Data Acquisition and Analysis Branch. His current interests focus onsolar-terrestrial physics, with special emphasis on field interactions of internal-externalorigin. He has published over 35 technical papers and is now writing a handbook onorbital space radiation.Mr. Stassinopoulos is a member of the American Geophysical Union, Pi Mu Epsilon,and the Philosophical Society of Washington.Joseph H. King was born in Malden, Mass., in 1939. He received the B.S. degree in physicsin 1961 and the Ph.D. degree in space physics in 1966 from Boston College, Boston,Mass.He has been a member of the Technical Staff of the Aerospace Corporation and aNational Academy of Science/National Research Council Postdoctoral Research Associateat NASA-Goddard Space Flight Center, Greenbelt, Md. Since 1969 he has been with theGoddard SFC National Space Science Data Center as Group Head for Particles and Fieldswithin the Data Acquisition and Analysis Branch. His areas of interest include galacticand solar cosmic rays and interplanetary magnetic fields, as well as information systemsdesign.Dr. King is a member of the American Geophysical Union.IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS JULY 1974450