Empirical Solar Proton Model for Orbiting Spacecraft Applications

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    Empirical Solar ProtonModel for OrbitingSpacecraft ApplicationsE.G. STASSINOPOULOSJ. H. KINGNASA-Goddard Space Flight CenterGreenbelt, Md. 20771

    Abstract

    An empirical model for energetic solar proton fluxes is presented.

    With this model the effects of such protons on geocentric space

    missions, 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 detailed

    discussion of the model's use, errors, uncertainties, and limitations,

    including sample calculations which demonstrate the application of

    specific or general project missions. Finally, for circular trajectories,

    percentage exposure maps are presented, depicting fractional

    mission times spent outside particular L shells as functions of orbit

    altitude and inclination.

    The distinguishing assumptions of this analysis are: 1) that the

    solar proton flux in the 10-100 MeV energy range, as accumulated

    over solar cycle 20 due to several discrete events, will be

    accumulated at a uniform rate for the seven active years of solar

    cycle 21; and 2) that all protons in the energy range of interest have

    a 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 Background

    A. The Media

    Manuscript 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 the

    IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL AES-10, NO. 4 JULY 1974442

  • geomagnetic 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 Particles

    Interplanetary 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 are

    able 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 and

    their variations is given by Lanzerotti [7], while Fanselowand Stone [3], and references therein, present more currentobservational data.

    C. The Observations

    The 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 3

    2) 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 I

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