A Model of the Near-Earth P!Ssma Environment and I Application To

(NAS_-TM-Z-'72611) & _ODT.L C1_ THE NE_-]_B_E N77-32661 PLAS_ E_VI_C_ AN£ _LICATION TO THE ISEE-A AND-E ORBIT (NASA) 5£ p HC AOW/Z_ A01 CSC/ 04A Onclas . G3/46 48631

A Model of the Near-Earth P!ssma Environment

and i Application to the ISEE-Aand -B Orbit

• NSSI)C/WI)C=A=R&S 77=01

A Model of the Near=Earth Plasma Environment and ,] J Application to the ISEE-A and -B Orbit

King W. Chan Donald M. Sawyer James I. Vette

July 1977

National Space Science l}ata Center National Aeronautics and Space Administration C;oddard .Space Flight Center Greenbelt) Maryland 20771 ! I I 1

CONTI!NTS

I I NTRODUCTI ON 1 • eeooeeeeoo oooooeoeee eoooeeeooeeooae e oe oe i II. TIIE SPATIAL STRUCTURE FOR 'rite NEAR-EARTII

PLASblA ENVIRONMENT ...... 3 _i

III. I)I!RIVATION OF COMPOSITE SPECTRA ...... 4 dt • he The Interplanetary Medium oo o&oo Qo oo oeoe • odJ o ooooo 4 ! B. The blagnetosheath ...... 6 t C. The Inner Magnetosphere ...... 8 D. The Plasma Sheet ...... 11 E. The High-Latitude Magnetotail ...... 12 F. A Summary of the Composite Proton and I Electron Spectra ...... 13 I

IV. TIlE ISEE-A/-B ORBIT ...... 14 i

V. TIlE APPLICATION OF TtlE ENVIRONMENT TO TIlE ISEE-A/-B ORBIT ...... 15

APPENDIXES

Appendix

A. The Conversion from Fluid Parameters to Energy Spectra ...... 17 B. The Derivation of a Time-Averaged, Solar Wind Proton Spectrum ...... 21 C. The Derivation of a Spin-Averaged, Solar Wind Proton Spectrum ...... 23 D. _le Derivation of a Spin-Averaged, Magneto- sheath Proton Spectrum Using a K-Distri- bution Function ...... 26

TABLES

_ Tab 1e ]..

ment for lligh-Altitude Satellites ...... 28 2. [Slili-A/-B Orbit-Averaged Spectra ...... 29 3. Proton Solar Wind i'arameter Relationships ...... 30 f. 1. Spatial Regions of the Near-l!arth Envi.:'on- I I I- ) 1 I I 1 I ; I ' , _"_ , ' _ "'

i I,LUSTRATIONS

Fisure Page

1. ISI'I!=A/-B Orbit Rotated into the GSE I X-Y Plane ...... 31 2. Interplanetary Electron Spectra ...... 32 . 3. Interplanetary Proton Spectra ...... 33 4. _lagnetosheath Electron Spectra ...... 34 5. Magnetosheath Proton Spectra ...... 35 ._ 6. Magnetosheath Proton Spectra Compared _'ith Spin-Averaged Spectra ...... 36 7. Inner Magnetosphere Electron Spectra ...... 37 8. inner _lagnetospt-ere Proton Spectra ...... 38 9. Plasma Sheet Proton Spectra ...... 39 10. Plasma Sheet Electron Spectra ...... 40 11. lligh-Latitude Magnetotail Spectra ...... 41 12. Composite Proton Spectra ...... 42 13. Composite Electron Spectra ...... 43 14. ISEE=A/=B Orbital Coverage (period -2.3 days) ...... 44 15. ISEE=A/=B Orbit-Averaged Proton Spectra (revolutions 1-76) ...... 45 16. ISEE=A/=B Orbit-Averaged Flectron Spectra "I (revolutions 1-76) ...... 46 ! 17. ISEE=A/-B Orbit-Averaged Differential 4 Spectra (revolutions 1-76) ...... 47 1 18. ISEE-A/-B Orbit-Averaged Integral Spectra l for E < 10 s eV (revolutions 1-76) ...... 48 19. Spin-Averaging Geometry for Area Flux Computations ...... 49

lIE FI._ RENC ES ...... SO

i V _ J • _s • i I _ I

I . I N'I'P,OI)UffI'I0I_

The purl)ose of this report is to present a model of the near-Earth environment and use it to obtain a best estimate of the average flux of protons and electrons in the energy range from 0.1 to 100 keY for the International Sun-Earth Explorer (ISEE)-A mid -B spacecraft. This report is the result of a study initiated by a concern for the possible radiation damage to the thermal coati_,.; on these spinning spacecraft, both of which will be placed in a geocentric orbit with initial apogee . of 21 RE, perigee of 280 km, and inclination of 28.5 °. Applications of the model to other high-altitude satellites can be obtained with the appropriate orbit averaging.

To the best of our knowledge, this is the first attempt to synthe- size an overall quantitative environment of low-energy particles for high- altitude spacecraft, using data from in situ measurements. In formulat- ing model environments of the more energetic (_ 100 keY) particles trap- pod in the radiation belts of the Earth (e.g., Scrtogm* and Yet.t.c, 197o), the spatial cells used are small volumes of the tubes of force formed by the geomagnetic field, llowever, the general morphology of the near-Earth plasma dictates a much grosser spatial structure in which the average particle fluxes need to be obtained. The appropriate spatial regions for the plasma environment consist of various parts of the magnetosphere and the interplanetary medium in which the character of the low-energy particles and the magnetic field have provided a natural identification. Within these regions, there are large spatial and temporal variations.

The five spatial regions (interplanetary medimn, magnetosheath, plasma sheet, high-latitude magnetotail, and inner magnetosphere) have been chosen as the spatial structure for the present study. Since the real geometries of these regions do vary with time, model boundaries for the regions must be used; then, the average character of the fluxes uith- in each region must be ascertained. In the application of this environment, the final objective is to derive an orbit-averaged, differential energy, spin-averaged spectra for protons and electrons. To obtain the best available environment, all quantitative high-altitude satellite measurements published in the literature have been considered, regardless of the energy or angular resolution of the instrument, llata from low- altitude, polar-orbiting spacecraft have not been included. Public"tie/Is of qualitative data will be referenced to confirm the trend of the quan- titat;,,' results. Only fluxes that are long-term or reported :m typical will be included, b;hort-term, transient phenomemt will generally be ne- glected, unless thcy make an obvious and significant contribution to the average environmt, tlt. No attempt wit1 be made to give a comprehensive review of tiw physics associated with thcse low-cn,.'rl..y particles.

• Tht' basic approach employed in the derivation ()f the orbit-;ivt,raged spectra is divided into two ._teps. In the first :_tcl) , p_ll_lishcd spectra

• I • I -- 7 belonging to each of the five regions are compiled, and a composite spectrum representing the environment of that region is constructed. In eases where there are substantial differences in data from several measurements, spectra of a high estimate, as well a:; a low estimate, are de- termined. The details will be given in Section III. In the second step, the composite spectra of each region are weighted according to the fraction of the orbital tilaethe spacecraft is located in the corresponding q region. As the orbits process about the north ecliptic pole, the weight- i ing factor of each region changes. The details of the second step, using • the first 6 months of the planned ISEE-A/-B orbit, will be described in Section IV.

To date, the abundance of the published data and the completeness of documentation for various regions cannot be viewed with the same standard• Because of the nature of the plasma characteristics, and perhaps because of the focus of interest in the scientific community, the solar wind in the interplanetary medium is the best documented region, while the magnetosheath has comparatively few publications with quantitative data in absolute flux units. Accordingly, the resultant spectra of one region may have an uncertainty factor quite different from that of the spectra of other regions.

,_s previously noted, the particle properties are distinctively different in the various spatial regions. Often, it is necessary to use simplifying assumptions to derive representative spectra for a particular region. The data on the solar wind proton bulk flow, for example, re- quire the computation of time- and spin-averaged fluxes. Details of the mathematics will be given in the Appendixes.

E II. TIIE SI'ATIAL STRUCTURE FOR Till! NI!AR-EARTII PLASMA ENVII_ONMENT

_ For the purpose of flux averaging along a given orbit, it is essen- , tial to identify the positions of the spacecraft with respect to those regions of the near-Earth environment that have distinctively different particle populations. The International Magnetospheric StudySatellite Situation Center (IMS/SSC) has developed a computer program that can merge a model configuration of the magnetosphere with the ephemeris of an Earth-orbiting satellite (Vet%e e% aZ., 1976). This program has direct application in,_he.-present study.

In a report presented at the 10th ESLAB Symposium, (Vette et aZ., ! 1976), eight regions of the near-Earth space were defined by the simple boundaries that are listed in Table i. Fairfield's model (Fairf_eZd, 1971) was used for the boundary locations of the bow shock and the r ag- netopause. Some of these regions are illustrated in Figure I. This classification of space is intended to provide a general frame of positions for the study of particles and fields in the I_,LS.

Because of the lack of sufficient low-energy particle data to estab- lish distinctively different statistics for a local time effect in the magnetosheath and the inner magnetosphere, the further separation of these two regions into dayside and nightside regions has been eliminated in the present study, l,'urthermore, the midlatitude magnetotail and the neutral sheet have been combined and named the plasma sheet, which is a popular term in the literature for the ]ow-energy particles found in this region. As a result of this slight modification, only five regions as defined in Table I have been used; the previously noted IMS/SSC computer program is still applicable without change. I 1

III. DERIVATION OF (:OHPOSITE SI'ECFIO_

A. The Interplanetary Hcdium

The low-energy particle environment in the interplanetary medium

near the Earth is dominated by the "quiet" solar wind. Sillce most of I the solar wind obserwttions found in the literature are described in ] • terms of fluid parameters (temperature, density, and bulk flow speed), I they must be converted to a differential energy flux; the method is given in Appendix A. Short-term variations in the interplanetary fluxes can be associated with transient solar activity. These include flare particle events, fluxes associeted witl,, active regions, and interplanetary shock- associated spikes (for a review, see Lin, 1974b). Shock-associated spikes, with a duration on the order of minutes, will not appreciably affect the average environment and are not considered in this study. The presence of the Earth and its magnetosphere can also add to the near-Earth, interplanetary environment through reflection and emission of particles at the bow shock (Asbrid_e et al., 1968; Frank, 1970b; Lin et al., 1974). i

The directionality of the various interplanetary fluxes varies widely and must be taken into account in the construction of a useful composite spectrum. The electron and proton components of the "quiet" solar wind are distinctly different in this regard, l'or the electron flux, the nearly isotropie thermal component of velocity is large compared with the bulk flo,q component that is commonly referred to as the solar wind velocity. For protons, the opposite situation is obtained in that the thermal component is small compared to the bulk flow coT,_ponent. 3_ms, the electrons in the solar wind are essentially isotropic, while the protons are highly anisotropi¢. (For reviews, see Mont_jomery,1972; Wolfe, 1972.) Typi- cally, the protons arrive within a cone of 20 ° , centered along the bulk flow direction (Hundhausen et al., 1967). In addition, the magnitude of the bulk flow speed varies within the approximate range of 250 to 700 km/s. To compare this flux with that from other regions of space where fluxes are more nearly isotropic, a time- and spin-averaged, solar wind proton flux is constructed. 'Ill is approach will bc discussed more fully in the following paragraphs, l)etails are given in Appendixes B and (1.

A typical low-cnergy, solar wind electron spectrum, with a density equal to 9 cm"3 and a temperature equal to 1.S x l0 s K, is shown in Izigure 2 (Mo_ltJomc'r U _:b _ZZ., 1908: ;lont:/omcrL t, !972). Also shown is a portion of the quiet-time composite spectrum (Lin c't al.., 1972), whicl, extends over 12 decades of flux for energies up to 100 keV. lIll' (_ ol_scrvations during a "quiet" period and during an anisotropic flare packet (/.'n,wzk a_z,/ Gzo_tet.t, 19721) are also shown. The remaining spectra from O(;0 5 (():{[/,,i,' ,'/: a7,., 1971), IHl' ,! and IHI' o (l¢,vz:! .'t a/,., 1971), Apollo 15 subs;ntellitc (Lz:_2, 1974a), and the ,.\l)ollo 1(, subsatcllitc (L,_n ,_{ ,_/., 1973a) _'cT'¢>all obtained during wlrious flare cvcnts. These events have I)cc_ ol,:;crved for ent, rgies as low as 1 kc'V.

4 / ¢ " . 3' I II ("' bo

From thin coml_:ilation of spectra, a representative i.sotropic composite spectrum lms been cons.tructed and is also shown in Figure 2, Without a statistkcal study of tile flare spectra at energies above 1 keV, :it is j difficult to determine their contribution to the average environment. llowever, by extending the quiet-time obserwltion of IMP (_ (Prank and auvne_t, 1972) to higher energies, a reasonable estimate of the flare contribut:ions to the quiet-time composite of L-;n e_ aZ. (1972) is obtained. The IMP 6 spectrum at lower energies joins smoothly with the Lin composite spectrum; and, therefore, they are used as the basis for the isotropic composite spectrum below 1 keV. Also shown is a spectrum representing the maximum anisotropic flare fluxes observed.

An interplanetary medium, quiet-time proton spectrum for energies ,! above 38 keY is shown in Figure 3 (Len e_ aZ., 1973b). Also shown is a ] derived, interplanetary medium, average proton spectrum based on enhanced fluxes associated with solar active regions and flares. This spectrum is ] three orders of magnitude below the IMP 6 proton fluxes seen propagating upstream from the bow shock with energies above 30 keY (LC.n et aZ., 1974). These IMP 6 protons are observed when the spacecraft is on an in:erplan- etary magnetic field line that intersects the bow shock. In the energy range from 6 to 40 l.eV, IMP 4 has observed transient events, which Prank (1970b) has •identified as magnetic storm-associated fluxes. 1hey were quasi-isotropic in the ecliptic plane but favored intensities arriving from the solar direction by factors of two to three. A nonstorm upper limit from IMP 4 for energies in the range of 11 to 18 key is also shown t in Figure 3. Protons propagating out from the bow shock along interplan- "t etary field lines have been observed by INI' 4 (Frank, 1970b). These ! particles, shown in Figure 3, are quasi-isotropic over a hemisphere look- i ing toward the bow shock and have energies in the range 0.2 to 4 keY. , llowever, for energies below about 4 key and looking in the solar direc- .] tion, the solar wind dominates. 1

The proton component of the solar wind can be characterized as a ]

highly anisotropic beam of particles with a narrow energy spread. The 1 peak flux occurs at an energy close to that given by a proton moving 1 i with the bulk solar wind speed. Two examples of instantaneous solar wind i I proton spectra, corresponding to bulk speeds of 300 and 700 kin/s, are ] shown ill Figure 3. Over a period of time, the solar _¢ind speed ranges t' between 250 and 700 km/s. Derived density and temperature parameters are _ found to correlate with the solar wind speed (for a review, see l¢oZj'e, t 1972)o Using obserwttions from Vela 3A and 3B obtained during the period July 19t_S to November 1907 (llu_zdhau_c;_t ek a/.., 1970), it :is possible to i derive a time-averaged, solar wind ';pectrum. This spectrLun is shown in Figure 3, and additional details of thc derivation are given in Appendix i B. Although this spectrum is derived using a distribution for solar wind i speeds obtained near solar minimmn and durinp a risinp portion of the l solar cycle, distributions obtained during other pha:;e:s of the solar cycle , are only expected to chanpe the aver;_l,e spectr,un sli_,htly. The highly ;mi sotropi c nature of thi s spc'ct ruln makes i t d J t'fi cult to comp;trc with the otlLer, mm'e isotropic fluxes. '1'o re:;olve this difficulty, an effective spin-averal.ed, isotropic :;pc'ctrtml lms lu,cn generated aml is ..;lun_'n "1 5 :in Figure 3. All area that is oriented perpendicular to the ecliptic plane and spinning about an axis that it also perpendicular to the ecliptic plane, will receive the same average flux from this spectrum as it would from the anisotropic, time-averaged, solar wind spectrum. The derivation of this spin-averaged spectrum is given in Appendix C. Similarly, a spin- averaged, bow shock spectrum has been constructed by smoothly joining the two bow shock-related spectra and then dividing the flux by two to account for the quasi-isotropic nature of these fluxes over one hemisphere. The resulting spin-averaged, bow shock spectrum is shown ill Figure 3.

A composite proton spectrum for the interplanetary medium near the ]i, Earth now can be constructed by adding together the spin-averaged, solar j wind and bow shock proton spectra. This spectrum, shown in Figure 3, is isotropic and simulates the effect of the observed anisotropic spectra on a plane area that is spinning as previously described. This is approximately the geometry for a unit area on the side of the spinning ISEE-A/-B spacecraft.

B. The Magnetosheath

The magnetosheath is the region between the bow shock and the magnetopause as shown in Figure 1. The bow shock is the boundary defined ob- servationally by the abrupt changes that occur in the characteristics of the plasma and the magnetic field (Mont_domery et aZ., 1970). The magne- j topause is the boundary formed by the geomagnetic field as a standoff limit to the solar wind plasma from the interplanetary medium.

In the magnetosheath, the post-shock plasma from the solar wind flows around the magnetosphere and is usually turbulent (itundYzausen et al., 1969; Scudder et al., 1973). For the low-energy particles in this region, the presentations of information in the literature are generally divided into two groups: (1) in the form of differential spectra constructed directly from the observed fluxes (e.g., Frank, 1970a; Rosenbauer et aZ., 1975); and (2) in terms of particle distribution functions and moments expressed as conventional fluid parameters that are also derived from the observed fluxes (e.g., Itundhausen, 1970). When awfilable, data obtained in absolute flux units will be used for analysis.

Figure 4 shows tile electron spectra measured by the Veli! 4B, IMP S, and Apollo 14 spacecraft with the source publication listed in the figure legend. '['he Apollo 14 data are given to shou that the electron spectra in the distant magnetosheath (~_,0 RI!) are similar to those observed by Vela 4B at about 18 Rli.

Because of tile lack of comparable statistical information almut these measurements, there it no simple way that the wu'ious spectra can be prop- erlg weighted to construct a single, smooth spectrum. For the present purpose o_ making a crude, quantitative projection of the enviromr, ent, an

() e _ " J I I I i i II b,

upper-1)ound and a lowe, r-1)ound envelopo aro constrtmted a,'; the COmlm_;ite spectra for ;t high and low e._itimate. As shm_; by tile dashed lines in Figure 4, the COml)o:iite spectra are generally l)ronder th;m any of the individual, measured spectra. (liven the uncertainty as rel)re:;ented I)y the ranl, e or variations :in the e:;timates, the coml)os.ite spectra Call be regarded Its representing the long-term, average fluxes ill the re_.ion. t

As is the case for electrons in tim interplanetary ]lledh|ln, the an_;,u- lar distribution of the magnetosheath electron fluxes shows re1 :tively little variation (witMn a factor of two) with respect to the bulk flow /i • direction (?4on_gomez,y e.t. ,z/..., 19701. Therefore, no spin averag:ing is needed for the present flux estimates.

Figure 5 shows the magnetosheath l)roton spectra observed by tile IIEOS 1, IIEOS 2, IblP 4, and Ibll' 5 satellites. For the low-energy protons in this rogion, tile bulk flow velocity is a major contributing factor ill the observed kinetic energies of the particles (llundhca_senel;aZ., 1969). The proton flux, therefore, is highly anisotropic with the peak flux in tile direction of the bulk flow as shown by the IIEOS 2 measurements at three azimuthal angles in leigure 5. llowever, in comparison with tile protons in the interplanetary medium discussed previously, tile Irrotons in the magnetosheath generally }lave a lower bulk flow speed and a higher mean thermal velocity. Consequently, the angular distribution of tile low-energy protons [s less anisotropic i.n tim magnetosheath than ill the interplanetary lnedium. In addition, proton spectra in tim magnetosheath show considerably "I more deviation from a blaxwell-Boltznlann distribution than in the case of 1

tile interplanetary medium (t"o_,m-:.mz_zv el; aZ., 1973). J i A. ,roviously described for the case of electron spectra in the mag- netosheatn, an ul)per-bound and a lower-bound envelope are constracted to serve as composite spectra representing a high estimate and a low estimate in the presumed flow direction. Because the composite spectra are generally broader than any of the individual, observed spectra, the result of the estimated flux, when integrated over all energies, will be conser- vatively higher than tile average situation, llowever, the differential i flux from the composite Sl)ectrun_ at a given energy wi.ll prolmbly be comparable to the average measurement within tile range of uncertainty as indicated by the high and low estimates.

In order to calculate the averaped proton fluxes received by a unit ] ar_a of a spinning surface with the spin axis perpendicular to the eclip- * tic plane, both tile flow component as well as the' thermal component of tile particle w'locity must l)e considered in the {tll_tllllr inte!lration and the sl)in-averagin ? l)r_)cesses. In practice, as described in det_lil ill Al)pendix I), it is coltvenient to ,mkt, the c;llcul;ttion ttsilU,, an analytic d i s tr ibut i on t'unct i on t ha t t'i 1s t lie EOIII])OSi t e spectra.

Ill _.tall('r;ll , lhc K-distril)ul ion t'ultcl:ioll with K := 2 (l",,_'_'l/';:,m. ,I ,zl., 1(.173) is t!ouml to _;ivt, a rt'a!;()l:;ll)le rit to a t),l)ic;ll, ob.'sL,rvvd pl'OIoll .4

r. 7 ¢ .- I i I I I I- J I ' I i "' "'

spectrum ill the magnetosheath. In the pre,Jent ,'umly._;is, the COmlm._;ite proton spectra of the magneto:;heath can b,.: well al)proximated I)y the K- ] distribution with a bulk flow speed of 230 kr,l/:;, therm:ll energy (kT) of 400 eV, and a density of either 17 cm'a, - or 2 em"a for the high and low estimates, resl)ectively.

The results of the calculation (se, z Apl_endix 1) for details) are presented in Figure 0. The effective isotropic spectra showll [11 the figure give the equivalent isotropic environment that the previously specified surface area will encounter in orbit. They can be used to compnre with other isotropic spectra for the purpose of making flux estimates on this area, but they cannot be used for other purposes such as calculating an omnidirectional flux. A procedure for correctly deriving an omn:idi- rectional flux spectrum is included in Appendix D.

C. The Inner Magnetosphere ! The inner magnetosphere, shown as region C in Figure 1, is composed of the entire dayside magnetosphere and that part of the nightside magnetosphere where the absolute value of the X-coordinate is less than 10 RI! in the geocentric solar ecliptic (GSI?) coordinate system. A further restriction for this study is the consideration of only near-equatorial latitudes. This large, asymmetric volmne, which includes the inner and outer radiation belts, is kllown to contain a sea of protons and electrons J, with energies in the range 100 eV to 50 key (cf., Vasuliunas, 1972). Observations of the elect_ons are considerably more complete than those i of the protons, but even they are lacking in spectral, temporal, and spatial coverage. This is in part a result of background problems, some of which arise from the presence of higher energy particles and solar ultra- violet radiation (arlnuauz, 1969), and some not yet clearly identified (Lyons and Williams, 1976). Nevertheless, the general picture for elec- l trons is one of considerable spatial structure and temporal variation in l the flux of this region. (For reviews, see (,r_l(la" T_,_, " 1969; VcwuZi_ola_, i i 1972.) 1! It is more difficult to characterize the proton population in the t inner magnetosphere since there are few observations covering the more ] distant parts of the dayside region beyond an I,(McIlwain parameter) of 1 about 7. O(10 3 observations (/,'rank and _en_, 1970) have provided a survey of low-energy protons in the evening to midnight quadrant. (For '_ reviews, see /"rank, 1970; V,:u:Ul{un,u;, 1972.) l'rotons in the plasma sheet continue across the inner boundary of tile plasma sheet up to tile plasmasphere. The evening plasma sheet boundary, as identified in the electron flux, is not observable in the proton I'lux. These protons ;,re most intense in the evening sector, form inp tile qLrict-t i,lc, proton ring current centered near 1, = (_.5. I)lu'ing :_torms, the intensity of these I:rotons greatly increascs, forming the storm-time ring ctlrrent (of., /.Ill(l}/,:9 19u71,).

[ s . _' I II fl I I ' m,

In addition, tile dayside mat_netosl)hure boundary (magnetol)au:;e) ha,i been el)served to contract s.ignificantly inward dm'inp large geomagnet:ic storms. The _,reatest observed contraction to date WI|.._associa.ted with the :;term of August 2, 1972, when the magnetopause was reported to be inside the l!xplorer 45 satell.ite po,;it:ion ;,t I, = .5.2 (lied'f man ct aZ., 1!)75). The effects of such a contraction on the lmrticles normally re- siding outside the synchronous orbit (I, ~ 6•(}) have not yet been observed but are certainly significant.

Vaspliunas (1972) has described the spatial structure of the electron it fluxes with energies from 100 eV to a few kcV. These electrons are found '1 • within the equatorial region of the magnetotail, where they form the plasma sheet. These intense fluxes te_nninate abruptly where they define the inner boundary of the plasma sheet in the evening side of the magnetosphere. This occurs at about 11 RE during "quiet" times, l_lis boundary approaches the plasmasphere (~6 RE) l_ear the midnight meridian. Noving !

finally,from eveningintersectsto earlierthe, magnetopauselocal times, nearthis noon.boundary Weakremainselectronat ~11fluxesRE and,are l observed between the plasma sheet and the plasmasphere in the evening sector. They are observed to be an order of magnitude or more below those in the plasma sheet at a few key (Schicld and Frank, 1970). They grow stronger as one moves to earlier, locaI times and expand in spatial extent until they fill the entire region between the magnetopause and the plasmapause near noon. In the morning sector, the fluxes show a strong radial gradient, ihcreasing toward the magnetopause. In the predawn hours, the fluxes become very intense mid exte"d all the way from the magnetopause in to the plasmapause. At these local times, they are an order of magnitude larger than at other local times. These fluxes must then decrease as one moves toward mianight so as to merge with the plasma sheet. During substorms, the plasma sheet boundary moves toward the Earth in the evening sector. It is, therefore, apparent that the innei" magnetosphere will also contain appreciable plasma sheet electrons that must be included in the generation of a composite electron spectrum for this region•

Figure 7 is a representative compilation of the differential electron spectra available in the. l[ter:tture. 0(;0 1 (VaruZiunag , 1968) and OGO 3 (Frank, 1907c; Sc.hie/d and l,'P,znk, 1970) spectra were ol)tained in the evening and midnight s_,ctors, r.?spectively. 'Ii_e Ot;O 3 spectra in the plasma sheet at L = 9.8 and in the edge of the plasma sheet at 1, = 9.25 are more than an order of magnitude higher than the electron trough spectrum at L = 8.8 for energies of a few keY. At h = 5.3 (in the plasmasphere) and at l, = 3.9, the :qmctra arc between those at l, = 8.8 and I, = 9.8 for energies of a few keY. At the lower energies, they continue to rise, while the plasma stleet spectra appe;Lr to fall. The O¢;O 1 spectrum was obtained during a substorm and shows tile typical pl_,sma simet SlmCtrum extending over the evening re_i,,,u frum 7 to ll Rli. At this time, the S-RE sI)ectrum has the al:l, earance of the 0(;()3 trough spectrum. The llmvk- eye 1 spectrum at I, = 5.8 ((he,neLl, ,t_t(L I,'mmJ:, 197(_) and the I!lectron 2 slu, c_rum at 1, = 8 (V_,_,,_,,z_,,1, ,zZ., 19oo) h'L're both oldaincd in thc' mornilD, :_eetor and are con._i..,_tent with the rad.ial gradient prev.iou:;ly d:i_cus._ed. In association with a large m;u,netic disturbance, the llawkeye 1 :_pectrum was ol_served to be an order ot! nl_gnitade larger than the more typical sl_ectram .M_own .in Fi.gure 7. The lixplorer 45 spectrmu at l, = 5.2 (]4tent; and I./l_ZZ'[.:um:, 1!175) and tile ATS 5 spectrum at 1, "-- (_.(_ were o_served in the evelling sector. These spectra were about an order of magnitude below the {'GO 3 spectrum at l, = 5.3. At lt) keV, the ATS 5 sl,ectrum (lhv'.["_cl.d c# a_. 13,7) is more than a factor of SO below the other spectra. Dur- ing a substorm, the ATS 5 spectrum increased two orders of magnitude for I'. energies in the range of 10 to 20 kcV. These dit'ferencos are indicative of the spatial and temporal variations that can occur. !

The average outer zone integral electron spectrtu|_ from the AE-4 model (ool..n£t,._oy and Vette, 1972) for L in the range 6 to 8, has been dif- ferentiated and included to show the trend above 50 keV. The corresponding spectrum for L = 10 wo'.,ld be about an order of magnitude lower at these energies.

From this compilation of spectra, a single composite spectrum to represent this region has been constructed and is shown in Figure 7. At energies above i0 keV, this spectrum is constructed to lie above most of the observations and still be within a factor of two or three of an average of the observations. At energies between 1 and I0 keV, this spectrum is constructed to represent an average between the intense fluxes en- countered in the plasma sheet and predawn hours and the much lower fluxes observed in the electron trough region for late afternoon and evening hours. At energies below 1 keY, this spectrum is constructed to reflect the rising trend of the OGO 3 data at L = 3.9, 5.3, and 8.8. Although the plasma sheet spectra appear to be falling a_ these energies, the lack of sufficient local time coverage requires a more conservative approach :in this energy range. This composite spectrum can be assumed to be isotropic for the purposes of radiation damage studies. The error associated with this approximation is small compared to the uncertainties assoc- Lated with the spatial and temporal wlriations, i

Figure 8 is a representative compilation of the differential proton spectra awdlable in the literature. All spectra were obta:ined in the early evening to midnight quadrant, except for the synchronous 0V2-5 spectrum (S'_cven_ c k aZ., 19711) obtained at noon with I, ,_ 0.(,. The corresponding midnight spectrum at synchronous altitude was about a factor of four lower for energies in tile Or) to 100 keV range. The eGO 5 obserwttions at L = 3.9, (_, and 11.8 (/,'vcml', 19(_7c) can be associated with the plasmasphere, ring currcnt and plasma sheet, respectively, dm'i|U' "quiet" times. The et'fect of a geonlagnetic storm on the O(]O 3 obserw_tions at 1, = 4, b, and 7.1 is also shown. 'the increased flux at l, = 4 in the 10- to ,10-keV range :is an observation of the storm-time ring current. An average spectrum, obtained from O{;O 3 dnrinp, ,hmc and July lg(_b, i s sho;_'n for l, = .1.5 and l, = o (1':::;::,,//,, ,t_L,i /,'_,_r_z]c, 19711. There arc considerable differences below ,1 key between the._t, avera_,e ,_peetra and tim s in!,,It,

I l(I i / [

¢. I IIIII II i' _ --.- "" [)

I observations at L = 3,9 and 6 discussed earlier. These differences are assumed to be indicative of the temporal variations. The l'xplorer 45 observations at L = 4.25 (Srn¢t;h _:t; aT.,, 1976) and L = 4.6 (W4Z/.iwn') _l; i at., 1973) correspond to relatively "quiet" conditions. The perpendicu- larly mirroring flux at L = 4.25 was about a factor of 25 higher at 30 !eV during the main phase of a geomagnetic storm. 'Hm two ATS 5 spectra (De- For,e,_#, 1972) at synchronous altitude (L _ 6.6) correspond to near-loss cone and near-equatorially mirroring fluxes in the evening sector. The similar magnitudes of these two spectra indicate a nearly isotropic flux. J As was the case for the electrons, the error in assuming isotropy will be " small compared to the other uncertainties. Ii

A single composite spectrum was derived from these observations and is also shown in Figure 8. This spectrum follows the upper range of the quiet-time observations for energies above 1 keV. Below 1 keV, the spectrum follows the rising trend of the spectra at L = 3.9 (OG0 3))4.25 (Explorer 45), and 4.6 (Explorer 45). This should provide a. conservative representation of this energy range, especially in view of the divergence of trends below a few keV.

D. The Plasma Sheet

In the model configuration of the near-Earth space described i.n Sec- tion II, the plasma sheet is a nightsiue region centered about the mid- plane of the magnetotail with a thickness of 12 RE. At a radial distance ._ of 18 RE from the Earth, Vela satellite measurements have shown the same thickness for the plasma sheet near the dawn and dusk edges of the magnetotail (Aka_ofu et aZ., 1973). ltowever, the Vela satellites observe that the apparent thickness of the region gradually reduces to about 6 RE near the local midnight meridian. Since the plasma intensity in the ad- jacent high-latitude magnetotail is comparatively much lower than in the plasma sheet, an overestimate of the size of this region will give a conservative estimate of the fluxes in this part of space.

Figures 9 and 10 show the low-energy proton and electron data record- i ed by the Vela 3B, Vela 4B, and OGO3 satellites during the 1965 to 1968 i time period. It is noted that the Vela 4B spectra in Figure 10 are com- posites that are based on a set of five spectra published by ltoneg et aZ. (1972). All the spectra used in this study are classified as typical plasma sheet protons or electrons by the experimenters. Effects of substorms and isolated localities of acceleration or injection are regarded as transient phenomena and have been tentatively excluded.

It can be _een in Figures 9 and 10 that the sl)ectra, as observed by different satellites or at different times, are quite variable in energy range as well as in flux lcvc}. Similar to the case of the magnctosheath, high and low estimates are constructed to serve as composite spectra and

[ 11

J, are shown by the dashed lines in l'ignres 9 :lad 10. ]Ira area enveloped by the compos:kte Sl:ectra represents the range of uncertainty in the esti- lllat es.

'Ilmre have been reports that the protons in the plasma sheet form enhanced flows (e.g., /tonc_ ct al., 1972, 1973, 1974) during magnetospheric substorms and sometimes produce explosive jet streams (called "fireballs") in some localities in the magnctotail (Frank et al., 1976). llowever, with the exception of these occasional events during substorms, the fluxes of low-energy protons and electrons in the plasma sheet have been characterized as "most often isotropic" (Akasofu et al., 1973; Bame et al., 1967). Because only long-term effects are of major concern in the present study, no spin averaging is required, and ai1 fluxes are taken to be isotropic.

E. The High-Latitude Magnetotail h The plasma intensity in the high-latitude magnetotail is generally very low during "quiet" times. It is usually below the detection thresh- old of the instrument or below the cosmic-ray background level. The Vela electrostatic analyzer, for example, can only measure the electron flux in the region, but cannot record the proton flux during nonstorm time, because the proton count rate is below the count rate produced by the cosmic rays in the instrument (Akazofu et al., 197_). Comparatively, the ] Vela instruments have documented very extensive data of both electrons ] and protons for the plasma sheet region previously discussed, d

In fact, there are only two spectra published in units of differential flux available in the literature for the high-latitude magnetotail region: one for protons from an IMP 4 measurement (Frank, 1970a), and one for electrons from Vela 5B, 6A, and 6B observations (Akasofu et al., 1973). These two spectra, shown in Figure 11, have already been quoted as representative spectra in many review articles (e.g., Vasyliunas, 1972; Frank, 1970a; Wolfe and Intrillgator, 1970). 1

The shapes of the spectra in this region are similar to those found j in tile magnetosheath, but the flux level is much lowcr titan in tile mag- ! netosheath. The high-energy skew of the proton spectrum above 2 keV I resembles in shape the skew of the reported r__ng current protons. (For a

review, see Va_yliuna. _, 1972.) i [sotropic angular distributions for the fluxes of protons and elcc- I trons in this region are reported as a usual feature (Frank, 1970a; Aka- i sofu ct aZ., 1973); and, therefore, no spin averaging is needed, t ! The validity of these spectra in the high-latitude magnctotail is limited to a radial distance below 22 RI!. 'l_,le high-latitude magnetotail at lunar distances of Oil l/li, for instance, can have quite different characteristics (/h1_,,_/ ,'t. a/., 197(_).

12 < ...... ---Ti 1 I

As previously noted in Section II, a region of relatively less extent just inside the magnetopause, named the plasma mantle (Ro_enbauer e_ el., 1975) or boundary layer (Akasofu e_ aZ., 1973), has not been treated separately in the present study. The particles in this boundary

layer have been observed to have the characteristics between that of the I magnetosheath and the plasma sheet. Since this layer is very thin, less than 1 RE in most cases, it is expected that the omission of this region will not substantially affect the accuracy of the present study. J

• F. A Summary of the Composite Proton and Electron Spectra

Composite proton spectra from the five regions are shown in Figure 12. High and low estimates are given for the spin-averaged, magnetosheath spectra and plasma sheet spectra. The high-estimates, corresponding to envelopes of observed differential fluxes, will give an overestimate or upper bound to the integral fluxes. Similarly, the low estimates yield a lower bound for the integral fluxes. _e high-estimate magnetosheath proton spectrum has the highest fluxes for energies in the range i00 eV to 6 keV; while above 6 keV, the inner magnetosphere spectrum dominates. The spin-averaged, interplanetary proton spectrum, which includes the time-averaged, solar wind spectrum, shows significant fluxes in the energy range from about 300 eV to 3 keV. The high-energy, interplanetary tail, with energies above approximately 4 keV, corresponds to protons propagating upstream from the bow shock. Its presence is dependent on the satellite location and interplanetary magnetic field orientation. The plasma sheet spectra tend to be an order of magnitude or more below those of the magnetosheath, while the high-latitude magnetotail spectrum is about an order of magnitude below those in the plasma sheet.

It should be noted that the interplanetary and magnetosheath spectra are not true isotropic fluxes; therefore, a true onmidi_ctional flux cannot be obtained by multiplying by 4_. However, the flux [protons/ (cm2.s.eV)] through an area oriented perpendicular to the ecliptic plane and spinning can be obtained by multiplying any of the spectra in Figure 12 by _.

Composite isotropic electron spectra from tile five regions are shown in Figure 13. The high-estimate plasma sheet spectrum told the inner meg- . netosphere spectrum show comparable fluxes for energies above 200 eV. . Below 200 eV, the high-estimate magnetosheath spectrum and tile inner magnetosphere spectrum show comparable fluxes. _le interplanetary spectrum is nearly identical with the low-estimate magnetosheath spectrum for energies above 50 eV, while the high-latitude magnetotail spectrum is one to three orders of magnitude below the other spectra.

Illc relative importance of a spectrum from a particular region, in regard to its radiation damage potential, depends on the satellite orbit• As an example, Scction V describes the apl_lication of this cnvirontttent to the ISIiI_-A/-B orbit• ..

13 IV. TIt_ ISI!Ii-A/-B ORBIT

As introduced earlier, Figure 1 shows the projection of the model magnetosphere and some of the revolutions of the ISEE-A/-B orbit rotated into the X-Y plane of the GSE coordinate system. _e schematic defini- tion of the five spatial regions is also shown in the figure. Because the Z-axis is not shown, regions D and E are represented by the same area in the X-Y projection. Of particular interest, in this case, is the evo- lution of the orbital position with respect to the various spatial regions. • Starting from launch on Day 288, 1977, the spacecraft crosses the bow shock until late January 1978. It enters the high-latitude magnetotail in late February of the same year. About 6 months after launch, the apo- gees of ISEE-A/-B precess 180 ° from the dayside to the nightside of the magnetosphere. 1 Figure 14 shows the details of the first 6 months of orbital time in which ISZE-A/-B are located in various regions. It can be seen that the major regional contributions to the orbit come first from the interplanetary medium; then from the magnetosheath plus the inner magnetosphere; and, finally, from the plasma sheet and the high-latitude magnetotail. When the orbit-averaged spectra are calculated, the fraction of orbital time in each region is used as the weighting factor for that region. Re- suits of these computations are presented in Section V. 1 As previously noted, the classification of spatial regions is limited by the constraints of the current computing programs and the availability of the low-energy particle data• Some areas of relatively less extent but of considerable scientific significance, such as the plasma mantle or boundary layer, are omitted in the present version of the environmental estimate. i V. Tile APPLICATION O1" TIlE ENVIRONMI_NTTO TIIE ISEI!-A/-B ORBIT

The number of days per revolution in a given region for each of the first 76 ISEE-A/-B revolutions is shown in Figure 14. _lis group of revolutions comprises approximately 6 months and corresponds to an apogee pre- cession from late morning to near midnight, q_ais sample of revolutions can be used to generate an average revolution in which the spacecraft spends a certain percentage of its time in each of the five regions. Weighting each region spectra by the corresponding percentage of time spent in the region and summing the resultant spectra yields an orbit- averaged spectrum. Figures 15 and 16 show the results of this analysis for the ISEE-A/-B orbit as applied to the proton and electron spectra, respectively. The percentage of time spent in each region is indicated in both figures along with the weighted spectra and the final orbit-aver- i aged spectrum. Most of the time is divided among regions of the inner magnetosphere (32 percent), interplanetary medium (25.2 percent), and magnetosheath (20.8 percent); while little time is spent in the plasma I sheet (12 percent) and high-latitude magnetotail (I0 percent). In order not to underestimate the final fluxes, the high-estimate spectra were used when available.

It is apparent from Figure 15 that the magnetosheath is the major contributor to the average proton spectrum for energies below 5 keV, while the inner magnetosphere is the major contributor at higher energies. If the low estimate had been used for the magnetosheath, the average spectrum would have been reduced less than a factor of three for energies below 5 key and an insignificant amount at higher energies.

The corresponding analysis for the electron spectra is shown in Fig- ure 16. Approximately half of the average spectrum is derived from the inner magnetosphere. The remaining half is contributed by the high-estimate magnetosheath spectrum for energies below 300 eV and by the high- estimate plasma sheet spectrum for energies above 300 or. If the low- estimate spectra for the magnetosheath and plasma sheet had been used, i the average electron spectrum would have been reduced less than a factor of two.

The significance of tile inner magnetosphere proton and electron ,i spectra for energies in the range 1(}0 eV to 100 keV is now apparont. As discussed in Section II1, this region is characterized by large :;patial i and t_mporal wtriations for low-energy particles. It is likely that tile , _posite spectra for this region overestimate the average situation, but 1 tt is difficult to say by what factor, l,lore obscrwltions, on the dayside i part icularly, arc needed.

The orbit-averaged proton and electron differential ener_,y spectra i from Figures 15 and I_, are compared in Figure 17. The differential flux J [protons/(cm".s.cV} ] throul.h , ttnit area, oriented perpendicular tt_ the

J, t

! /)

i I I ' . ,. I' b_

ecliptic plane and spinning, may be obtained by multiplying the spectra / in Figure 17 by a factor of it. If the radiation d': .age expected from these particles is not strongly energy dependent, it is useful to have integral flux values. These values have been calculated by integrating the spectra of Figure 17 from a given energy up to l0 s eV and then multiplying by _ to convert to units of integral area flux (JA) as shown in Figure 18. N_ omnidirectional electron flux can be obtained by multiplying JA by a factor of four. An omnidirectional proton flux cannot be calculated directly from JA, because the solar wind and magnetosheath proton spectra are highly anisotropic. Appendix C gives the procedure for an analytic calculation of the omnidirectional flux when the particle fluxes can be represented by a Maxwell-Boitzmann distribution moving with a bulk speed. A similar procedure for use with a K-distribution is given in Appendix D. As an aid to the user, Table 2 contains numerical values for the spectra shown in Figures 17 and 18.

l (_

/, 8 i I i , , _ , I

Appendix A. The Conversion From l'luid l'arameters to Energy S]_ectra /

it is sometimes possible to represent a particle population by an analytic function employing only a few parameters that have physical significance. One such function is the Maxwell-Boltzmann distribution, which is characterized by parameters of density (n) and temperature (T) (e.g., Sears, 1953). The Maxwell-Boltzmann phase space density distribu- i tion function fm can be written as / t

( m _/2 _,2 f_ = n _2--_) • e (A.I)

where fm is the number of particles per unit (position) volume and per unit velocity volume, having (thermal) speed v; m is the particle mass; k is the Boltzmann constant; T is a characteristic temperature; and n is the number of particles per unit volume.

Another function that has been found to be useful is referred to as the K-distribution, which can be written as

nK! 1 " v _ I (A.2) k 1+ )

where 1' is the ganuna function, W is a thermal speed characterizing the distribution, K is an integer, and the other variables are as previously given. In the limit of K approaching infinity, fk becomes the Maxwe11- Boltzmann distribution fro. Fanmi:;czno et al. (1973) have defined a K- i distribution temperature T in terms of W using the relation

lhL' two distribution._ give|| 1,y (A.1} mid (A.2) do not have an explicit :lngH la Y dcpemlence.

I;iven ;I goner, 1 l_l_ase space density distrihution t', it is usct'.l to dett, rmine the ctn'rcslmndin_, diffcrential-ener_,y unidirectional flux j.

/ • t ¸- ..

Expressing these quantities in terms of differential elements yields

f _ aN (i. 4) , dx dy d z dvx dry dv_ I

• dN J = dA dt d_ dE [A.5)

where N is the number of particles; x, y, z are position coordinates; 1 Vx, Vy, Vz are velocity coordinates; A is an area, t is a time, f2 is a solid angle, and E is an energy• By transforming the differential volume elements to give

,!vx dvv dr, = v 2 df_ dv (A.6) 1 1 dx dy dz - dA dz = dA VN dt (A.7) "_ 1 where vN is the component of particle velocity perpendicular to area dA, t f can be written as

I dN f " _ " dA dt d_ dv (A.8)

By restricting d_ to be perpendicular to dA, vN can be replaced by v. Differentiating the nonrelativistic particle kinetic energy

li = amW (A.9) , to obtain

dl! = mv dv (A.IO)

and substituting into (A.8), yields

n_ dN m . t" v' d,\ dt &! dl! v--'d (A. l l) i where j is the desired flux as given in (A.5). The peneral result o["

V 2 j = _m f {A.12)

can now be used with (A.I) to give the isotropic Haxwel1-Boltzmann energy i spe etrun jm:

• nnlI/2V2 ra, ? J_= (23Tk'l'):zT-" e (A.13)

In the solar wind and in the magnetosheath, the proton fluxes are anisotropie because of the bulk motion. It is found that an isotropic distribution, such as the Haxwell-Boltzmann or the K-distribution, trans- formed to a reference frame moving with the bulk velocity, provides a reasonable representation of these particle fluxes. Under these conditions, the particle phase space density distr:ibution is found by transforming the isotropic distribution f((_) to a coordinate system moving with a bulk velocity Vs. Using the Liouvillc Theorem, in which tlm phase space density remains constant under the transformation,

f_(@) = f_(b_s) (A.14) where

= _ - ?s (A. I5)

and w is the thermal velocity, _ is the observed particle velocity, _?s is the bulk velocity, and fl and f2 are the phase space density distributions in the stationary and moving reference fra,aes, respectively. Thus, referring to (A.1}, a t.laxwell-Boltzlnann distribution moving; _ith a bulk velocity 9 s can be written

f_ = n \)_/ • e _t (A. Ic,1

b.I. and using (,\.12), the flux .is ,_iven by.

M_-Vd' mn','e v:' " "'_k-ff A.171 -- L _ . ,- J" i I I I I b,

where

]_-Vsl2 = v_ + Vs2 . 2v Vs cos 0 CA.18) and @ is the angle bctweon tile observed particle velocity and tile bulk velocity. In a similar manner, the K-distribution flux can be found for t " a moving reference frame by combining equations (A.2), (A.3), and (A.15) i to obtain the new phase space density distribution function; then, using I (A.12) to obtain the differential-energy unidirectional flux. The result gives

nK! (_) _ v2 I JK = F:(K'!_)(K-_,j_'(kT)'/' " [i + m2(K-_)kT,_-?s,2]''' (A.19)

where JV'Vs[ is as given by (A.18).

All calculations for this study have been made using the following values for the physical constants: proton mass (rap)= 1.67 x 10 -27 kg (1.04 x 10 "12 eV.s.cm'2); electron mass (me) = 9.11 x 10 "31 kg (5.66 x 10 "is eV.s.cm-2); Boltzmann constant (k) = 1.3g x 10 "2a J.K "1 (8.025 x 10 -s eV.K-1),

21) f ! I [ _,

APl}endix B. The I)c,riv;_l i()n ()r, 'l'inle-Av¢_r._cd,,()l.ll Wimi I'r()t()n %j)ectrLull

TYl>iCal ,._)l;ir _ind t!l_lxt,._, ol,served over a per]_)d ¢)f m¢mths, ]nay _" :dlow bulk .qpced wlri;ition:_ or more than a t'act(rr of t_qo. ll.qing a Haxwell- B¢)lt::m;mn di:;tril)_tion t!mlct, ion in a r¢,rerence t'rmJ|e moving with the ])_.lk i :;peed t() repre.;ent Vel:_ 3A ;Ind 3B data, :h.ouU_,u._c_,Jl,_I. ,_/_. (197{).) have J

made a stat i.sti c;11 study or the relationshil)S [lhR)ilJj, vari otis solar wind ] l)ara,leters. These observations, covering the time interwll ,]uly 1905 to ,i Nt_vember 19()7, uere made near solar minimum and during a ri._.ing portion J of the solar cycle. Based on an ll-year cycle, the aext corresponding period (197(_ to 1978) should overlap the [SI!I!-A/-B launch date. In any event, a strong solar-cycle d_I)e]ldellce for tile solar wind parameter rel_t- tionships is not expected.

Table 3 presents the Vela 3A and 3B correlations between the solar wind velocity (Vs) aJld density (n) and temperature (T). Also given is the 1 normalized frequency of occurrence (probability) of solar wind velocities in spec.ified ranges. By combining these data with the expression for a _',laxwell-I',oltz]na]m distribution in the moving frame as given by equations (,\.i5) and (A.I()) of ,\ppendix A, it is pos._il)le to construct a time-averaged, solar wind proton spectrum (Js). Writing the solar wind proton spectrlu, (Js) to show the explicit dependence of n and T on solar _h}d speed, yields

j, (Vs) nlVs) nl_2 v:' - : [2.nl.'rtVs).}_a • e _-f_-l.2.v]-2. v, ¢o,.) (B. l )

uhere parmneters not defined here arc as given in Appendix A. The tilne- averaged spectrum ()-s) can now be obtained from

dF J, : f 3, tvs3 dg s lB.2 _.;..

W]l C Pe

fdl.

1' i_; dcl'il_t'd ;_:; tile [)r¢_l);ll,ility that tht' 1)1_11.,solar wind .,;l_t,t,d i:, \'_,

:llld \'lilill ;llld VIII;IX iLl'L' lilt' lllillilI)lllll ;lilt] lll;l.\illllllll '.;t)l;ll" Willd vt'l_u'it i('_; ])l't'- ".t'l_tt'd il_ l;_l,lt. :,. lhv rv:_Itin,_,, .q]>t.ctr_m_, l,,_)l, il ,, into 11_. In_ll. flow

( .... t) l , h:_. :t il..'h l,r,,ad¢_r (,m,rl,,y ,_l)rt.,al than ;_nv indivi,h_;_l _,l_,._.Iv:_ i_,n

'I t

I" I I t b_

and is shown ±n Figure 4. The peak flnx occurs near 61)0 eV and nearly all the flux lies between 300 and 2000 eV. A technique for obtaining a useful average spectrmn fronl this highly anisotropic flux is _,iven in ] Appendix C.

i l Apl)endix C. The Ik.riwltion of n ,qpin-Avera,ed, Sol,r Wind l'roton .qpuctrLmt

The highly anisotrol)ic solar wind proton fll_x can lie rc;l:a)nal)t)' al)- proximated I)g a Haxwell-IIoltzmann distril)utiozl in a rcfercacc t'ral_c, luov- zing with the I)ulk l;low .,;peed. From Al)l)endix ,\, the differential cm, r),y spectrum (Js.] can he written as

where v is the observed Darticle velocity, Vs is the solar wind (bulk flow) velocity, (t is the angle betwceli v al_d Vs, alld kT is a characteristic thermal energy. The other parameters are ;is defilled ill Appendix A. ! Typical values for the bulk flow energy (l!f), given b y

Ef - IalnVs 2- (t;. 2 ) are two orders of magnitude larger than the characteristic thermal energy (kT). This anisotropic flux calmot easily be used for this study in the form given by equation (C.1). Since one objective of this study is to assess the radiat:i.on flux receiv(:d by the spiiming ISIili-A/-B spacecraft, it is approl)riate to consider the specified geometry.

Figure 19 shows a schematic representation ot; a l)lanc area (dA) as an approximation to tile s£de of the spkmling ISlili-A/-B Slmcecr_lft, where the spin axis is Perl_endicular to the ecliptic (X-2) ];lane and to the bulk flow direction (Vs). The radiation received l)y this plane area will vary with the angle tl as the spacecraft spins in the I)rescnce ot" ml anisotropic flux 1.ike the solar willd. The approach adopted is to construct an effective isotropic flux (jse) that will provide the same radiation through the plane area {dA) as tile average received d, ri)H', one rot_ltio)). This effective isotropic flux m_.:y then be COml)ared alld coml)incd with other isotropic fluxes, with the restriction 1-tlat it only be Iiset] t() de= termine the average radiation on a Sl_,inn:ing pl,ne ;nre;i wl_cn the sl>it_ axis is I)crI}endictllar to the bulk flow. whore d,_, is a differential solid angle, and typ:ical units of JA are [l_ar - ticles/(cm2;s.eV)]. It is now necessary to calculate the sp:in-averllged area flux (jA) :in tile solar wind. lJsing equation (C.1) mid referring to the geometry of l::igure 19, JA for a given angle n can be written as

j^ (n) = fj, t_)) cos C ds_ (C.4) ,

where

• cos O = cos _ cos _ + sin (_ sin _ cos _ (C.S)

dfl = sin _ dg_ de (C.O)

_le spin-averaged area flux (JA) is now found by averaging over the angle n to give

1 _A = _- f j^ 01) an (c.7) 0

where, by symmetry, _he integration need only be carried out over a half rotation.

In general, combining equations (C.4) mid (C.7) requires a triple numerical integration, llowever, an approximation is possible in this case since the thermal component of particle energy is a small fraction of the bu!k flo_q component. Rewriting equation (C.4) with _ = 0, gives

_/2 2n nmV2 V 2 m 2 2 cos • • cos f, sin _ d_ d$ (t;.8) j^(0) =f f (2lrk'l')Yi e" 2_-"/T(+v" , -2, v, _1 _=o ¢=0

where O = _; from equation (C.5). Performing these integrations yeilds

nckr', [ m Vs l)e" j^ (0) = (2_rmy, mVs_gL\ _ e" It:.',))

where jA(o) is the area flux for a unit area that is l_erl_t, nd:icular to the bulk flbw. By making the approximation that this flow ]ills no thermal componen', the area flux at angle rl is t,iven by

2,1 j^ (_l) " JA (o) cos _1 ((:.1o)

for ]rl] 11/2 and zero elsewhere. Substitl_ting jA(q) into equation (('.7) yields

for the spin-averaged area flux. This approximate expression is accurate to better than 1 percent as indicated by computing the triple ntmmrical integration implicit in equations (C.4) and (C.7) for the solar wind parameters given in Table 3. Therefore, the effective isotropic flux

(Jse), using equations (C.3) and (C.II), can be expressed as I ! jfo) J,e = _ (C. 12)

where JA(o) is given in (C.9). Time averaging of JA(O) has been performed using the procedure given in Appendix B. The resulting time- and spin- averaged effective isotropic flux is shown in Figure 4.

Other geometries, besides that given in Figure 19, may be useful in some cases. One of these is the radiation received by a sphere of unit cross section, which requires a determination of the omnidirectional flux ': (Jo). For the solar wlnd, Jo is given by

Jo = fJ, (o) dS] (C.13)

where is(0) is given by equation (C.I), and d_% is given by equation (C.O) with O = _. The result gives

Jo" mvV---7[j, 2"¢T- j, (,:. -'

where @pi_,tl un:,t:-; _}f Ju "'"' [P"vticl'_sllcm2"s'eV)l This spectrum may i also be t:ime averaged tlSillg the procedure in Appendix B. I 1

Jv Append:Ex 1_. The I)er:iwltion of a Sl_in-Averaged_Magnetosheath Proton S]}ectrum Using a K-I)istribution Function

The anisotroI)ic magnetosheath proton flux can be reasonably approx- imated by an isotropJc distribution function in a reference frame moving with a bulk flow speed. The K-distribution function, with K : 2, has been found to be appropriate in many cases (],'o_nC._Jano at aZ., lO73) and also approximates the composite spectra shown in Figu*'e 7. From Appen- dix A, the differential energy spectrum (JK) with K = 2 can be written as Q

4nm V2 v 2 1 = •

JK2 llZ(kT)_ 1 + _- (v 2 + Vf - 2v Vf cos 0) _ (D.1)

where v is the observed particle velocity, Vf is the bulk flow velocity, @ is the angle between v and Vf, and kT is a characteristic thermal energy. The other parameters are as defined in Appendix A. Unlike the situation in the solar wind, the bulk flow energy (El) given by

E( = ';_nVf 2 (D. 2) 1 is of the same order as the characteristic thermal energy (kT). Never- theless, the anisotropy is generally sufficiently large that it is necessary to calculate an effective isotropic magnetosheath proton flux (JKe) as was done for the solar wind protons. This flux will provide the same radiation through a plane unit area as the average received by a spinning unit area with its spin axis perpendicular to the bulk flow velocity. If the spin axis is not I)e rlendlcular) " to the bulk f'lo_v velocity, this al)- proech will overestimate JKe" A detailed description of the geometry is given in Appendix C and is shown in Figure 19. J The flux through the unit area (area flux -JA) for arbitrary an_.le n can be written as

= j, (n) fJK_ ((I) cos i; d_, (1).3) I t t wh e re ! 1 cos 0 = cos ,_." cos rl + sin _ sin ?1 co!; t' 11).,11 :

t d_ = sin _ d_ d_ (D.5)

and JK2(0) is as given by equation (D.1). The spin-averaged area flux is now found by averaging over the angle n to give

It 1 YA= _ f j^ (n) on (D.6) 0

where, by symmetry, the integration need only be carried out over a half rotation. Using equation (C.3) from Appendix C, the effective isotropic flux can now be written as

£. = _-7T (D.7) !

where the calculation of JA involves a triple numerical integration.

Tae high- and low-estimate magnetosheath spectra of Figure 7 cor- respo,a to J K2(0=0) with Vf = 280 km/s and kT = 400 eV. These spectra differ only in the density parameter with n = 17 cm"3 and 2 cm"3 for the high and low estimates, respectively. _le derived effective isotropic spectra (JKe) are also sho_cn in that figure.

As discussed in Appendix C, flux estimates for other geometries may sometimes be useful• In particular, the omnidirectional flux (Jo) from a K-distribution, with K = 2, may be readily found from the expression

J0 = fJ K2(0) d_q (D.8)

where JK2(0) is given by equation (D.1), and d_ is given by equation (D.5) with 0 = F_. The result can be written as

Jo = 2mvVf_kT jK2(0=O) • 1 + _(v-Vf)m 2 - jK_ (0=lr) • 1 * _-@v+V_) (I).V)

where typical units of jo are [particles/(cm 2*s.ev)].

27 To.ble 1. Spatial Regions of the Near-liarth linvirmunent [ for lligh-Altitude Satellites

Eight Regions (Vcttc ot aZ., 1976) Five Regions (Present Study) 1. interplanetary medium 1. interplanetary medim_ ] 2. dayside magnetosheath I 1i " z 2. magnetosheath 3. nightside magnetosheath }

4. dayside magnetosphere 3. inner magnetosphere S. nightside magnetosphere 1 (-IORE

6. midlatitude magnetotail 1 (XGSU<- 10 P,E, j_l 2RE6Rli) i 1 1

t I • - I i J' I | | ('" i,, |- I I I I

Table 2. IS}!I!-A/-B Orbit-Averaged Sp(:ctra /

.le Jap* Differential Flux 1/ffoctive Differential Flux Energy (eV) [electrons/(cm 2 .s,sr,eV)] [protons/(cm 2 ,s,sr.eV) ]

1 x 102 1.6 x 10 _ 1.2 x 104

4 x 102 2.0 x l0 s 4.2 x 104

6 x 102 1.2 x 10 s 4.7 x 104

1 x 103 6.8 x 104 2.7 x 104 !

4 x lOS 9.0 x 103 1.8 x 103

1 x 10_ 1.3 x 103 4.7 x 102

4 x 104 7.0 x 101 1.7 x 102

1 x 10 s 1.i x 10 ° 8.5 x 101

Jae Jap* Integral Area Flux** Effective Integral Area Flux** Energy (eV) [electrons/(cm2,s)] [protons/(¢m2.s)]

1 x 102 1.1 x 109 2.25 x l08

4 x 102 5.6 x 10 e 2.0 x 10 e

I x 103 3.4 x l0B 1.2 x l0B ' i 4 x 103 1.0 x 108 6.2 x 107

1 x 104 3.5 x l0 T 4.8 x l0 T

4 x 104 5.0 x l0 G 2.3 x [07

8 x 10" 1.7 x 1(16 0.0 x 10r'

1 x i0s 0 0

*The proton fluxes have been spin averaged (see text) in such a way tlmt they will give the average flux Imssing throul,h a spilming area when the spin axis is pcrl)endicular to the ecliptic plane.

**Note:., _ _,10 _cVr A, V/ ' :i dl,_ L

I i \ I I I I d I I I I I I _,

Table 3. Proton Solar Wind Parmneter l_elationships*

dF Vs Frequency n T Velocity Interval In Density Temperature (km/s) Interval (cm" 3) (K)

250 - 300 .050 9.2 2.50 x 104

300 - 350 .245 8.5 4.50 x 104

350 - 400 .270 7.8 7.50 x 104

400 - 450 .190 7.5 1.12 x 105

450 - 500 .ii0 6.9 1.45 x i05

500 - 50 .065 6.5 1.75 x iO s

550 - 600 .040 6.0 2.05 x 105 1 I 600 - 650 .020 5.8 2.20 x 10 s

650 - 700 .010 5.5 2.45 x i0 s

*Vela 3 - July 1965 to November 1967 (Hwndhau_cn et aZ., 1970). 3O

'XBow Shock

Magnetopause X J 20 "_--_

0 110.21 'hf__" ®Lau2,,', .-. 77.288.15.5 h %=o @® /_ ! _ _289.18 h ° ) -10 n _ 312.11 h

-20 51.21 h :,, j h I.--. _ 31.11 /h ,v 78.4.5 h 7 -30 f -30 -20 -10 0 10 20 30

XGsE(RE) i

@ Interplanetary Medium @ PlasmaSheet ]

Magnetosheath @ High-Latitude Magnetotail

Inner Magnetosphere

Figure I. ISEE-A/-B Orbit Rotated into tile GSE X-Y Plat_e i 108 _ , I

107

i,__ 10s, SolarWind Electrons T 1.5 x 106 K N 9cm 3 105

\ ,.--., \ > \

L¢ 10 4 Solar Event ° l OE 103! \ i U) \ ¢ i y\ O 10_ 21 Flare i

10 ; Quiet Time rj _1 i Composite M. ! (Lin eta/., 1972) ..J \ 10°i: Z ! -- Composite Spectrum IJ.J i (isotropic average) t'_ J Flare IJJ j - - Maximum Spectrum

u. 101' Maxwell Boltzmann IJ. i (anisotropicRepresentationflare)of Solar Wind '\\ ",\ ! Electrons \ IMP 6 I (Fr_rpk _md Flar_ia Gurnett, 1972)

102! • eGOIMP6f 5:3/114/6/68/71 (Ogilvie et al., \ 1971) \ \ 10.3; ' IMP 4: 7/3O/67 i (Wvmg et _rl." \ _' : IMP6:3,'21/7I 11971) \ !i_ '\ ,

i • Apollo 15 subs_ltellite: 9/1/71 "', - "_/U-4 (Lm, 1974a) • Apollo 16 subsatollite. 4 27/72 i (Lin et _1., 1973a) \

10:00 101• 102 103 104 105 ENERGY (eV)

Figure 2. Interplanetary Electron Spectra ! i

I" J' I I I I I [" ,=,

380 km/a A KT 4,3 aV /I 108 ' N 7.5, cm 3 j. ].,_-Proton Sol,ar Wlnd 107! //\ \.odia,.,ow

TimeAveraged Solar Windd/t \ / 700 km/s Derived from Vela 3A, 3B / I I \/ ...... Observations f I I \1 .,,.- zl.=ev 106 (Hundhausen et el., 1870) | }_ N 2.5 cm

(July 1868-November 1867 IIII

105

Composite Spectrum _/_'_ (effective flux; time. and ._

>¢.104 spin-averaged) _ \

103 I _ J ¢o t

=..1°2 I

X _ ,_ .' Magnetic ,.I 101 _, Storm

_1 'Propagatil _g =1_ ,.: Out from i/ _. • p-- - 100_ _.; Bow Shock _ \%1\ z ,_ ' ,r '_,\ mI,M Nonstorm _ \_ gJ LL A U. 10"1 Propagating Out \\

from Bow Shock \l\i

Derived Average _i 10.2 ! Quiet Time (Linet el., 1973b) 1 l i • Composite Spectrum (spin-averaged) t IIt -: Effective Solar Protons (time- and i spin-averaged) i 103_ Sow Shock Protons (spin-averaged) ' !

IMP 4:8/2/67 I 10-41 • IMP4:8/11/67[ (Frank, lS70b) ._ IMP 6:4/27/71 (Linet el., 1974)

10-5 .... 100 101 102 103 104 105 ENERGY (eV)

Figure 3. Interplanetary Proton Spectra • ;> L 105- Low Estimate,,// E

¢ O L- ¢J _ 104- x

u_ ,,J

p. Z - uJ 103 - ua u_ tL --- Composite Spectra O Vela 4B: 8/10/67 (Hones et al., 1972) 102 - • Vela 4B: 6/20/67 (Montgomery et al., 1970) /_ IMP 5:7/11/69 (Frank. 1971) o Apollo 14:4/6/71 (Reiffand Reasoner, 1975)

101 I ] I 1 100 101 102 103 104 05 ENERGY (eV)

Fi_]ure 4. Ha_]n(_tosheath El_-ctrc)I_ SlJectra I I I I I" I I

lOe I I I I /

¢, 104 _ High Estimate _ _ , w ,'_ 50° O• ' •, Low Estim_ 103 - X .J EL

I..- Z uJ 102 - ,,o 90° _ ul IJ. u_

--- C_mposite Spectra o HEOS 2:12113/72 (Rosenbauer etal., 1975)

101 - ( _A is the azimuthal angle) _ D HEOS 1: composite (Formisano et al., 1973)

<> IMP 4: 1116167(Frank, 1970a1 1 l z_ IMP 5: 11769(Frank, 1971) I

. I I [ I _ 100 101 102 103 104 10'5 i ENERGY (eV) i i J I t t

Figure 5. Ma!]netosheath Proton Spectra i

-, t / t

'f b l i i £ j. !

107 I I 1 I

10 6 - _

• I \

/ \ • / \ 105-- I _ - ? I /I--"\ / I _ I / \

High_ / / '\ / _ - 4 Estimate /

Low \ I

gJ 103 Estimate -- I LL

\ ]

102 CompositeSpectra (flow direction) \ - \ - , j

Effective Isotropic Flux (spin-averaged) I i

%o 101' 10'2 10'3 10,4 105 I ENERGY(eV) i 1 !

Figure 6. llagnetosheath Proton Spectra Compared with Spin-Averatled Spectra t

_. , , I" J [ I I I b,

107 I [ 1 i

L _-.5.3 \. Composite Spectrum _.

10_ - - t

L = 3.9 Ii L:: "" i ¢ L = 9.8 (plasma sheet)

105 - Substorm mL { _5_7-11RER E E

4o_ L = 9.25 _¢__ 104- (edge)

X L = 5.8 .J u. L 8 ..I -_ L=

I.Mz 10 3 - --- Composite Spectrum LUn" -- - AE-4 (Singley and Vette, 1972) LL _ OGO 3 6/15/66 (Frank, 1967c) LL u • OGO 3 L=6 ,'_ OGO 3 7/17/66- (Schield _nd Frank, 1970) • OGO 3 7/19/66 ', OGO 3 102 - • OGO 1 10/17/64 (Vasyliunas, 1968) ; OGO 1 _ Electron : 1/31/64 (Vernovet al., 1966) 0 Hawkeye : 10/14/74 (Gurnett and Frank, 1976) Explorer 45 : 12/9/71-12/16/71 (Lyons and Wil/iams, 1975) _, ATS 6 : 12/17/71 (Barfie/d et aL. 1977) L = 6-8

107 I ,t 1 I 100 101 10 2 103 104 105 ENERGY (eV)

Figure 7. Inner lla!lrl(,'Lo_,l)here lilectr(m Sl)ectra

37 10s I I I I

_'_o 104 --

'...L=4,25 - , _X_ ' C_ _/_'L=4.6 (magnetic -- L = 3.9r_ _ _._ storm)

L_6.6 "" _ 103- (near losscone)_ \_'E_.-_ _°_ "" __ 1

102 =

----- Composit_-eSpectru__--_ OGO 3: June-July Average, 1966 (Pizzella and Frank, 1971) _ /

. 101 • OGO 3 _ (magnetic storm): 7/9/66 (Frank, 1967b) L ='6.6 _. • OGO 3 / ' OGO3 o OGO 3 _ 6/15/66 (Frank, 1967c) n OGO 3 ) Explorer 45:12/17/71 (Williams et el., 1973) 10° O Explorer 45:2/24/72 (Smith et el., 1976) 0 ATS 5 | i _' ATS 5 (near loss cone)j 10/16/69 (DeForest, 1972) OV2-5:10/2/68-10/13/68 (Stevens et al., 1970)

101 I 1 1 I i 100 101 102 103 104 105 ,_ ENERGY (eV)

Figure 8. Inner flagnetosphereProton Spectra I 103 _ High Estimate-___

(n 102 -

,-- ]u I _ X ..I It. <-_ -- Composite Spectra Z uJ 100 (_ Vela 3B: 10/8/66 (Hones et al.. 1971) u."- _ Vela 3B: 4/8/66 omm @ Vela 3B: 10/17/65 1 r_ <_ Vela 4B: 10/27/67 (Hones et al., 1972) ®OGO3:6/14/66I 10"1 (_)OGO3:6/15/66 t (Frank, 1967b1

10.2 I I I [ 100 101 102 103 104 105 J ENERGY (eV)

Figure 9. Plasma Sheet Proton Spectra

.39 107 I I I I /

106 --

% ., _ %% High Es:imate

105. _ -

Low Estimate/_

-_ 104j

uJ 103

UJ LL It. ------Composite Spectre 1_i Vela 3B:11/3/68 J(Hones etal., 1971) :2"_ Vela 3B: 10/22/65I (3 Vela4B:8/10/67 I Compositeof FiveSpectre 102 - _4 Vele 4B: 5/16/67 J(Hones et al., 1972) _5 OGO3:6/14/66 I t (Frank, 1967a) 60GO 3:6/15/66 J 7_ OGO3:7/17/66 (Schieldand Frank, 1970)

101 I I I I 100 101 102 103 104 106 ENERGY (eV)

Figure I0. Plasma Sheet Electron Spectra

4(I 105 I I I I

I 10 4 -

m 3 S _ v)

'- I02 - --//._\\._- \ - - -X / \' \\ u. / _ Protons -, / \\

I-- I \ Z 101 - I \ - ua \

I.mL _

10o _ u Vela 6A: 9/5/70 (Akasofu etal., 1973) _ Vela 6B:5A: 92//323/70/71 } -- IMP 4:2/3/68 (Frank, 1970a)

1 t ( 101 i00 101 102 103 104 05 ENERGY (eV) b'

, Figure II. lligh-Latitude llagnetotail Spectra

i, .li

I" ____. _ . - _ ...... r-_ _ ; t I

" ! i I

lOe I T i I f

/ /

> / \ /

_ 103- !

e,. / \ o / \ 102 - / \

X= (_)// \

u. \ _< \ I,- \ .Z 101 _ \\ _ ,_ w \ u_"- \ 5

® 10o -

(_ Interplanetary Medium (spln-averaged)

(_ Magnetosheath (spin-averaged) I _ HighLoEstimateEStimatew 101- (_ Inner Magnetosphere

(_ Plasma Sheet I_-__ HighLow EstimateEstimate C5) High-Latitude Magnetotall J

10 .2 I I I I 10 0 101 10 2 10 3 104 10 5 ENERGY (eV) i

z Figure 12. Composite Proton Spectra ._

J (.;J_Interplant'_ary Medium I-- High estimate _2_ Magnetosheath I--- Low estimate 10° _3) Inner Magnetosphere I_ High estimate _4_ Plasma Sheet I --- Low estimate _§_ High-Latitude Magnetotall

...... l ...... J...... ] ...... 1 . 10:10 0 101 10_ 103 104 10_ ENERGY (eV)

Figure 13. Composite Electron Spectra

.;3 t

I 1

' II I i t I t • t " t _ _ f"

288 3 55 102 DAY 1977 1978 1978 1978 YEAR 2.O I I I [ InterplanetaryMedium M Magnetosheath O High.LatitudeMagnetotail • PlasmaSheet P InnerMagnetosphere

0.0 I I I I I I M I I _i 0 10 20 30 40 50 60 70 80 NUMBER OF REVOLUTION

Figure 14. ISEE-A/-B Orbital Coverage (period_2.3 days)

,I4 / 107 I I I I P = Percent of Orbital Time

Interplanetary Medium Ispln-averaged); P = 25.2 (_ Megnetosheath (spin-averaged;high estimate); P -- 20.8 m 10e / (_ Inner Magnetosphere; P= 32.0 (_) PlasmaSheet (high estimate); P = 12.0 (_ High-Latitude Magnetotail; P = 10.0 •-_--Orbit-Averaged Flux (spin-averaged};P = 100,0 105-

104

103

z _o

eL 101

100 (5___)j

10 ..... l ...... L ...... I...... _ . 10_ ..... 101 102 103 104 105 ENERGY(eV)

Figure 15. ISEE-A/-B C)rbit-Averaged Proton Spectra (revolutions 1-76)

45 107 I I ] I /

® ® 104 -- :>

i,,, ¢/l

u 103 _

_ 102 - u. (s/ ti z 2

a. 101 _

10o --

P - Percent of Orbital Time 11 Interplanetary Medium; P 25.2 '2, Magnetosheath (high estimate); P 20.8 '3 Inner Magnetosphere; P 32.0 10 - 4_ Plasma Sheet (high estimate); P 12.0 i 5 High-Latitude Magnetotail; P 10.0 ] -_- Orbit-Averaged Flux; P 100.0 i

...... / 102...... 1...... l ...... l...... 1 .... J 10o 101 10v 103 104 105 ENERGY (eV)

Figure 16. ISEE-A/-B Orbit-Averaged Electron Spectra (revolutions 1-76) I ! "'

107 I I I I

106 Elect

10s _

104 i

-:_ = (Effective isotropic flux for a \ \ 1 _" spinning area with the sp_ \ \ t

axis perpendicular to the \ \

103 ecliptic plane Isee u. 0

lO2

[ ", 101100 101 102 103 104 106 ENERGY (eV) i

Figure 17. ISEE-A/-B Orbit-Averaged Differential Spectra (revolutions 1-76)

,17 I I

I J I • li { _,

lll:l'l:l{hNt]:o

Aka.sofu, S•-[., l!.W. llones, .Ir., S.J. Bame, .I.R.A.sbridge, and A.T•Y. 1,ui, "Magnetotail and Boundary l,ayer Plasmas at a tlcocentric l)istance of -18 Ill!: Vela 5 and 6 Observations," J• (,'opl_9:_• 1¢(','_., '/11, 7257-7274, 1973. J Asbridge, J.R._ S.J. Brahe, and l.B. Strong, "Outward l:low of Protons • from the Earth's Bow Shock, " J. (,t_J ol,h,j_:. ]¢cc,., /a,e -J 5777-5782, 1968 i

Bame, S.J•, J.R. Asbridge, II•E• Felthauser, E•i_. llones, Jr., and I•B. Strong, "Characteristics of the Plasma Sheet in the Earth's Magnetotail, ! J. aGophy_, l?e_., 72, 113-129, 1967.

Barfield, J•N., S•E. DeForest, and D.J. Williams, "Sinmltaneous Obser- _, vations of Substorm Electrons: Explorer 45 and ATS 5," d• (TeophTjs. l_ec•, 82, 531-536, 1977•

DeForest, S.E•, "Spacecraft Charging at Synchronous Orbit," J• (JeoIj,huG• RerJ•, 77, 651-659, 1972.

Fairfield, D.ll., "Average and Unusual Locations of the Earth's Magneto- pause and Bow Shock," J• Geol)hq' o o. ]_c_•, 76 , 6700-6716, 1971.

Formisano, V., G. bloreno, F. Palmiotto, and P.C• lledgecock, "Solar Wind Interaction with the l!arth's Magnetic Field, 1, Magnetosheath," J• Geo- phyo. ges•, 78, 3714-3730, 1973.

Frank, L.A., "Initial Observations of Low-Energy lilectrons in the Earth's Magnetosphere with OGO 3," J. Ceophu_. fi'cr,., 72, 185-195, 1967a.

Frank, I,•A•, "On the Extraterrestrial Ring Current During Geomagnetic Storms," J. C;uotU_U_• Re,J•, "/::, 3753-3767, 1907b.

Frank, L.A., "Several Observations of Low-Energy Protons and l_lectrons in the liarth's Magnetosphere with 0(;0 3, " J• (,(.oI_/zU]__c_•,. ?2, 1905- 191o, 1967c.

[:rank, I,.A., "Further (:onnnents (]oncerning Low-iincrgy Charged Particle l l)istril,utions within the l!arth's Magnetosphere and its linvJrons," in _ t',_r, L L,/,c,_J (nzd I'L'/_l_" ;_z L]u: L!_e,f_zct(_:/h,'_'_:, 319-331, edited by B•M McCormac, D. Rekdel Pub. Co., IIordrecht, The Netherlands, 1970a,

Frank, 1,.,\., "On the Presence of l,ow-Energy Protons (5 Ii'50 keY) in the Interplanetary :.ledium," ,t. _;,,_,]tz_t_:: _,',';_., ,/l,, 7t17-716, 1970b.

Frank, 1,.,\., "Pla:;ma in the liarth's ])()far Magneto:;l_here," ,1. ,,',',.l']_i_;_. .,M)_-.,_ l!), 1:)'71. i ¢ 5() Frank, L.A., K.I,. Acker._on, and R.P. l,epl)inl,, _ "On llot Tcnuou:; l'la:una, Fire, balls, awl J'mund;.try I,ayers in the liarth',4 H;|gncttJt:ti 1, /

Frank, I,A., and I).A• (;urnett, "l)irect ()bservat]on-; of l,ow-lincrl,y Solar Electrons t_ssociated with n Type I1 I Solar Radio Burst," ,'h,L/p l']l/t;:., 27, 44(_-4(_5, 1972• I l:rank, L.A. and II.D• Owens, "Omnidirectional intensity Contours of Low- Energy Protons (0.5"1! 5(1 keY) in the I_arthts Outer Radiation Zone at 1 , the Magnetic Equator," d. (,'cophq_.. /_'(3_:., Y/i, 12o9-1278, 1970

Gringauz, K•I., "Low-Energy Plasma in the l!arthts Magnetosphere," h',.o. of geophu(_., 7, 339-378, 1969.

Gurnett, D.A., and L.A. Frank, "Continuum Radiation Associated with l,ow- Energy Electrons in the Outer Radiation Zone," d. aeophy_, h'(:'._., 81, 3875-.3885, 1976.

llardy, D.A., J.W. Freeman, and ll.K. llills, "Plasma Observations in the Magnetotail," in Madne_O.Jl)hez,_(_ Pm_gcZc_ and FicZdc, 89-98, edited 1)y B.M. McCormae, D. Reidel Pub. Co., l)ordrecht, 'llm Netherlands, 197(_.

Iloffman, R.A., L.J. Cahill, Jr., R.R. Andersor, S.C. ,Maynard, P.ll. Smith, T.A. Fritz, D.J. Williams, A• Konradi, and D.A. Gurnett, "l!xplorer 45 (S 3 - A) Observations of the bktgnetosphere and Magnetopausc During the August 4-6, 1972, 5ktgnetic Storm Period," d. &.'oF]zy_;. /i'c._., ,90, 4287- 4296, 1975.

Hones, 1".1_., Jr., J.R• Asbridge, S.J. Bame) bl.i), blontgomery, S. Singer, and S.-I. Akasofu, "Measurements of blagnetotail Plasma Flow blade with Vela 4B," d. (;coi,hEs•lCes., 77, 5503-552 _., 1972.

llones, E.W•, Jr., J.R. Asbridge, S..I. Bame, and S. Singer, "l{nergy Spec- tra and 3a_gular l)istributions of Part:icles in the Plasma Sheet and their Comparison with Rocket Heasurements over the Auroral Zone," ,/. (;(._q,it_/a:. l¢e_., 7(i, 63-87, 1971.

llones, li.W., Jr•, J.R. Asbridge, S•J. Bruno, and S. Singer, "blagnetotail Plasma Flow bleasured by Vcla 4A," ,I. C_:c,],h:t_'. h'.;_:., 7.'_, 54¢)3-5,17(_, 1(.173.

l[ones, I;.W., Jr., A•T.Y. LuJ, S.J. Bame, dlld S• Singer, "l'rulongcd Tail- ward Flow of lqasma in the Thinned Plasma Sheet Observed _lt 1"~18 RII During Sttbstorms," d• ¢;_,_q@;_:. /,,._:., 70, 1385-1392, 197,1.

JJtllldllaUSell, A.J., "P]asrll;l ble/lsllYc'lllcIlt5 ;|crL)ss thc P,o_ ,%]lock ;llltl ill lilt blagnetosheath" in l,,t.('P,'.c, Pm'/,t! _: ,; g/,'g/l',{. _i,;:, ,,_' l.e.m;' ,_,, ;,, : .':,,{(_P /.!_('*zki_, laa-lO.), edited 1)5' V _,lallio, l). Rcidcl Pill,. (;t,., IR)rdl'cchl, The Netherlands, 1!)7(). t

I J f _, J , l , II i b,

lhmdhausen, A.J., .I.R. Asbridge, S..I• game, 11•1!• {'.:ill)err, and I.lt. Strong,, "Vela 3 Satellite Observations of Solar Wind Ions: A l_relim:lnriry I_eport," d• (/coldly_;. /_'(;:_•, 72, 87-100, 1967. llundhausen, A.J • , S..1. Bame, and o.R. Asbridge, "Plasnm Flow Pattern in the Earth's Magnetosheath," J. Geophu_d. l_'c_t_., 74, 2799-2806, 1969. ltundhausen, A.J., S.J. Bame, J.R• Asbridge, and S.J. Sydoriak, "Solar Wind Proton Properties: Vela 3 Observations from July 1965 to June 1967," [ J. aeophUs, l_es., 75, 4643-4_,57, 1970.

Lin, R.P., "Non-relativistic Solar Electrons," Space f;o{• Ray., 16, 189- 256, 1974a.

Lin, R.P., "Suprathermal Particles," in So£ar Wind 3, Proceedings of 3rd Solar Wind Conference, 187-194, Pacific grove, Calif., March 25-29, edited by C.T. Russell, 1974b.

Lin, R.P., K.A. bmderson, and T.L. Cline, "Detection of Interplanetary Electrons from 18 key to 1.8 MeV during Solar Quiet Times," Phua. Rev. Lett., 29, 1035-1038, 1972.

Lin, R.P., L.G. Evans, and J. Fainberg, "Simultaneous Observations of Fast Solar Electrons and Type iiI Radio Burst Emission Near 1 AU," Astrophys. Lett., 14, 191-198, 1973a.

Li:i, R.P., R.E. McGuire, and K.A. N_derson, "Observation of 38-334 key Interplanetary Protons during Solar Quiet Times," PhUs. i_ev. Left., 31, 1268-1271, 1973b.

Lin, R.P., C.-I. _leng, and K.A. /_lderson, "30 to 100 keV Protons Upstream From the Earth's Bow Shock," d. Geophy_. Rea., 79, 489-499, 1974•

Lyons, L.R., and D.J. Willimns, "The Quiet Time Structure of Energetic i (35-560 keY) Radiation Belt Electrons," g. (;eophys. l_e_., 80, 943-950,

1975. D

Lyons, L.I',., and l).J. Williams, "Storm-Associated Variations of liquator- ially Mirroring Ring Current Protons, 1-800 keY, at Constant first Adiabatic Iw, ariant," J. GeophyJ. t_'c:.s., _1, 216-220, 197(_.

Nontgomery, M.D., "Average 'll_ermal Characteristics of Solar Wind lilectrons," in oo_' laa, W2nd, NASA SP-308, 208-211, edited by C.P. Somlet, P J. Coleman, Jro, and J.M. Wilcox, I_'ashington, I).C., 1972. biontgomery, M.D._ J.l/. Asbridge, and S.J. B_une, "Vela 4 Plasma (}bscrva- t[ons Near the liarth's Bow Shock," ,1. _;,'ol.hy_:. /_'_:_., Y;,, 1217-1231, 11t711.

Nontgomery, hi.l)., S..l. Bame, and A..I. lhmdhauscn, "Solar 1;'ind lilectrons: ,_ela 4 _leasurements," ,1. W_wl.hU_'. ii_'_;., 7.;, ,1!1:19-5(103, 1:1o8.

52 Ogilvic, I(.W., .I.D. Scudder, and M. Sugiura, "l!lcctron I!nerpy Flux ill / the Solar lVincl," J. :;cc_t,/tj_. /_'cc., 7(_, 8165-8173, 1!)71.

Pizzella, (;., and I,.A. Frank, ':lincrgy ,_pectra for Proton (21)O_cV.:li 1 ?,leV) Intensities in the (_tcr Radiation Zone," ,1. (Jcc_phy_. h'c_., 70', 88-91, 1971.

Reiff, l'.]l., and ]).L. Ite;_soncr, "The ;,lagnetosheath l!lcctron Population at Lunar l)istance: (;cneral Features," J. (;cot)hu._. Res., 80, 1232-1237, ] 1975.

Rosenbauer, 1t., 11. Grunwaldt, M.D. 14ontgomery, (;. Paschmann, and N. Sckopke, "lleos 2 Plasma Observations in the Distant Polar t.lagnetosphere: The Plasma Mantle," d. Geophus. Yes., 80, 2723-2737, 1975.

Smeyer, D.M., and J.I. Vette, "AP-8 Trapped Proton Environment for Solar ] Naximum and Solar tlinimum," NASA-GSFC, Greenbelt, Md., 1976.

Schield, M.A., and L.A. Frank, "Electron Observation between the hmer Edge of the Plasma Sheet and the Plasmasl_here," J. Geophys. Res., 75, 5401-5414, 1970.

Scudder, J.D., D.L. Lind, and K.W. Ogilvie, "Electron Observation in the Solar Wind and Magnetosheath," J. (;:'ophys. Res., 78, 6535-6548, 1973.

Sears, l:.Iq.,An Introduction to '_hermodun:_mLas, the Kinetic Thcory of Gases, and Statistica_ Mechanias, Addison-Nesley l'ublishing Co., Cam- bridge, Mass., 1953.

Singley, G.iV., and J.I. Vctte, "A Model Environment for Outer Zone Elec- trons," NASA-GSFC, (;reenbelt, Nd., 1972.

Smith, P.H., R.A. lloffman, and T.A. Fritz, "Ring Current l'roton l)ecay by Charge l!xchange," J. (;e:_phy._. Ras., 81, .,01-2708, 1976.

Stevens, J.R., l!.F. Martina, and R.S. White, "l'roton Energy Distribution from 0.0b0 to 3.3 _IoV at 6.6 l!arth llad:ii, " J. :_.opny.,J. h'c.,'_. 75, 5373- 5385, 1970.

Vasyliunas, V.tl., "A Survey of Lou-l!nergy l_lcctrons in the l_vcning Sector of the Magnetosphere with 0(;O 1 and O(;O 3," J. (;,',,}hU:. 1_',:_'., 7_;, 2839- 2884, 1968.

Vasyliunas, V.M., "_lagnetospheric Plasma" in ,':wla_, 'l'_,,_,.'_:t),;,z/ l'hi/_:,._b / 7870, l'roc, of' the Intern. Syrup., l,cllinprad, U.S.S.R., flay 11-19, 1970, edited 1,y li.R. I)ycr, I1. Rcidcl ]'ub. Co., l)ordrecht, The :qethcrlalld_, 1972.

55 !

i I I I I J I ' I i ' I "'

Veraov, S.N., V.V. Mclnikov, I.A. Savenko, alld B.I. Savill, "H(.,asure,lOllt._ of Low Energy Particle Fluxes from tile Cosmos and l!lectron Satellites," L'paoe A'e_:., 6, 746-75(_, 196{_.

Vottc, J.I., R.]l. llilberg, and M.J. Teaguc, "Identification of Satellites Possibly Active I)uring the Iris and Other Orbital Confi2urations," Jn The s'aientifia L,'at.oll'[.te Pro,ifrall_ne L_o,inj th,; ./-ntern, zt-Zonal t4a:fnc,l.OUl,iW.m;c; Study, 45-59, edited by K. _lott and B. Battrick, I). Reldel Pub. Co., l)ordrecht, The Netherlands, 197(_. / Wang, J.R., L.A. Fisk, and R.P. Lin, "Observations of the Scatter-Free Solar-Flare F.lectrons in the Energy Range 20 - 1000 keV," presented at the 12th Intern. Conf. on Cosmic Ray._, 65-70, llobart, Tasmania, Australia, 1971.

Williams, l).J., T.A. Fritz, and A. Konradi, "Observations of Proton Spec- tra (1.0

Wolfe, J.ll., "The Large-Scale Structure of the Solar Wind," in SoZar Wind, NASA SP-308, 170-196, edited by C.P. Sommt, P.J. Coleman, Jr., and J.M. Wilcox, Washington, I).C., 1972.

Wolfe, J.ll., and D.S. Intriligator, "The Solar Wind Interaction with the Geomagnetic Field," Space, Sci. /?ev., _0, 511-596, 1970.