On Positron Radiation Belt in the
Earth's Magnetosphere
A.A. Gusev 1
,U.B. Jayanthi 2
, I.M. Martin 1
, G.I.Pugaheva 1
, and W.N. Spjeldik 3
1
UniversityofCampinas, InstitutodeFsia/DRCC,13083-970, Campinas,SP,Brazil
2
InstitutoNaionaldasPesquisas Espaiais,INPE,S~aoJosedosCampos,SP, Brazil
3
Department ofPhysis,WeberStateUniversity,Ogden, Utah84408-2508,USA
Reeived28February,2000
Theratioofpositron/eletronuxesoriginatedinnulearspallationreationsintheEarth`s
magne-tosphereisonsidered.Itissupposedthatpositronsaswellaseletronsareproduedinthedeayof
hargedpions(
!
!e
)borninnulearollisionsoftrappedrelativistiinnerzoneprotons
withthe residual atmosphere. These positronsand eletrons are aptured inthe magnetosphere
andreatepositronand eletronradiationbeltsofnulear origin. Thepositron/eletron trapped
magnetospheriuxesformedwiththismehanismaresimulatedandtheresultingomputede +
=e
uxratio4appearsinagreementwiththereentobservations. Thisratioissigniantlydierent
fromtheratio1obtainedfromtheprimaryosmiraysourethroughthesamemehanism.
I Introdution
In our reent papers [1,2℄ we showed that signiant
uxes of trapped anti-partiles must exist in the
in-nermost magnetosphere of the Earth. However they
are not of that primordial nature of origin, whih
at-trats the generalinterest of astrophysis ommunity,
but are born in a more trivialproess, as seondaries
from nulear spallation reations of energeti trapped
protons andprimaryosmi rays(CR) withthe
resid-ual terrestrial (or other planet's,for example, Jovian)
atmosphere. These seondary partiles being trapped
bytheEarth'smagnetieldanbeaumulatedthere
andformmoreradiationbelts,forexample,anti-proton
andpositronradiationbelts,inadditiontoalready
ex-istingones i.e. thoseofprotons, eletronsand
anoma-lous CR nulei. These trapped uxes of anti-protons
andpositronsouldbeevengreaterthantheseondary
interstellaruxeswhiharegeneratedbyCRononly5
- 7g.m 2
of interstellarmatter. These uxes are
pro-dued on the 2-3 radiation lengthsof eletronsin the
air[3℄,thatis363=108g/m 2
. Thus,theyould
beabout 15-20 timesgreater than interstellarones at
ertainenergies. Duringgeomagnetiunstableperiods
theyouldpossiblypreipitateinto theatmosphereor
ouldleavethemagnetosphereandappearinthe
inter-planetarymedium,ausingnewpuzzles.
In the same spallation reations the trapped
en-ergeti protons also produe the isotopesof light
ele-3
and 3
He isotopes were atually observed reently by
SAMPEX and CRRES satellites [6,7℄. This disovery
supportstheideathatsigniantuxesoftrapped
se-ondarypositronsouldbeproduedbythetrapped
pro-tonsontherareeddensityoftheresidualatmosphere
at thealtitudesof300{1000km.
Signianttrapped energeti positron uxes ould
beobservedaordingtothis ideaintheinnerestpart
ofthegeomagnetospherewhereatmosphereisrare,but
still existsand whereasuÆientux ofenergeti
pro-tonsexiststosustainthepositronpopulation.
However,until last yearthere wasnolear
experi-mentalonrmationoftheexisteneofapositron
radi-ation belt. Inthepreviousexperimentswithmagneti
spetrometerperformedonboardoftheCOSMOS-1669
and MIR station ontraditoryresults were obtained.
It seems that the new generation of experiments
-nallymanagedtoprovetheidea: InJuly's1999issueof
CERN Courieritwasommuniatedthat Alpha
Mag-neti Spetrometer(AMS)[8℄observedhigh energy(>
200MeV)positronux in theequatorialregionat the
altitude of 400 km with the intensity about 4 times
higherthan theeletronux ofthe sameenergv. The
authorsharaterizedtheresultasverysurprisingand
puzzling. However,wethink thatthis observation isa
onrmationoftheaboveformulatedmehanismwhih
hasbeendevelopedsine1982[3,9℄.
Inthis paperit will be demonstrated that the
II The soure of positrons
Fromatheoretialpointofview,thepositronradiation
beltgenerationisabitmoreompliatedthanthe
for-mationoftheisotoperadiationbelts. The
geomagneti-allyonnedpositronsdonotappearasanimmediate
diret produtofanulearreation. Rather,thebasi
mehanism of positron and eletron nulear ollision
generation isthemuon-positron deayof harged
pos-itivepions andkaons, resultingfrom thesamenulear
reationswheredeuterium,tritiumand 3
Heseondary
nulei are born. The other dierene is that for pion
prodution,thereexistsanimportantminimumenergy
threshold of 290 MeV per inident proton on an
ex-ospheri neutral. This largeinident proton energyis
neessaryforaprotontoprodueapioninthereation
withtheatmospheritargetnuleus.
To be spei, in nulearspallation reationsboth
negativeandpositivepionsandkaonswillbeprodued
alongwiththeseondarynulei. Onetheseshort-lived
partilesareborntheydeayinto:
;K ) + )e
+~+ (1)
Infat,theyaresoshort-livedthattheydeay
pra-tially at the sameplae in the magnetospherewhere
theyareborn. Theirshort lifetime
0
isof26
nanose-onds for harged pionsand 2.197 sfor muons. They
ould travelfrom thepoint of generation for only the
distaneofabout:
0
v,herev-pion's,muon'sveloity,
is a partile Lorentz fator. For example, for 1000
MeVpionthistraveldistaneis: 1000/139.57*2.610 8
s*310 5
km/s=56m. Fora1000MeVmuonthetravel
distane is: 1000/105.66*2.19710 6
s *3.10 5
km/s=
6.25 km. Thus, from the point of view of
magneto-spheri partile apture, it means that the positrons
are born and trapped in the same region of
magne-tosphere, where energeti trapped protons exist. The
onnement areaat L<1:2 isonentrated in avery
restritedanglenearthegeomagnetiequatorialplane.
Duetothatonlythepositronsbornwithveloity
dire-tionwithinthisangle(i.e. neartheplaneoftheparent
proton Larmourrotation)an beaptured andwillbe
takenintoaountinthefollowingonsideration.
In Fig.1 we depit the loation of > 400 MeV
trappedproton uxat thealtitudeof 400km over
at-mosphere based on the AP-8 magnetospheri proton
model[10℄.
Reognizing, however, the strong dynamis of the
eletron radiation belt observed reently [11℄, the
positron belt spatial loation may sometimes be
dif-ferentfromthatoftheparentprotonsandthepositron
uxes ould even disappearfrom the areaand appear
intheinterplanetarymediumastheresultofhigh
geo-magnetiativity.
Figure1.Thespaedistributionofthe>400MeVtrapped
protonsatthealtitudesof400kmaordingtoAP-8model
(Vette,1991).
III The positron beltformation
ToalulatethepositronuxF
e +
(E)wemustintegrate
thepositron dierentialprodution spetrumP
e (E
0
)
(i.e. uxes generated in 1g/m 2
of the air) alongthe
positrontrajetorytakingintoaountthatapositron
ofenergyE wasbornwithenergyE 0
atthedistaneof
X 0
g/m 2
fromthepointofobservation. Ifthepositron
energy losses are (dE=dX); it results in the
relation-ship: F e (E) = R 1 0 P e (E 0 )(dE 0 =dE)dX 0 = P e (>
E)=(dE=dX) [2℄, i.e. the e +
=e ux ratio is
propor-tionaltotheratiooftheirintegralprodutionspetra.
Themeanfrationofenergyarriedawaybyamuon
inapion'sdeayandbyaneletroninamuondeayis
typiallyequaltoq
1
=0:80and q
2
=0:33respetively.
With this simpliation, we an relate the positron
(eletron) P
e
and pion produtionspetraQ
with
thefollowingrathersimpleexpression:
P e (E)= 1 q 1 q 2 Q (E=q 1 q 2 ):
Fromthissetofphysial ideasandamodest
math-ematialonstrutiononeanrathertransparentlysee
that positron/eletron ux ratioat equalenergies per
partileisproportionaltotheratioofpositiveand
neg-ativeintegralpionprodutionspetraQ
(>E)atthe
l=q
l q
2
greaterenergiesthaneletronones:
F e +(E)=F e (E)= Q +(>E=q 1 q 2 )
Q (>E=q
1 q
2 )
Thepionprodutionspetrafor
pionswere
ear-lieromputed[1℄fortrappedprotonuxesat L=1:2.
These arepresentedin Table1. Fromthis oneansee
thatthissouremehanismprovidesfourtimesgreater
positivepionuxesthannegativepionuxesatpion
en-ergiesofmorethan600-800MeV.Consequently,these
produtionspetraofseondarypartileuxesan
sup-ply four times greater positron uxes than eletron
uxes at energies morethan 150- 200 MeV on these
geomagnetiL-shells.Indeed,thisispreiselythesame
positron-to-eletronuxratiothatwasobservedinthe
AMSexperimentnotedaboveforpositron/eletronux
ratio at energies of more than 200 MeV per partile.
Wethusonludethatthepuzzleappearsresolved,and
thatthereexistsasimplephysialexplanationbasedon
the knowledge of the nulear ollision reations from
whihmostpositivepionsareborn.
Table1. Thepionprodutionspetra.
The geomagnetially trapped protons have
rela-tivelylowenergies(fromanulearinterationpointof
view) and less than 1 seondary pion per reation is
generated. Certainlytheyhavepositive(!) hargedue
to thehargeonservation law. Inomparison, in the
aseofpositronsbornbyprimaryCR,havingtensGeV
energies,agreatermultipliity ofpionsgenerated,and
thepositronux exessis negligible.
TotheoretiallysearhapositronuxfromtheCR
soure,weusedaversionofanulearreationomputer
ode SHIELD for Monte Carlo simulation of hadron
asades in matter[12℄. Usingthis ode weomputed
positiveandnegativepionprodutionspetrafrom
pro-tonswith variousenergiesorrespondingto the
upper-most range of trapped proton energies (500 MeV - 2
GeV)intheinnermostpartsofthemagnetosphereand
toCRprotonomponent(morethan8-10GeVforthe
magnetospheri equatorial region). The ratios of the
integralprodutionspetraofpositiveandnegative
pi-ons for various parent proton energies are plotted in
Fig. 2. Aswementionedabovethis ratio isthe same
ase +
=e ux ratio. Fromthis gureonean
immedi-soureislessthanfromthetrappedprotonsoureand
equal1formorethan100MeV positron energies.
Figure2.Curve1: Thedependeneofthee +
=e -uxratio
ontheparentprotonenergy;urves2-7: Thedependene
ofthe +
= integralprodutionuxratioande +
=e ux
ratioontheande
energies,orrespondingly.
Intheinnermostpartof magnetosphere,at low
L-shells of L 1:2 it is diÆult to expet an existene
of hundredsMeVtrappedeletronsof diusiveorigin.
As it was shown in [13,14℄ the eletrons an not
dif-fuse there from the boundary of magnetosphere
be-ausetheylossitsenergyduetosynhrotronradiation
andundergostrongpith-anglesatteringwithplasma
wavesattheregionofL3onthewayintoinner
mag-netosphere. Thus, a diusive eletron omponent at
those energiesdoesnotdereaseomputede +
=e ux
ratioobtainedfrom nulearsoureandinobservations
in theinnermostpartofmagnetosphereexatlye +
=e
ux ratio equalto 4 is expeted to be registeredin
the ase of nulear reationsoure of magnetospheri
positrons.
IV Conlusion
A mehanismforgeneration oftheterrestrial positron
radiationbeltduetonulearreationsoftrapped
radi-ationbeltprotonswiththenuleioftheneutralatoms
in the upper atmosphere/exosphere region is
onsid-ered. The ratio of positron/eletron uxes omputed
four times the ambient eletronux in theequatorial
region for partilesof morethan 200MeV.That is in
exellentagreementwiththeAMS-instrument
observa-tions reported in the literature. In ontrast, the CR
soure in this region providesa positron/eletron ux
ratioaboutequal1. TheCRuxesarethusnot
respon-siblefortheobservedinnermostradiationbeltpositrons
and eletrons. We believethat this physial
onsider-ation will help to solvethepuzzle of theuniqueAMS
positronbeltobservation.
Aknowledgements
TheworkwassupportedbyFAPESP-SP
(93/4978-0) andCNPq(300015/99-2).
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