PROCEEDINGS OF THE IRE

A Study of the Effect of Geomagnetically TrappedRadiation on Unprotected Solar Cells*

J. W. KELLERt, R. D. SHELTONt, R. A. POTTERt, AND L. LACYt

Summary-The problem of solar cell damage by proton andelectron radiation is treated analytically from a theoretical andempirical viewpoint. The general approach is to form a damage inte-gral, consisting of the integral over the energy spectrum, for bothelectrons and protons, of an integrand formed by the product of thedifferential energy spectrum and a damage function, and to relatethis damage integral to the deterioration of solar cells under irradia-tion. The damage function is considered theoretically from themicroscopic viewpoint of collision theory and empirically by usingavailable experimental data.

By making several approximations and assumptions, the datafrom the solar cell patches on Explorer XI is compared with predic-tions based upon the empirical relationship developed for the damageintegral,

O NE OF the principal problems in the explorationof space has beeni anid will be the provisioni ofadequate power for satellites and probes which

are required to operate conitiniuouslv over lonig periodsof time. Power in the formn of solar radiationi has beenreadily available in the space explored to (late, anidsilicon solar eniergy converters, comnonly called solarcells, have founid popular anid depenidable applicationi inmany smnall satellites and probes as the imieanis of c-on-verting solar radiationi energy to electrical energy.Very sooIn after the discovery of eniergetic clharged

particles trapped in the magnietic fieldl of the earth, itwas recognized that solar cells mliust be used witlh cau-

tioIn because of their susceptibility to radiationi damlage.Satellite designiers began to miiake studies to (letermiinlehow miiuch transparent coveritig of what materialshould be use(d to protect solar cells for the requiredsatellite operatinig lifetimne in a giveni orbit. The shield-ing of solar cells was doine reluctantly because of theincreased weight, labor, cost and asseimblv timiie inl-volved. The shieldinig also reduced the solar cell ef-ficiency anid created additionial problemls inl passivetemnperature conitrol and systems enginieerinig.

GENERAI. COTIPt TATIONAI PROCED RE

The solar cell depends for its operationi onl a highly-ordered arranigemiienit of the atoms comprisinig the cellin1to a sin1gle crystal. Eniergetic charged particles presenitin space canl create disorder in the crystal by collidingwith the atomls anid displaciing themi from their propersites in the crystal lattice. This inicrease in disorder is re-flected in several aspects of the operationi of the cell.

* Received Jnnlie 11, 1962; revisedl manuLscript received, August27, 1962.

t Research Projects Division, George C. Marshall Space FlightCeniter, Huntsville, Ala.

The damage to a solar cell by space radiation is as-sumed to be a function of the damage integral D de-fined by

D -r r[f(t), E] D(E)dE dl, (1)

where E is the particle energy, t is the time, 4[4(t), Elis the functioni representing the distributioni in spaceand energy of the charged particle raditioni anid D(E)is a damage function dependent onl the kinid of solarcell, the kind of particle radiation and the energy of theparticle. The position vector f(t) locates the satellitein the radiation belt and is a functioni of timiie and theorbital parameters.The distribution functioni k [(t), E3 is separated for

computational purposes into a space and timle part,despite the general agreemiient that the shape of theenergy distribution funiction must varv with positioni,and is written in the formii

44r(t), E] = N[f(t)]44(E), (2)

where N[r(t)] represents the radiation initensity inparticles/cm2 sec as a funiction of position and +(E) isa normualized functioni giving the shape of the energydistributioni. The directionial properties of the spaceradiation are iginored, except that /(f, t) is reduced by afactor of two to accounit for the fact that self shieldinigin a satellite is quite sufficient to protect the solar cellfrom attack fromii the uiiderside.

Because of the difficulty of calculating theoreticallythe damage to solar cells froml space irradiation, thereis conisiderable advantage in developinig eiiipiricaldamiiage formulas fromii the data resulting fromii thelaboratoryt irradiationi of solar cells b-y miiotnoeniergeticbeaims of charged particles.The starting poilnt for our empirical development

is (1), which conltains the assumnption that the damiiageis indepenident of the rate of irradiationi aid suchi eni-viroinmeintal factors as the temiiperature and the miianniierin which the cell is operated during irradiationi. Awealth of radiationi effects iinformatiotn supports theviewpoint that this is not always a com-ipletely safeassumption. In using (1), we will assume that damiiagein-tegrals are additive and substituLtive, which will evokecriticism fromi the strong believers in syrnergismn. Withthis last assumptioin, we can state that two irradiationisproduce the same damage if their damage initegrals areequal. In particular, a laboratory irradiationi witlh

N\lovember2320

Keller, et al.: Effect of Geomagnetically Trapped Radiation on Solar Cells

particles of energy Ek is equivalent to a space irradia-tion if

1DY(D(Ek)D(Ek) =- O[Jf[(t), E]D(E)dE dt, (3)2Et

where 1P(Ek) is the integrated particle flux, measured inparticles/cm2, to which the solar cell is exposed in thelaboratory, and D(Ek) is the damage function for par-ticles of energy Ek. The factor of 2 is included becauseof self shieldinig in space irradiation. The left side of(3) is formally equivalent to a damage integral, and ifthe damage function is appropriate, does not necessarilyarise from irradiation with the same kind of particle asis associated with the right side. We may, for example,attempt to equate a laboratory irradiation with mono-energetic protons to a space irradiation represented bythe sum of an electron damage integral and a protondamage integral of the form shown on the right side of(3). In this case we could write

4?p(Ek)Dp(Ek) =-I I4v [f(t), E]Dp(E)dE dt2 E t

+ +ff e[*(t, E]De(E)dE di2 E t

_ (Dp + De)= 2

(4)

where the subscripts p and e refer to proton and elec-tron functions, respectively, and Dp and De are theproton and electron damage integrals.

It is found that the deterioration of the power outputP froml a solar cell under irradiation by charged par-ticles canl be represented by an equation of the form,

P

where Po is the inlitial power, (D(Ek) is the integratedflux associated with the laboratory irradiation and A,B anid C are constants. In Figs. 1 and 2, (5) is fitted toexperimental data to obtain the constants A, B and C.It is uniderstood, of course, that the constants in (5) de-penid onI the type and loading of the solar cell. As seenin Figs. 1 and 2, the power output under optimumloading and the short circuit current follow roughly thesaimie decay law.By solvinlg (4) for 4D(Ek) and substituting into (5)

for 4(Ek) we obtaiii

- = A - B In [C + (Dp + De)/2Dp(Ek)j (6)

as the expression for the power during a space irradia-tion. The constants A, B and C are obtained by acurve fit of (5) to the experimental data obtained dur-

x

vE

7.00-

wav R- V--fl-

5.00 -

A-Bln((D+C)

4.00-

3.00 - _1.0

A=32.401B 1.1075C= O.IxiO"

2.0 3.0

INTEGRATED FLUX (particles/cm) x 10-'

Fig. i-A fit of the curve Pmax=A -B In (C+4) to the data ofLoferski and Rappaport [3]. In this equation, P is the power out-put of a solar cell exposed to a constant source of light during anirradiation with a beam of 17.6-mev protons; 4 is the integratedparticle flux; A B C are constants.

I10

INTEGRATED FLUX , (particles/cm2)

Fig. 2-A fit of the curve I/lo=A -B ln (C+4+) to the data ofDenney, et al. In this equation, I is the short circuit current oult-puit of a solar cell exposed to a constant source of light duringirradiation with 740-mev protons; Io is the output at the begini-ning of the irradiation; (F is the integrated particle flux; A B Care constants.

ing laboratory irradiations and the quanitities

D p(E,) rESt d(t) E] [Dv(E)/Dv(Ek)]dE dt (7)

and

D- [De(El)!Dp(Ek)iD:p(Ek)

J ,[f(t),E][De(E)/De(Et)]dE dt (8)

are calculated from a knowledge of the satellite orbit,which yields f(t), a knowledge of the radiation field,which yields 4, [r(t), E] and Pe[f(t), E] and a knowledgeof the damage functions Dp(E) and De(E).

o3

23211962

PROCEEDINGS OF THE IRE

To illustrate how Dp(E)/Dp(Ek), De(EZ)/Dp(Ek) andDe(E)/De(Ei) of (7) and (8) are determined experi-mentally, suppose that a number of solar cells areirradiated with particles of different types and energiesuntil the power output decreases by 25 per cent.

Following the same reasoning as before we equatethe damage integrals associated with equal damage andobtain

4p(Ej)Dp(El) = 4Ip(E2) Dp(E2) = .*Dp(E,) Dp(E.)= Ie(Em) De(Em) =- * - X (9)

From this system of equations we can write

Dp(En)/Dp(Ek) = 4p(Ek)/4p(E.) (a)

De(Em)/De(E 1) = 4P,e(EI)/4.e(Em) (b)

De(EI)/Dp(Ek) = 4Ip(Ek)/4?e(El) (c) (9)

where m and n are free indexes and k and I are ref-erence indexes, as in (7) and (8). Since the I),(En) and4)e(Em) are experimentally measured as the integratedfluxes required to cause 25 per cent deterioration, thepreceding set of equations determines the ratios ofdamage functions, which can be plotted as curves toyield Dp(E)/Dp(Ek) anid De(E)/De(Ei). Eq. (9c) pro-

vides the ratio De(Et)ID,(Ek) needed in (8).

PROTON DAMAGE

If we assume that the proton damage function D(E)is proportional to the number of atoms displaced, thework of Seitz and Koehler [1] can be used to computethe ratio Dp(E)/Dp(Ek) of (7). The number of dis-placements Nd per incident particle is given by

Nd(E) = n(E)v(E) (10)

where n(E) is the number of primary displacementsper incident charged particle and v(E) is the average

number of displacements per primary displacemenit. Inthe proton energy range from 1 to 1000 inev, theCoulomb collision cross section varies inversely withenergy so that

K

n(E) =- (11)

and

D(E) _Nd(E) v(E)Ek~~~~~(12)

D(Ek) Nd(Ek) v(Ek)E

The quantity v(E) is given by Seitz and Koehler as

)v(E 0.85+ 0.561 In 13/

101

IoO

02

LOFERSKI &.~~~~~ _~~~~1 'PJ104 105 106

E tev)

'ATTERSON

8OS 109

Fig. 3-A plot of D,(E)/Dp(Ek) based on the theory of Seitz anidKoehler and normalized to the 17.6-mev proton irradiationi ofLoferski and Rappaport [3].

where

X .+

4MIM2 E0.0103E. (14)

(Ml + M2)2 Ed

In (14), M1 and E are the mass and energy of the protonand M2 and Ed are the mass and displacemnenit energy

of the silicon atom. Ed is given by Loferski ani(d Rappa-port [2] as 12.9+0.6 ev. To transfer this almounit of

energy to a siliconi atonm, the proton en-ergy m11ust ex-

ceed 98 ev.

In Fig. 3, the theoretical expression for D(E)ID(Ek),equal to EkV(E)lEV(Ek), is tnormalized to the data of

Loferski and Rappaport [3] for 17.6-mev protons anidplotted as a funictioni of E. By usinig (9a) a:nd (latasupplied by Patterson [4], a checkpoint att 440 imiev

was provided. The apparent lack of agreemient between-Browni [5] aind Denney [6] on the relative importanceof Coulomb displacenments at high energies is niot par-

ticularly critical to the calculationi of solar cell dama,_tgeby space radiationi, since Imlost of the daniage is doneby protons of comnparatively low energies. IFlor protoniswith energies of approxinmately 3 miev or lower, thedamage function as expressed by (12) and Fig. 3 be-comnes iniappropriate because of the rapidl change ofD(E) over distanices comiiparable with the thickiness ofthe active layer of the solar cell. Obviously, the theorycannot be expected to apply for protonis of energiesmnuch less than 1 m11ev, sinice the total ranige at thiseinergy is less than the thickness of the optical coatin1gand dead layer oni most solar cells. Elowever, sputterinigof the outer layer cani be produced by protonis havingenergies as low as the 98-ev threshold energy previouslymentioned.

I04r

0o2

November2322

Keller, et al.: Effect of Geomagnetically Trapped Radiation on Solar Cells

To examine the nature of the damage integral forprotons, we will assume that the distribution functionhas the form

[rf(t), E] = N [f(t) ]E-n (15)

with n> 1. By assuming that Xm>>l in (13) and re-membering that Ek/v(Ek) is a constant, (12) can bewritten in the form

D(E) = (F + GlnE)/E *. (16)

where F and G are lumped constants.Using (15) and (16) the damage integral becomes

t=T r E=oo

D = N[f(t)]dtf It=0 =-Et

The integral over eniergy can be calculated in closedform and D becomes

rt=T-

D = fTN[f(t)]dt FEt-n/n=0++

InEt 1I\+ GEt-11 n- + n2J (18)

Cb

E (MEV)

Fig. 4-The proton energy spectrum showing data from Hess[8] Freden anid WNhite [7] anid Naugel and Kniffeni [91.

Em is the minimum energy capable of being countedand N[r(t) ] is defined in (2). It follows that

This integral is quite sensitive to the damage thresholdenergy Et, and indicates the importance of the lowenergy protons in producing damage. This finding com-plicates the damage prediction immensely, since it isin the low energy region of the proton spectrum thatthe greatest uncertainties exist. Freden and White[7] show a maximum of c(E) at 35 mev and nothingbelow 17 mev, a region of great interest in predictingsolar cell damage.The difficulty of dealing with a damage integral

which is extremely sensitive to the threshold energy Etand the problem of treating proton trajectories alongwhich the energy changes rapidly can be avoided byassuming that there is a maximum in the proton energydistribution function occurring somewhere below 1mev. By combining the theoretical spectrum of Hess[8] with the experimlental spectrum of Freden andWhite [7], the composite spectrum [10] of Fig. 4 wasobtained. Shown also in Fig, 4 are spectral shapes fromNaugle and Kniffen [9].

In the study of proton radiation in space, it happensthat very good data on energy spectra are provided byemulsion pack experiments whereas charting of theintensity of the radiation regions is best done byefficient threshold detectors in the form of shieldedgeiger tubes or scintillation crystals. In our calcula-tions, the threshold detector has a normalized countrate R(f) given by

rE=oo

R(r) = TN[r(t)]4.(E)dEE=m

(19)

E(fE=xNff[(t) ] = R(r) / O(E)dE.

E=E171

(20)

Using (2) and (20), the protoni damage integral becomiiesE=oo t=T

DP = f J R [f(t) ] ( (E) Dp(E)dE diE=Et t=0 / E=oo

4O(E)dE, (21)E= E,n

ort-T rE=oo

Dp= f R[f(t)]dtf E (E)D(E)dEt=0 E=Et

E=oo

,O(E)d.EE=Em

(22)

where Et is the threshold energy for daiiage. Eq. (22)is substituted into (6) to compute solar cell behaviorunder space irradiation, where

Dp r t=T rE=ooDP(EA=) J R[qr~m7(t)]dt +(E)[Dp(E)1Dp(Ek)]

Dp(Ek) t=0 E=Et

/ E=

/J (E)dEE--E

and Dp(E)/Dp(Ek) is given by Fig. 3.In Fig. 5, a plot ofJ E=oo fE=

J E(E) [Dp(E)/Dp(Ek)]dE J (E)dE=EB E=Em

(23)

(24)where the shape of +(E) is supplied by emulsion data,

1962 2323

E- (n+') (F + G In E)dE. (I 7)

PROCEEDINGS OF TIHE IRE

0'

1072

cr

LLJF--z

LiJ

:E

10o

00

10-1 10°

Et (MEV)

Fig. 5-A graph of

0p(E) [Dp(E)/Dp(Ek)]dE/ fE-t o=40 mev

as a function of the threshold energy Et.

op(E)dE

as a function of Et is given, using the composite spec-

trum of Fig. 4, Dp(E)/Dp(Ek) of Fig. 3, and Em equalto 40 mev, corresponding to the threshold of thecounter used to map the proton belt.

In computing the time integral of (23) for the case ofExplorer XI, the ephemeris of the satellite was ob-tained in geomagnetic coordinates and used in conjunc-

tion with a map of the proton belt to obtain R [r(t)],which was then integrated with respect to time toyield a proton exposure of 12.0 X 107/cm2 day above40 mev.

ELECTRON DAMAGE

Because of its relatively small mass, an electron musthave approximately 0.145 mev of energy to transferthe displacement energy of 12.9 ev to a silicon atomon collision. The graph of De(E)/De(Ej) shown in Fig. 6was obtained by normalizing the electron damage func-tion of Brown [5 ] to the data of Loferski and Rappaport[3] for vacuum irradiation with 1.7-mev electrons.Data from Bill Cherry of Ft. Monmouth for 0.750mev electrons is also shown in Fig. 6.The energy spectrum assumed [10], [II] for electrons

is shown in Fig. 7. A plot of

(E) [De(E)/Dc(Ei)JdE/ 4(E)dEEt Em

vs Et is shown in Fig. 8. The integrated flux above

20 kev was estimated to be 16.6X 10ll/cm2 day. Fromthe data of Loferski and Rappaport, the ratio ofDe(El)/Dp(Ek) for 1.7-mev electrons and 17.6-miiev pro-tons is 3.5 X 1010/5 X 1011 or 7 X 10-1.

THE DAMAGE ( URVETable I is a compilationi of the data presented in the

previous discussions of electron- and proton damage,and contains the information iiecessary to write anequation of solar cell output as a fuinction of time. Be-cause the damage integral for electrons is conisiderablysmaller than that for protoins, because of the greateramount of experimentationi withl electroni beams ofvarying energy and the relatively greater knowledge ofthe energy spectrums in the region where mnost damnageoccurs, and because of the shape of De(E) and Ne(E)shown in Figs. 6 aind 7, we can assume with little errorthat Et is zero for electronis. If we assume E==0.1 imievfor protons, which is justifiable wvith the spectrum wehave assumed, the damage equation becomes

-= 3.335 -0.103 In (7 X 109 + 1.32 X 10't), (25)Po

where t is measured in days. This equation can be usedalso for the decay of the short circuit current output.Patterson [4] notes that there is little difference be-tween the relative decay of the power output underreasonable operating conditions and the short circuitcurrent output. This viewpoint, which can be deducedfrom elementary theory if the internal resistance of thecell is assumed not to change radically, is also supportedby the data of Loferski and Rappaport. On the otherhand, if the cell is loaded externally for operationi inearmaximum power output as was the case for Explorer XI,the decay in power ratio P/Po is roughly twice as fastas that of voltage ratio l JVo, where the voltage outptitis measured across the external load.

SOLAR CELL DECAY ON EXPLORER XI

Explorer XI (NASA S-15 payload) was placed inorbit on April 27, 1961, with an initial apogee of 1799.05km, perigee of 490.81 kti, and an inclination of 28.80degrees. The satellite was initially spinninig about itslongitudinal axis at approximately 400 rpm, butgradually over a 30-day period in orbit this unstablespin decayed into a tumble about an axis perpendicularto the longitudinal axis of the satellite. It can be seenfrom the geometry of the satellite shown in Fig. 9 thatthe area normal of the unprotected solar cells is per-pendicular to this tumble axis.The satellite carried two solar cell test patches, each

consisting of ten cells in series. The cells were Hoffmann on p type with an efficiency of approximately 10 percent. The circuit was designed to give the mnaximum

2324 Novrember

Keller, et al.: Effect of Geomagnetically Trapped Radiation on Solar Cells

100

0~~ ~~L)

z tO-'

LL

w

00Iz0

w

w

l0-3

0 0.500 1.0 1.5

E (MEV)

Fig. 6-A plot of De(E)/De(El) based on a curve by Brown [5] andnormalized to the vacuum data of Loferski and Rappaport [31for 1.7-mev electrons.

C,)

z

w

I-

w

cc

10' -

10 ' -

10' -I 1 -I.0 0.10 0.20 Q30, 0.40 Q50 0.60

ELECTRON ENERGY (MEV)

Fig. 7-The electron energy spectrum [101, [11].

0.25

0.20

ct-0

w

z

CD

0

0.15

0.10

0.05

0

0 0.1 0..2 0.3

Et (MEV)

0.4 0.5

Fig. 8-A graph of

f 'ke(E) [De(E)/De(EX)]/ fiI ej(E)dE.E=Et 2 kev

TABLE IRADIATION DAMAGE PARAMETERS

Quantity Magnitude Note

Em 40 mev proton counter threshold20 kev electron counter threshold

rtTRp[f(t)]dt/2 12X107/cm2 counts/day on proton

t-O counter with 40-mevthreshold

t=T counts/day on electronR.(r(t)Idt/2 16.6X 10"1/m2 counter with 20-kev

t=0 threshold

Ek 17.6 mev proton energy in labora-tory experiment used asdamage standard

Et 1.7 electron energy in labora-tory experiment used asdamage standard

Dp/2Dp(Ek)Et=0.1 mev 1.3X108t t measuired in daysEt= 1.0 mev 1.OX108tEt= 10.0 mev 0.32 X 108t

D8/2Dp(Ek)Et=0 mev 2.0X1O7t t measured in daysEt=0.3 mev 2.0X107tEt=0.45 mev 1.6X106t

A =3.335B =0.103C=7X109

I

1962 2325

PROCEEDINGS OF TIIE IRE

SOLAR -CELL TEST PATCH LOOP ANTENNA

17;~4' --I 09t E2744 - ------445

TA WEIRHT 95.3f LBS.

Fig. 9-Conifigurationi of Explorer XI showinig locationof solar cell test patch.

81' T -- V -.180 7 2i--

160

40

10

20 j--- ---

80

40

20

o i _ 11 1_ 1~~I I111 1l_Li50 70 90 110 130 150 170 190

DAYS AFTER FIRING

Fig. 10-The angle the momentum vector makes with the solarbeam vs days after launch for Explorer XI.

4.0-

ik 3.0-

0

J 2.0-

o 1.0-

I I1 I 1 1, J

44

~4-4L 4-

3.8

3,634-

34.0;

3.2

3, o

30

CPoc°o

(W 0 0icGE o o',

A

GO 9b I

a ~ ~ ~ ~ --- -- - t + _ _1-- i-50 70 90 1O 130 150 170 190

DAYS AFTER FIRING

Fig. 13-Solar cell decay vs (lays after lauinch with voltagecorrected uising Explorer VI! calibration curve.

LLJ(9

0

inLLI

LUJcccr0(-

4+73

4.3

4.-O03.9

e

3.7 0

3.5

3.3 -

2.9

2.7

-I I I T - - I

o eoIA A)?00 %

0

oo09 W%oo0 A A

0 00

I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~50 110 17050 70 90 10 30 i50 70

DAYS AFTER LAUNCH

Fig. 14-Solar cell voltage vs days after launch using linearfit of Fig. 12 for angular correction.

Li 1~ T i- -I20 40 60 80 100 120 140 160 180 200

DAYS AFTER FIRING

Fig. 11 -Average solar cell voltage vsdays after launch for Explorer XI.

.8 - /

. .4 .5 .6 J7 .8 , .SINE a

Fig. 12 -Calibration curves for voltageangular dependence of solar cells.

P

P. 48

.40 _

.32

.24 _

.16

.0800

( 20 40 60 80 100 120 140 160 180DAYS AFTER LAUNCH

Fig. 15-The comparison of experimental and predicted behavior ofsolar cells on Explorer XI. Curves I and II were compuited usingspectra I and II of Fig. 4.

2326 Nozvember

vVmoX

n-l I -1 1 1- Ifi 11 II It Itu

Keller, el a!.: Effect of Geomagnetically Trapped Radiation on Solar Cells

power to the external load of 100 ohms when the patchwas looking directly at the sun. The voltage drop acrossthe load was fed to the telemetry and used to deter-mine the deterioration of the cell.The problem of experimentally determining the solar

cell decay was approached by trying to determine themaximum voltage output of the solar cells as a func-tion of time after launch. As used here, the maximumvoltage output is defined as the value of the voltageoutput when the solar cells would be looking directlyat the sun.The orientation of the satellite's angular momentum

vector was determined from the method used byNaumann, et al. [12], [13]. This method of determiningthe angular momentum vector makes use of a RFsignal transmitted by the satellite. The satellite pay-load itself forms an asymmetrical dipole resulting in afour-lobed antenna pattern which Naumann used todetermine the astronomical coordinates of the angularmomentum vector. The solar aspect angle a was foundby taking the dot product between the sun vector andthe angular momentum vector. A plot of a vs daysafter launch may be found in Fig. 10.

Voltage readings from the solar cell test patch weremeasured for approximately 120 days. For each daycare was taken to insure an average voltage readingfrom a group of five passes which were the same passesused to calculate a. Fig. 11 shows the average voltagereadings as a function of days after launch.A calibration curve was obtained by a least squares

curve fit of the points in Fig. 12. From Fig. 12 in theratio VI Vm, Vm is the true value of the maximum solarcell voltage for those days when a= 900. Since Vm itselfvaries as a function of time (caused by solar cell de-cay), different values of Vm, were used. For each valueof V,m, a period of approximately 10 days was used toobtain 10 points of Fig. 12. We assumed Vm to be ap-proximately constant over this ten-day period.

For the points of Fig. 12, a first degree curve fit wasassumed and a voltage decay curve prepared in Fig. 13.Fig. 12 also shows the experimental calibration curvefor the solar cell patch of Explorer VII. Using thiscalibration curve, Fig. 14, showing maximum voltageoutput vs days after launch, was obtained.

In Fig. 15, the voltage output of Fig. 14 has been con-verted to power output and compared with predictionsbased on various assumptions of spectrum and damagethreshold energy.

CONCLUSIONSWith the data presently available, the prediction of

solar cell lifetime in the radiation belts is not straight-forward and reliable. The proton damage function nieedsto be studied experimentally in the energy regioni from0.1 to 10 mev, especially in view of the recent measure-ments of Freeman [14]. The damage integral is sensi-tive to the energy distribution, and it appears thatthe radiation measured by Freeman is an importantunknown factor in solar cell lifetime, and will remainso until good measurements of the energy distributionare made.The prediction of solar cell lifetimes is another illus-

tration of the fact that, although a wealth of radiationmeasurements have been made and much is knownabout trapped and cosmic radiation, we are still farshort of the detailed description necessary for goodengineering design.

REFERENCES[1] F. Seitz and J. Koehler, "Advances in research and applica-

tions," in "Solid State Physics," F. Seitz and D. Turnbull, eds.,Academic Press, Inc., New York, N.Y., vol. 2, pp. 305-448;1956.

[2] J. Loferski and P. Rappaport, "Radiation damage in Ge and Sidetected by carrier lifetime changes: damage thresholds," Phys.Rev. vol. 3, pp. 432-439; July, 1958.

[3] J. Loferski and R. Rappaport, "The effect of radiation on sili-con solar-energy converters," RCA Rev., vol. 19, pp. 536-554;December, 1958.

[4] J. L. Patterson, NASA, Langley Res. Ctr. (private communi-cation).

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