N 4S4.-U<.-/ 71) 590 AEROSPACE REPORT NO. A TR-83(9990)-3 

NASA-CR-174596 19840004988 

'The Mimas Ghost Revisited: An Analysis : of theEle~tronFll1x and Electron Microsignatures 

Observed in the Vicinity of Mimasat Saturn 

-----------

Prepared by 

D. l"CHENETTE Space SdencesLaboratory 

The A~rospace Corporation EI Segundo, calif. 90245 

and 

E.C. STONE California Institute of Technology 

Pasadena, Calif. 91125 

8 June 1983 

I: j'j eli"' 1983 ut.. ... r (J, l '.,., \-' 

.LANGLEY RESEAR(;f.; ,-::ENTER LIBRARY. NASA 

HAMPTON, VIRGINIA 

Laboratory Operations 

THE AEROSPACE CORPORATION 

1111111111111 1111 11111 11111 1111111111 11111111 NF00414 

--------

! 

, r~~:l' , , .. 

! / 

LABORATORY OPERATIONS 

The Laboratory Operations of The Aerospace Corporation is conducting exper­

imental and theoretical investigations necessary for the evaluation and applica-

tion of scientific advances to new military space systems. Versatili ty and 

flexibility have been developed to a high degree by the laboratory personnel in 

dealing with the many problems encountered in the nation's rapidly developing 

space systems. Expertise in the latest scientific developments is vital to the 

accomplishment of tasks related to these problems. The laboratories that con­

tribute to this research are: 

Aerophysics Laboratory: Launch vehicle and reentry aerodynamics and heat transfer, propulsion chemistry and fluid mechanics, structural mechanics, flight dynamics; high-temperature thermomechanics, gas kinetics and radiation; research in environmental chemistry and contamination; cw and pulsed chemical laser development including chemical kinetics, spectroscopy, optical resonators and beam pointing, atmospheric propagation, laser effects and countermeasures. 

Chemistry and Physics Laboratory: Atmospheric chemical reactions, atmo­spheric optics, light scattering, state-specific chemical reactions and radia­tion transport in rocket plumes, applied laser spectroscopy, laser chemistry, battery electrochemistry, space vacuum and radiation effects on materials, lu­brication and surface phenomena, thermionic emission, photosensitive materials and detectors, atomic frequency standards, and bioenvironmental research and monitoring. 

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Space Sciences Laboratory: Atmospheric and ionospheric physics, radiation from the atmosphere, density and composition of the upper atmosphere, aurorae and airglow; magnetospheric physics, cosmic rays, generation and propagation of plasma waves in the magnetosphere; solar physics, infrared astronomy; the effects of nuclear explosions, magnetic storms, and solar activity on the earth's atmosphere, ionosphere, and magnetosphere; the effects of optical, electromagnetic, and particulate radiations in space on space systems. 

,( RJ:.\iS[)-TR-'i33-2.'j '3 HtJ/\:; I t~ijER.E~ R.~ P: 

t 5 AlJ;, ,-JCsf'.iE5 ~ D : H ~ "3'2. A\.J/~(J4'{SER~ U: c:: "2.:) ~\j/R.ll~E.~ c:: \J ~ 

·-"-------~ ... -'f 

.---. - - ~-. - .. -- _....-'. __ .- . ---~~.---.-

---···-~3-·3·,-~-~--·-~t--~·-~'--r~·--R~.!/81R-8·3 ('3'3\30) '~3-' D I SPLR~-l 13/ 2;~ 1" 

1 ~ 2b: t 745\36 RT~.-i33 ~·3jijf1)-3 \jl\it~,LAS:~ I f 1 ElJ DOf~\Jl't\El':rT Tt\e \~l\1rnas f~r!Qst re\j~s\te(l: ~n\t~rQs\gr!atl)r-f::S QDser':.!efj \f"! tr1e :·!lC1f";\t·l (li t:11tftaS at S·3.tt~rr~ 

A'.J1H: ·A/~~HE.r;!E.T1E~ u: L:; B/STl}~\iE.~ F - f.~ PRR~ 8/ (t~a1 \ f()rr~\a if1St: Qf Tecr·~: -.:' l~l)f~P: Aerl)SpaC:2 C:C)fP:! E) :=.f;9t)r!O{); ~~cli it: t~R\jS: ;' :~ELE.t~.TR.(j~·:,15/t~i'~' I r:1H~i/~!~::' It-;l\~HTtJR,E fif:.!HLV5 IS ttt I t:.\S: / ABSt)R.f'11 t)r:.\ SPEt~ 1" R.Hl ELEl=.TR.f)~':,iS/· RAL: I Al DIS TR.t BljT I (}t;i 

-~·ABS:' Ar"! ar-!dl':lS1S c~i tr-!e e1ectr0r·~ a~)s()rt=!t10r~ si!~r;c{tt\rr: f)~)S~r\lE:(~ t)'}" trv:~ Cosrn\c R~r:.l S'::lstern (C.RS) t)f!' \io'/age 2 r~ear trv:~ f)rb it of \'~1 rnas 1 S t=!reseritec\: l).~e f 1 r·~d­tt,at t~-v?se l)flser':.lat.\Of"!s Cariri(Jt rJe e}~_pla'r!e(l as t\-'it: absorpt10fi s19r!att~re crf l\:~1fnaE;: ~~()In\)1r·!9 P1c~rleer l"i arv:j \i(r/a9~r 2 rneaStH"erner·!ts (if trv2 e1ectrc;!! fW\l.J){ at \":11rnas's ort:1t i.L=3~1)~ tne t1r~d ::!r~ e'Ectrejr{ spectrtJ,Hl \)~ri,ere t~~f)stw of tr~e 1'lJ)~. ab(j\!e appr())~, 'i~)(j ~·,.e\l 1S {~:[)r~c-f:r~tratec~ ["lear 1 to 3 t!\e\l: Tt'!e e)~.t=H~~ctec\ ~1mas absorpt1on s1gnatufe \s calculated from th\s spectrum neg\ect1ng 

electrons1s obtained. ~'th a d\ffus\on coeif1c\ent thts large, both the \'o':'ag~r 2 ar~(\ tl--!e P1Qr~e~r l'i srna~\~~sca1e e1ectrfj!1 abS(JfPtiof", Si9r"!atlJfe o'Dser\lat1!)f"!b .ir'~ l·i\~rnas's Qrt)i\ are er!19rnatic: Tr-it~S ~}.~e refer to trv:~ rnf:;r:riar~;~sfn 1()r. f-.ltC;CtJC1f"!9 tr1E:Sf: S1gnatt~res as t(~e 1~;11H!.3S f~riQst~ R C":)t~(\ Qf 

Aerospace Report No. ATR-83(9990)-3 

THE MIMAS GHOST REVISITED: AN ANALYSIS OF THE 

ELECTRON FLUX AND ELECTRON ~rrCROSIGNATURES 

OBSERVED IN THE VICINITY OF MIMAS AT SATURN 

Prepared by 

D. L. Chenette Space Sciences Laboratory The Aerospace Corporation 

and 

E. C. Stone California Institute of Technology 

Pasadena, Calif. 91125 

8 June 1983 

Laboratory Operations THE AEROSPACE CORPORATION El Segundo, Calif. 90245 

This Page Intentionally Left Blank 

Report No. ATR-83(9990)-3 

THE MIMAS GHOST REVISITED: AN ANALYSIS OF THE ELECTRON FLUX i~D ELECTRON MICROSIGNATURES OBSERVED IN THE VI CINITY OF MIMAS AT SATURN 

Prepared 

7Jt<--lil!~,/..~vL--,--_-." _ D. L. Chenette 

Approved 

?iY,&'~ J. Blake, Head Space Particles and Fields 

Department 

iii 

Space Sciences Laboratory 

This Page Intentionally left Blank 

Abstract 

An ana:ysis oj' the electron absorption signature observed by the Cosmic Ray Sys­

tem (CRS) on Voyager 2 near the orbit o.r Mimas is presented. We find that these 

observations cannot be explained as the absorption signature of Mimas. Combining 

Pioneer 11 and VClyager 2 measurements of the electron flux at Mimas's orbit (L=3.1), 

we find an electron spectrum where most of the flux above ..... 100 keV is concentrated 

near 1 to ~3 MeV. This spectral form is qualitatively consistent with the band-pass filter 

model of Van Allen, et aI. [1980b]. The expected Mimas absorption signature is calcu­

lated from this spectrum neglecting radial diffusion. Since no Mimas absorption signa­

ture was observed in the inbound Voyager 2 data, a lower limit on the diffusion 

coefficient for MeV electrons at L=3.1 of D > 10-8 Rs2 s-l is obtained. With a diffusion 

coefficient. this large, both the Voyager 2 and the Pioneer 11 small-scale electron 

absorption signature observations in Mimas's orbit are enigmatic. Thus y;e refer to the 

mechanism for producing these signatures as the Mimas ghost. A cloud of materiai in 

orbit with .Mirnas may account for the observed electron signature if the cloud is at 

least 1% opaque to electrons across a region extending over a few hundred kilometers. 

v 

At::kn.olriedgments. 

We greatly appreciate the efforts of RE. Vogt and other members of the team 

from Caltech, Goddard Space Flight Center, the University of Arizona. and the Univer­

sity of New Hampshire who were responsible for the success of the CRS investigation. 

Useful discussions with AW. Schardt and M. Schulz are gratefully acknowledged. We 

thank the Voyager Navigation Team of the Jet Propulsion Laboratory for providing 

accurate positions of the satellites of Saturn. This work was supported by NASA under 

NAS7-91B and NGR 05-002-160. DLC acknowledges additional support by the 

Aerospace Corporation's sponsored research program. 

vi 

CONTENTS 

Abstract: ...... I' •••••••••••••••••••• <). • • • • • • • •• • • • • • •• • • • • • • • • • • • • • • • • • • • • v 

Acknowledgments •.. 

1-

2. 

3. 

4. 

5. 

6. 

7 • 

Int:roductj~on ........................................................ . 

Proton and electron profiles at Mimas ••••••••••••••••••.•••••••..••• 

Mimas absorption signature calculation ••••••••••••••••••••••••••.••• 

Expected Mimas absorption signature •••••••• 

Limits on the radial diffusion coefficient ••.••••••..•••••••••.•..•• 

Possible causes for the observed signature •••••••••••..•••..•.•••••• 

Discussiorl and Su11l11lary .............................................. . 

vi 

1 

2 

9 

16 

21 

22 

27 

Referen(~es •.•• IJ •••••••••••••••••••••••••••••• 0 •••••••••••••••••• f/. • • • • • • • 33 

vii 

1. 

FIGURES 

Electron and proton counting rates from the CRS instrument on Voyager 2 as the spacecraft crossed the orbit of Mimas both inbound and outbound .......................................... -

2. A plot of the electron signatures from Figure lb on an 

4 

expanded scale...................................................... 7 

3. 

4. 

5. 

The heavy solid lines illustrate the trajectory of Voyager 2 relative to Mimas in (L, longitude) coordinates •••••..•••• 

The integral electron spectrum in the vicinity of Mimas .•••. .•.••••• 

The shaded regions labeled inbound and outbound indicate the range electron energies that would have been absorbed by Mimas during its most recent orbit as the Mimas absorption shadow crossed the position of Voyager 2 ........................... . 

6. A comparison between the electron microsignatures observed on Voyager 2 and the microsignature that would be expected 

11 

12 

19 

from Mimas, neglecting radial diffusion............................. 20 

TABLE 

1. Thresholds, geometry factors, and radial gradients at L = 3.1 for CRS electron rates ..................................... . 3 

viii 

1. Introduction. 

The satellitEls orbiting within the magnetospheres of Jupiter and Saturn have pro­

found effects on the dynamics of these magnetospheres and the distributions of the 

trapped radiation. Some of these satellites are sources which contribute significant 

amounts of low emergy material to the magnetosphere (e.g. the 10 torus [Broadloot, et 

ai., 1979; Bagenal and Sullivan, 1981]), while others may be viewed as primarily as 

radiation sinks, absorbing energetic charged particles [Mead and Hess, 1973; Thomsen, 

1979, and references therein]. As magnetospheric probes, these satellites have contri­

buted greatly to our understanding of the structure, dynamics and the transport of 

the magnetospheric radiation. Conversely, the characteristic absorption signatures 

left in the radiation "wake" of orbiting malerial has led to the confirmation or 

discovery of several new satellites anel rings [Fillius, et aI., 1980; Simpson, et ai. , 

1980a,b; Van Allen, et ai., 1980a,b]. In this paper we exploit both of these aspects of 

charged particle - satellite interactions. 

During their encounters with Saturn, both Pioneer 11 and Voyager 2 crossed the 

rr..agnetic L-shell ra.'1.ge occupied by Saturn's satellite Mirnas. Energetic charged parti­

cle detedors onboard both of these spacecraft have measured transient decreases in 

the local electron flux which are similar to the characteristic signatures of charged 

particle absorpti.on by rr...ateriaI orbiting Saturn [Simpson, et al., 1980b; Van Allen, et 

al., 1960b; Vogt, et ai., 1982; Carbary, et aL., 1983]. The interpretation of these 

features, howev!;r. has led to differing conclusions concerning the abundance cf 

material sharing Mimas's orbit. The resolution of these dif!erences is important in 

order to assess the nature and the abundance of co-orbital material. Both Dione and 

Tethys have satellite companions [Smith. et a.l., 1982] and these observations at Mirnas 

may lead to a better understanding of the formation and the evolution of such multi­

body systems. Also, differences in the interpretation of these features have led to 

widely varying estimates of the radial diffusion coefficient for eiectrons near Mimas's 

1 

orbit [Simpson, et al., 1980b: Van Allen. at al., 1980b]. The value of the radial diffusion 

coefficient is important for understanding the processes responsible for the fonnation 

a.'1d maintenance of Saturn's radiation belts. 

in this paper we present an analysis of the energetic charged particle em-iron­

ment and the charged particle Signatures observed in the vicinity of YJmas. In addi­

tion to summarizing the characteristics of the charged particle flux near YJmas, we 

derive limits on the radial diffusion coefficient for electrons in this region. Several 

candidate mechanisms are examined for producffig the observed electron signature. 

Absorption by a cloud of material in orbit with Mimas appears to be a plausible expla­

nation, and we derive limits on the characteristics of the additional material which 

may have been responsible for the absorption signature that we observed. 

This analysis is based on data obtained from the Cosmic Ray System (CRS) on Voy­

ager 2 [Stone. et al .• 1977]. During the Saturn encounter this instrument was 

operated in special modes to optimize its performance in the intense radiation regions 

of Saturn's inner magnetosphere [Schardt and McDonald. 1983]. Table 1 summarizes 

the characteristics of the CRS detectors which produced the data analyzed in this 

report. No corrections for nonlinearities between the incident flux intensity and the 

r:s.easured counting rate have been applied to these data. Such corrections become 

Significant at measured rates greater than 2.4x 10' S-1, which is greater than the 

rr..aximum counting rate in Figure 1. 

2. Prcwn and e1.ectron profiles at ~Iiu;as. 

Samples of the data obtained by t!le CRS instrument across the orbit of :"-:iw..as 

inboll..."1.d and outbound are displayed in Figure 1. The prcfUes of four different count­

fig rate channeis are plotted versus time (upper scale) and magnetic L (lower scale). 

Throughout this paper, the L-shell coordinates of Voyager 2 have been calculated froD 

the final spacecraft trajectory coordinates by assuming a magnetic dipole aligned ""ith 

Saturn's axis of rotation and offset along Saturn's rotation axis by 0.0';' Saturn radii 

2 

Table 1. Thresholds, geometry factors, and radial gradients at 1=3.1 for CRS electron 

rates. 

Detector Electronic Minimum Ge()metry Incident Electron Counting Rate 

Threshold Shielding Factor Energy Threshold Radial Gradient Name 

(MeV) (g em -2; AI) (em 2 sr) (MeV) (Rs•1) 

B2 2.2 0.2 25. 2.5 1.0 

D4 0.5 2.8 2.3 5. 4.7 

C4 5. 1. 28. 6.5 7.3 

C2 5. 1.5 28. B. 20. 

C3 5. 2. 11. 9. ~O 

3 

.p-

Time of day 238,1982 

I 06 c,~v C'JV c·ov <-to JV 't·'tv 4: 50 

I I i I Iii i i 

(A) Inbound 

105 >2.5 MeV e (/) 

-0 C 0 >5 MeV e ~ 104 (j) 

-1O c .- 3 (/) 10 ..-C :J 0 

U 102 

101 , I I '" I I 

3.3 

Fig. 1. 

3.2 3.1 3.0 3.0 3.1 3.2 Magnetic L Magnetic L 

Electron and proton counting rates from the CRS instrument on Voyager 2 as the spacecraft crossed the orbit of Mimas both inbound (A) and outbound (B). BS4 labels a rate which is responding to the product of the >2.5 MeV electron rate and a rate due to >6.5 MeV electrons in this region. The rate ratio BS4/(>2.5 MeV e) is thus roughly proportional to the flux of )6.5 MeV electrons. The broad minimum in the >60 MeV proton counting rate from L = 3.02 to 3.14 marks the region swept-out hy Mimas due to its orbital eccen­tricity, the Mimas macrosignature. Dashed lines in (ll) mark the smaller electron ahsorption signature. 

(~) north [Smith. et al., 1980; Connerney, et al .. 1982; Chenette and Davis. 1982]' If 

the octopole moment term of the Zs magnetic field model [Connerney. et al.. 1982] 

Y1l;~r~ included in our calculation. the L-she11 coordinates would change by less than 

1%. Exact L values are not essential to the analysis that follows. 

The counting rate of Figure 1 labeled BS4 is nominally the coincidence rate 

between detect.ors with nominal thresholds of 2.2 MeV (detector B2) and 5. MeV (detec­

tor C4). In the region plotted in Figw"e 1. this rate is dominated by accidental coin­

cidencE!s between these two detectors. Therefore the BS4 rate is roughly proportional 

to the product of the two single-detector counting rates. Since the >2.5-MeVelectron 

rate is from thE! BZ detector. the ratio (:If the BS4 to >2.5-MeV electron rates is roughly 

proportional to the flux of the >6.5-MeV electrons which can trigger the C4 detector. 

In Ji'igure 1. the proton and electron profiles are s4~nificantly different. The >60-

MeV prr:>ton flux from the CRS instrument [Vogt. et al., 1982; Schardt and McDonald, 

1983] has a broad minimum. from L=3.02 to 3.14 which is coincident with the semima­

jor axis of Yimas's orbit at 3.08 Rs' The size of this large-scale proton absorption sig­

nature i.s not related to the size of Mimas. Rather, it is due to 1-Iirnas's 0.02 orbital 

eccentricity. As a result. the radial diffusion of these protons 'must be negligible ov!~r 

the .... 11 hours required for Mimas to move from its minimum to its maximum orbital 

radius. Thus, as recognized from the Pioneer 11 observations [Van Allen, et al., 1980b; 

Simpson, et al .• 1980b; McDonald, et al., 1980; Fillius and McIlwain, 1980] tr...is minimum 

in the proton fiux is a stable. stationary feature of the energetic proton flu..x in 

Saturn's inner magnetosphere. ln contrast, the electron profiles show only smaller­

scale fluctuations in intensity superimposed on an overall increase in flux intensity 

with decreasing distance to Saturn. No broad minimum is observed in the electron 

data of Figure 1 coincident with Mimas's orbit. 

The difference in the large-scale "macro signature" of 1Hmas between electrons 

and protons is the result of the large ditrerence between the drift periods of these two 

5 

species relative to Mimas [Van Allen, et al., 1980b]. Since the proton drilt velocity is in 

the same direction as Saturn's rotational velocity, protons drift downstream in the 

cOl"otational !low. Thus the drift period of protons relative to Mimas is always less tban 

...... 20 hours. Mirnas's period relative to Saturn. The electron drift velocity is in the dir.ec­

tion opposite to Saturn's rotational velocity, however. Electrons drilt upstream. 

against corotation. Relative to Mirnas these velocities are similar in magnitude. As a 

result, the drift velocity relative to Mimas is very small for electrons near 1 MeY. 

These electrons are rarely exposed to absorption by Mimas and thus show no 

significant large-scale absorption signature. This electron resonance phenomenon and 

the differences in the frequency of encounters with Mimas between electrons and pro­

tons have been discussed in· a number of papers [Thomsen and Van Allen. :960; 

McDonald. et al .. 1980; Fillius and Mcllwain. 1980; Simpson. et al .. 1980b]. 

The large difference in the p~oton intensity between the inbound and outbound 

passes, a factor ot 3 to 5, resulted from the lower latitude of the o:utbound pass (-6°, 

as opposed to +19 0 inbound) and the fact that the proton flux pitch-angle distribution 

is sharpiy-peaked near 90° [Schardt and McDonald, 1983]. Thus the proton !lux is 

more intense nearer the equatorial plane. Beyond L=3.2 outbound. there is a srnall 

contribution from these protons in the >5-MeV and BS4 electron rates. Between 

L=3.02 and 3.14. however, these energetic protons did not contribute si6n:L.4.cantly to 

the electron rates in Figure 1. 

From 04:46 to 04:48 of day 238, during the outbound pass (Figure lb). a transient 

decrease was observed simultaneously in all of the electron rates. The depth of this 

electron signature ar:.d the detailed ~b.ape of the profile are energy dependent (Figure 

2). The higher-en.ergy rates s.hcw· m:)re evidence of a secondary minimum at 04-:4-6. 

The separation between these two rninilT'..a is & '" 0.02. equivalent to an equatorial 

radial distance of "'1200 kID. The full-width at half of the minimUI!'. of the majo:" 

decrease wa.s ...... 600 km.. somewhat greate..- than the effective geometrical sweeping 

6 

a.> ..... a 

(:t: 

0'1 c: .+-C :J 0 

C) 

·'0 CJ) N 

0 E ~ 

0 :z 

Fig. 2. 

I. I >2.5 MeV 

854 

o. 4 ~--L-_",,-----,-___ -,I_~_.&..-.--..I-_...!.-___ --' ~5.06 3.10 3.14 

Magnetic L 

A plot of the electron signatures from Figure lb on an expanded scale. These counting rates have been normalized to emphasize the differences between the signatures. 

7 

diameter of Mirnas DlI=2{rll+8rg )=450 kIn. where rll=195 km is the radius or Mimas 

[Smith, et al., 1988], and Tg =14 km is the gyroradius of 8.5 MeV electrons at L=3.13. No 

comparable electron signature was observed during the inbound pass of Voyager 8 

across tbis region (Figure la). The smaller fluctuations visible in the inbound >5 Y..~V 

and the BS4 rates may have resulted from the spacecraft roll maneuver taking place 

at this time which resulted in these detectors sampling difierent parts of the anisotro-

piC electron pitch-angle distribution in this region. No maneuve!"s were being executed 

during the outbound pass through the region in Figure 1. 

The electron signatures of Figure 1b are displayed in Figure 8 on an expanded 

and normalized scale. The profiles plotted in Figure 8 were calculated from the 

corresponding counting rates of Figure 1 b by dividing each rate by a function of the 

form A exp( -LI La). ln each case, A and La were determined by a least squares best 

fit to each rate over the region L = 3.00 to 3.16, but excluding the signa~ure from L = 

3.105 to 3.145. 

Figure 2 illustrates the energy dependence of the shapes of these signatures. For 

the major decrease at L = 3.135, the >8.5-MeVrate decreased by 17% while the >5-1~eV 

rate decreased by 30%. The 50% reduction in the BS4 rate coupled with the fact that 

the B2 rate decreased to 83% of its nominal value suggests that the C4 rate (>6.5 MeV) 

was reduced by 40% at L = 3.135. Samples of the C4, C3, and C2 rates were obtained 

only once for each :6 samples of the B2 rate. While the samples of these rates which 

were obtained are consistent with the other data, there are not enough of them to 

deBne the signatures in these rates by themselves. The secondary minimum at L = 3.115 had a similar, but more dramatic, energy dependence. Tbis feature appears as 

only a shoulder in the >8.5-MeV rate (3% reduction), while in the >5.-MeV rate there is 

a clear minimum (18% reduction), and a comparison of the B2 a.."1d BS4 rates suggests 

that the C4 rate must have decreased by nearly 35% in this secondary rri1"'...imum 

Since the orientation of these detectors was fixed over the interval when the signature 

8 

/ "­\ 

was observed, and since most of these detectors were sensitive to electrons over most 

of a full hernispht~re, we cannot infer any pitch-angle dependence of these signatures, 

and we prefer to attribute the differences between these signatures to an, energy 

dependence. 

The absence of any significant absorption signature in Ll).e inbound electron flux 

profiles lEld us to conclude in an earlier report [Vogt, et at., 1982] that YJ.mas could not 

have been responsible for the outbound signature. In this report we now present a 

more complete analysis of these data, t.aking into account the remarkable electron 

spectrum characteristic of this region. We will again conclude that Mirnas could not 

have pro(:luced t.he signature that we observed. In addition, our analysis permits us to 

place limits on the characteristics of any absorber which could have produced the sig·· 

nature, as well as limits on the radial diffusion coefficient for electrons at the orbit oJ: 

Mimas. 

3. l:lim.as absorption signature calculation. 

In the energy range to which the CRS instrument is sensitive, the primary effect 

of a satellite like Mirnas orbiting within Saturn's rn,agnetosphere will be to absorb the 

radiation incident on it. Due to the longitudinal motion (drift plus corotation with 

Saturn) of the radiation. any absorbsr wi.llieave an absorption "wake" on any L-shell it 

passes. The maximum possible longitudinal length of the wake for any particle energy 

or species is equal to the product of the energy-dependent drift rate of that particle 

type relative to the absorber and of the length of time that the absorber occupies the 

drift shell, assuming the absorber's orbit. or the drift shell are eccentric. The fraction 

of particles absorbed within the wake is determined by the probability that a charged. 

particle IleaI' the longitude of the absorber cannot "leapfrog" or "corkscrew" past the 

absorber via latitudinal bounce motion [Rairden. 1980]. P'or electrons 'wi.th the ener .. 

gies considered in this report this probability is negligible ut Mimas. Thus Mirnas 

absorbs virtually all of the electrons on magnetic field lines that it crosses. After the 

9 

absorber passes an lrshell these wakes separate due to the energy dependence of the 

drift velocity. Thus to a detector with a broad energy response, the absorption signa­

ture will decay with time as older wakes are spread over a longer longitude range. In 

addition to tbis energy-dependent dispersion, the absorption signature will be 

dispersed by radial ditIusion. 

In an initial attempt to model the electron absorption signatures of Figure 1, we 

assume that they were produced by Mimas. The expected llJimas absorption signature 

profiles in the electron rates of Figure 1 are calculated from the local electron spec­

trum, and these profiles are compared to the observations. The effects of radial 

diffusion are neglected in this initial calculation. 

Figure 3 illustrates the inbound trajectory of Voyager 2 in a coordinate system 

which corotates with llJ.rnas. Due to its orbital eccentricity, Mimas oscillates at 00 

longitude between L = 3.02 to 3.14 every 22.73 hours. In this coordinate system, elec­

trons with energies ~1 MeV drift to the west (left to right) while lower-energy electrons 

and protons drift to the east (right to left). For any single electron energy, the 

absorption wake of Mimas is nearly a sinusoid in longitude, extending from }Jimas with 

a "wavelength" equal to G).o x 22.7 hours where G)]) is the energy dependent electron 

drift frequency relative to Mimas, as defined in the following section. Examples of 

such a sinusoids are shown in Figure 3 for 2.9-MeV electrons. An important charac­

teristic of the Voyager 2 trajectory illustrated in Figure 3 is that the'longitudes of the 

inbound and outbound legs, relative to Mimas, difIer by only ...... 10% (20 0 out of >200°) 

when measured in the direction that energetic electrons drift. The inbound and out­

bound passages of Voyager 2 across this region were separated by 2 hours (see Figure 

1). 

The electron energy spectrum also must be kno'wn to determine the e>"'l'ected 

profile of ~imas's absorption signature. The remarkable electron spectrum in the 

vicinity of Y.:imas is illustrated in Figure 4, which shows the integral electron spectrum 

10 

3.15 

3.10 -, ._, ..0, '-I 0, 

L. (/), 

0' EI .-, 

3.05 :E' '0 , c '0 :::J C 0 :::J a ..0 0 - ..0 

b :::J C 0 H 

3.00 

I I I I I I I I I I I I , , I , , I , , 

-60 120 180 240 300 

Fig. 3. 

Longitude from Mimas (degrees t + West) 

The heavy solid lines illustrate the trajectory of Voyager 2 rela­tive to Mimas in (L, longitude) coordinates. The coordinate system rotates so that Mimas remains at 0° longitude while oscillating between L = 3.02 and 3.14. The sinusoidal bands extending to the right from the positions of Mimas at: the times of the inbound (a) and outbound (b) passes illustrate where any absorption wake of Mimas in 2.9-MeV electrons would be at the times that Voyager 2 crossed this region both inbound and outbound. (For 2.9-MeV elec­trons Voyager 2 would have crossed the wake at the position of the observed electron signature.) Numbered tic marks along the wakes label the time in hours since that region passed Mimas. Similar wakes may be drawn for any other energy. The wavelength of the wake in this display would increase with increasing electron energy above the ~l-MeV resonant energy. Below the resonant energy the wakes extend to the left. 

11 

Fig. 4. 

' ... (/) 

.(/) 

N 

'E ~ 

w ~ '"? 

(/) 

c: 0 ... ..-u a> 

W -0 

>< :::l 

lJ.. 

0 ... 01 

.$!: c: 

106 

0 -.~-¥\-\ 105 L= 3.1 \ 

Mimas Gap 1 j \ 

104 

103 

102 

lot 

10° 

\ I I I \ I 

I • I I 

I 0-1 ~_--'L..-~ __ -L...--L __ --I_.1-__ ..I.-...J 

10-2 10- 1 10° 101 102 

Electron Energy (MeV) 

The integral electron spectrum in the vicinity of Mimas. The shaded boxes are data calculated from the CRS instrument and the open circle is from Krimigis, et al. [1982]. Both of these data sets were obtained from instruments aboard Voyager 2 in August 1981. Open squares are from Van Allen, et al. [1980b]; open triangles are from Fillius and McIlwain [1980]; solid circles are from McDonald, et al. [1980]; and crosses are from Simpson, et al. [1980b]. These are observations from the Pioneer 11 spacecraft taken in August 1979. Error bars assigned to points reflect the variability in the counting rates during both inbound and outbound passes. The dashed and solid lines indicate model spectra chosen as limiting cases of the true spectrum (see text). 

12 

at L=3.1 as determined by the available Pioneer 11 and Voyager 2 measurements of 

the electron flux. 

The shaded boxes in Figure 4 are flux measurements tram the CRS instrument. 

They were calcuJ.ated from counting ratHs of single detectors with different amounts_of 

passive shielding and different electronic thresholds (Table 1). The size of the box at 

each enE:rgy reflects our estimate of the uncertainty of the electron energy threshold 

and of the effective geometrical factor. The measurement at 2.5 MeV labeled with a 

small arrow may not have been fully corrected. This point was calculated from the 

counting rate oj' a 2 mm silicon detector with a 2.2 MeV threshold. Due to the high 

threshold, the electron detection efficiency of this detectc)r is small. The plotted value 

includes a correction for this efficiency (calculated to be a maximum of 10%) using the 

method of Lupton and Stone [1972]' Since that method provides an upper limit to the 

detection efficiency, the corrected flux value is a lower limit. The fact that this value 

is inconsistent with the rest of the data suggests that the real effiCiency may be 

significantly smaller. 

The CRS counting rates in Mimas's orbit may confidently be attributed to elec­

trons because, as illustrated in F~ure 1. the proton flux is greatly reduced at L=3.1 

by Y.imas. Only the highest energy box at 9. MeV could have a significant contribution 

from enElrgetic protons. ThUB it may be viewed as an upper limit to the electron flux. A 

detailed analysis of these counting rates [Schardt and McDonald, 1983J suggests that 

protons may be responsible for 70~ of the observed counts in this 9-MeV electron flux 

rate at 1,=3.1. Finally, since t.he counting rates, R, on which the CRS flux measure-

ments at'e based have different radial gradients ( ~ ~~~ ) in this region, gradients 

which are steeper with increasing energy (Table 1), and since the shape of the micro­

signature varies systematically with increasing electron energy (Figure 1), -",e believe 

that these counting rates truly measure diJ.1erent portions of the energy spe(:trum, 

rather than, for example, pUe-up or bremsstrahlung from a cornmon, lower-energy flux 

l3 

source. The radi.a.l gradients of each rate across Mirnas's orbit (L=3.02 to 3.14) are 

nearly the same inbound and outbound (excluding the outbound signature), thus indi­

cating that the instrument was measuring the same fiux distribution along both legs of 

its trajectory in this region. 

The other electron flux measurements displayed in Figure 4 were calculated from 

published electron counting rates and geometrical factors [Van Allen, et 01. 1980b; 

Fillius, at aI., 1980; Simpson. st al., 1980b; Kr imig is , at aI., 1982] or from published 

dii1erential fluxes [McDonald, at al., 1980]. The point at 3.4 MeV from Simpson, et 01., 

[1980bJ is from their electron current detector (ECD). In view of the steepness of the 

electron spectrum and the response characteristics of the detector, the true 

equivalent energy threshold is likely less than 3.4 MeV (R. B. McKibben, private com­

munication) so that this point would shift to the left in Figure 4 by perhaps as much as 

1 MeV (as indicated in Figure 4) if it were corrected for the shape of the spectrum. 

The 1 g crn-2 beryllium shield surrounding the ECD detector shields it from electror:s 

with energies below 2 MeV. 

Qualitatively, the electron spectrum at L = 3.1 is consistent Vtith the model pro­

posed by Van Alien. at al. [1980b]. Since this integral spectrum is almost flat between 

""100 keV and ..... 1 MeV, and falls as E-? with "I = 5 to 10 above several MeV. nearly all of 

the electrons above ..... 100 keVat L = 3.1 have energies of 1 to 3 MeV. Van Allen. at al. 

[1980b] have proposed that this form of the spectrum is produced by the "band-pass 

tlltering" action of Saturn's satellites on the inwardly diffusing electron population. 

The fiitering action arises because electr-ons can have drift velocities that are compar­

able to a satellite's angular velocity. Near the resonant electron energy, i.e. where 

these two velocities are equal, the reSOrl.al1t electrons can. di:euse a~ross the satellite's 

orbit with r.J. very sr:::ra1l pl-obability of beL"},g absorbed by the satellite. Thus. the action 

of a satellite on an inwardly difIusing electron population is to preferentially pass 

electrons in a certain energy band. Through this mechanism Enceladus passes elec-

14 

trons which arrive at Mimas with energies of -1.6 MeV (assu.rning the conservation of 

the first two acli.abatic invariants, and for equatorially-mirroring electrons). While the 

data of Figure 4 are not precise enough to determine the characteristic energy to 

better than 1 MeV, they are COI1sistent with 1.6 MeV, hence qualitatively consistent 

"With the model. However, the band pass fllter model would not explain the increase in 

electron flux intensity at lower energies reported by Krimigis, et al. [1982]' 

Another conclusion of Van Allen, et al. [1980b] concElrning the electron spectrum 

at the orbit of Mimas, namely, that the spectrum is nearly mono-energetic with r5E '" 

0.1 MeV about 1.6 MeV is not supported by the data of Figure 4. Rather, the data of Fig-

ure 4 indicate that 20% or more of the electron flux above 0.1 MeV is above 2 MeV. Th.e 

0.1 MeV 13StimatEl of the width of the spectrum was not based on the "band-pass filter" 

model. but rather, on the analysis of an electron absorption Signature and the 

assumption that this signature was due to Mimas. If this Pioneer 11 signature was not 

due to Mimas [Simpson, et al., 1980], a conclusion that we support in a later section of 

this paper, then this constraint on the width of the electron energy spectrum is 

removed. 

To use this electron spectrum' in calculating the expected Mimas absorption sig-

nature, we have adopted the two n:.odels shown as the solid and dashed lines in Figure 

4. The two models are adopted as probable lL'Iliting cases of the true spectrum to 

assess the effect on the calculation of changes in the spectrum. Both models are of 

the form. 

Jo J(>E) = l+(E/ Eor' (1) 

In case 1. (solid line) ?' = 5 and Eo = 1.6 MeV, while tor case Z (dashed line) ?' = 10 and 

Eo = 3.0 MeV. Fe)r both cases Jo=3x 1 05 electrons cm-2 sterad-1 s-l, although this con·· 

stant does not affect the calculation, or the results in the rest of this paper. 

15 

4. Expected ~Jjmas absorption signature 

To calculate the expected absorption signature of Mimas from the spectra of Fig­

ure 4, the true orbit of Mimas (provided by the Navigation Team of the Jet Propulsion 

Laboratory) was converted to obtain the orbit in magnetic L coordinates, LJl(t). This 

function, together with the radius of Mimas, was used to construct the functions t;. (L) 

and tf (L) which are the times when Mimas last entered (ti) and left (t J) the drift shell 

labeled by 1. The expression for the angular drift velocity of electrons of kinetic 

energy E relative to }/Jrnas which we used is based on the dipole approximation (see 

Thomsen and Van Allen [1980] and references therein): 

(,)D = ALE a(E)[F / G(t..m)] - 0 (2) 

where a(E) = (E+2m)/ (E+m) is a relativistic factor which takes values between 1 and 

1.2 for our data, m is the electron rest mass, FI G is a factor (between 0.9 and 1.0 for 

these data) which depends on a particle's mirror latitude, Am. , and 

0= (')Jl- r-Js = 8.70x10-5 radians s-l is the angular velocity of Mimas relatiY"e to Saturn's 

magnetic field, where c,.l]J = -7 .6ox 1 0-5 radians s-l is the inertial angular velocity of 

YJrnas and r-Js '= -1.638x10-4 radians s-l is the magnetic (SLS) rotation rate of Saturn 

[Desch ru.'l.d Kaiser, 1981]' The constant A = 1.96x10-5 radians MeV! s-l, c:l.ifl8rs slightly 

from that used by Thomsen and Van Allen [1980] due to revised values for Ll-).e nominal 

equatorial radius of Saturn (60330 krn rather than 60000 km) and for Saturn's dipole 

moment (0.21 gauss Rs3 rather than 0.2 gauss Rs3) [Ness, et al., 1982]' For electrons 

'Yvith energies E > 1.1 MeV the first term of equation (2) is the larger. Thus r-JD > 0, 

where, for the purposes of this paper. the positiv:e angular direction is from east to 

west (clockwise as vie,Yed from tr.e north of Saturn). If the inbound or outbound legs 

of the Voyager 2 trajectory are expressed in Mimas-fixed coordinates, Le. a coordinate 

system that corotates with Mimas, in the form I"(t), Let). A(t). where I" is the longitude 

angle from Mimas to Voyager and A is the latitude of the spacecraft, then at any time t 

along the Voyager 2 trajectory in the region or L s--;vept by M.Jmas, electrons with ener-

16 

gtes. E. such that E;, < E < EJ will have been absorbed. where 

(Ji') - reCt) ~D .~ - t-'~[L(t)] (3a) 

... , (1i' ) _ rp(t) IMD .J' - T:-t,[L(t)] (3b) 

The resulting shadow of Mimas in the electron energy spectrum along the Voyager 2 

trajectory. both inbound and outbound. is plotted in Figure 5. The shaded regions of 

Figure 5 correspond to the regions ~ < E < E, that Mimas produced during the - 20 

hours prior the passage of Voyager 2. ThE~ normalized absorption signature for each 

rate (neglecting diffusion) is calculated by integrating the spectra of Figure 4 above 

the rate Emergy threshold. but excluding the region from E;. to E,. 

If the effects of radial diffusion were negligible over the -10 hour interval 

required for -2.5 MeV electrons to drift from Mimas to the position of Voyager 2. the 

absorption signatures observed by the CRS instrument should have resembled the 

dashed or dotted curves drawn in Figure 6. The solid line drawn in each panel of Fig-

ure 6 is t.he r.J.easured >2.5-MeV or >5-MeV counting rate which has been normalized 

by dividing the observed rate by its least-squares best-tit exponential in 1. The signa-

tures from L = 3.105 to 3.145 were excluded from these fits. The dashed lines are the 

signatures calculated using the model spectrum with Eo = 3.0 MeV and a = 10 (the 

dashed-litle spect.rum of Figure 4) while the dotted lines are based on the Eo = 1.6 MeV 

a = 5 model spectrum (the solid line of Figure 4). 

Even though the real electron spectrum may differ in detail from these model 

spectra. these calculations indicate that the qualitative characteristics of the absorp" 

tion signatures are not sensitive to the exact form of the electron spectrum. However, 

there are quantitative differences between the calculated absorption signatures of 

Figure 4 which resu1t from ditrerences between these II1..odel spectra. An examination 

of the ortgin of these differences provides insight into the nature of such signatures. 

For the >5-MeY rate. the dashed-line signature is deeper and narrower because with 

this steeper spectrum more of the counts are from electrons just above the detector 

17 

threshold. The calculated outbound signature is generally deeper than the inbound 

signature because the spacecraft passed closer to Mimas along the outbound pass and 

thus the signature was "fresher", it spanned a larger energy range. For the >2.5 :MeV 

rate and the Eo = 3.0 MeV spectrum. however, the calculated inbound signature is 

deeper. This is due to the combination of two etre::ts. both or which are illustrated in 

Figure 5. First, for both the inbound and the outbound passes the maximum caku­

lated absorption above 2.5 MeV occurred at the maximum radial excursion of Mimas. 

the region where }.fimas spends the most tiI:ne at the same L. resulting in the longest 

(in longitude) or widest (in energy) absorption wake. Secondly. for the inbound pass 

this wake spanned 3.0 MeV whereas for the outbound pass this wake extended to only 

2.8 MeV. Thus the calculated inbound wake is deeper since for the Eo = 3.0 MeV spec­

trum. most of the fiux is concentrated near 3.0 MeV. 

k3 F"tgure 6 illustrates. the outbound >2.5 MeV signature was observed at the loca­

tion where a Mimas signature would have been expected. However, if that signature 

were due to Y.imas. the >5.0 MeV Mimas signature should not have been coincident 

with the >2.5 MeV signature. rather the >5.0 MeV signature should have appeared at L 

;::,j 3.05 due to the energy dispersion of the electron drift velocity. The signature in the 

>5.0 MeV rate should appear closer' to YJmas's current position because higher-energy 

electrons driit more rapidly. Thus we conclude that it was entirely fortuitous that a 

2.5-MeV signature was observed where Mimas's signature was expected. Secondly. and 

perhaps more· convincingly, ii the effect of radial diffusion were small enough to be 

neglected (Le. if the diffusion coefficient. D, were smaller than 10-10 Rs2 s-l) then 

absorption signatures due to Mimas should have been observed on both the inbound 

and outbound passes. Thus we conclude not only that Mimas could not have produced 

the observed signature, but also that no absorption signature due to Mimas was 

observable. Since Mimas cannot have produced the observed signature, we are 

motivated to search for another cause for it. Since no absorption Signature due to 

18 

9 I 

Electron Shadows 8 of Mimas at 

~ ...... :> Voyager 2 Q) .,- 7 .. ~ ~ ...... I.JJ 

6 

>. 0'15 ~ 

Q) 

c tJJ 4 

c 0 3 ~ ..... u "--- ----Q) 2 --.. -tu 

o _._I~--..~ __ ~ __ ~~_~I ____ ~ __ ~ ____ ~ __ ~ ____ ~ __ ~ ______ ~ 

3.04 3.06 3.08 3.10 3.12 3.14 

Magnet ic L of Voyager 2 

Fig. 5. The shaded regions labeled inbound and outbound indicate the range electron energies that would have been absorbed by Mimas during its most recent orbit as the Mimas absorption shadow crossed the posi­tion of Voyager 2. Horizontal dashed lines at 2.5 MeV and 5 MeV indicate CRS counting rate thresholds. The higher-energy ends of the shaded regions asymptotically approach the L-shell position of Mimas at the time Voyager 2 passed. The age of the signature increases with decreasing electron energy. 

19 

N 0 

Inbound Outbound 

Q) 1.0 "~ .. ~.::.~.... --.~, : 

a n: 0.8 

'"\" j \\/: Electrons >2.5 MeV 

CJ> 

.~ 06'-c J 0 

U 

-0 

~ 1.0 -a § 0.8 0 Z 

0.6 

3.02 

Fig. 6. 

':;'1 1 , , , , , " I, 

" • 

,-.-------:.0-__ -----..... :~ ... , 

". " .... ~\ .. I' 

\ ... .j! , , '.f Electrons >5.0MeV " > 

3.06 3,10 3.14 3.18 

Magnetic L 

---.... r.::.~~ ........ " ....... \ 

.. \ " " :1 

(; .... :: , -, , , . , . , " V 

Electrons >5.0 MeV 

~.02 3.06 3,10 3,14 3,18 

Magnet ic L 

A comparison between the electron microsignatures observed on Voyager 2 and the microsignatures that would be expected from Mimas, neglecting radial diffusion. The solid curve of each panel is the normalized rate of >2.5 MeV electrons (upper panels) and >5.0 MeV electrons (lower panels) both inbound (left panels) and outbound (right panels) across the orbit of Mimas. The dashed and dotted lines in each panel are the microabsorption signatures due to Mi.mas that would be expected neglecting the effects of radial diffusion. The dotted curve was calculated using the model spectrum displayed as the solid Ii.ne in Figure 4, and the dashed curve corresponds to the dashed-line model spectrum. 

Mirnas was observable, we can calculate a lower limit for the radial diffusion coefficient 

of MeV elElctrons at 1 ..... 3.1. 

5. Limits on the radial diffuBion coefficieut 

To estimate the importance of the etIect of radial difIusion on a satellite absorp" 

tion signature it is convenient to use a nonnalized diffusion time ,I defined as 

4Dt i' = --2-

b (4) 

where D is the diffusion coefficient, t is the age of the signature, and b is the radial 

size of the original signature. This nonnc'ilized time is convenient because the max" 

imum fractional depth, Z, of an absorption signature in a one-dL'1lensional Cif!usion 

model like the mDdel used by Van Allen, et aI. [1980b] is given by 

(5) 

where erf 0 is the error function. For the case of electron absorption by }limas, t is '" the drift time from Mirnas to the spacecraft and b is the effective radius of Mi.rr~s for. 

absorbing electrons (see section 2). 

In their analysis of electron data in the vicinity of Mimas, Van Allen. et al. [1980b ] 

estimated the radial ditIusion coefficient, D, at 1=3.1 to be in the range 8xl0-12 to 

4xl0-11 P..s2 s-l. If this value for D were correct, then for the >2.5-MeV electrons 

observed at Voyager 2, 1 would have had a value less than 1 both inbound and out-

bound. H i' < 1, t...~en Z > 0.8, thus the signatures should. have been at least .... 80% as 

deep as the calculated signatures of Figure 6. Since any Mimas absorption signature 

along the Voyager 2 inbound pass must have been very small, the real dif!usion 

coefficient must be much larger. 

The lower bound on the radial diffusion coefi'l..cient for MeV electrons at 1=3.1 that 

we obtain from these Voyager 2 data is similarly based on the one-dimensional 

diffusion. model. The fluctuations in the normalized inbound >2.5 MeV electron rate 

are <5% Since in the ab::;:ence of radial diffusion a 30% to 50% deep signature would 

21 

have been expected, we estimate a limit on Z of Z~O.l, thus 7"~ 100. Using b =220 km 

for the effective radius of Mimas and t = 7.5 hours as the drift time from ~imas to Yoy-

agel'. the estimate tor a lower limit on the radial diffusion coefficient which results is 

D > 10-8 ~ 2 S-1. This estimate is consistent with the value obtained by Simpson. at-ai. 

[1980b]. for ..... 10 MeY electrons of 4xl0-8 ~ 2 s-1, which was inferred from the depth of 

the large-scale electron macrosignature that results from Mimas's orbital eccentri-

city. 

6. Possil:le causes fer the observed signature 

Since Mimas cannot have produced the small-scale electron absorption signature 

obser.red by Yoyager 2 'we are led to search for other possible causes. Several candi-

dates are examined in this section. Compression of the magnetic field could produce a 

dip in the observed electron flux through the combined effects of the steep electron 

energy spectrum and a radial gradient in the flux intensity. This mechanism may be 

reversible in the sense that few electrons are lost from the region. Vihen the fluctua-

tion passes. the region returns to its original state. Alterllatively. an absorption signa-

ture. could be produced by intense, localized (in L and perhaps longitude) wave-

particle interactions 'which dump the electrons in·;j Saturn's atmosphere. Tne final 

possibility that we consider is absorption by additional material sharing Mimas's orbit 

in or near Saturn's equatorial plane. 

6.1. 11agnetic fluctuations and turbulence 

Barfield, at al. [1971J, in a study of compressional micropulsations, provide a for-

mula for the expected change in flux intensity, J, for equatoriaUy mirroring particles 

given a fluctuation in the local magnetic field magnitude, Bt , the particle energy spec-

trum, and the radial particle gradient: 

81nJ I [1 - dlnBc 1 alnBc ~ ~ d lnB, 

22 

(G) 

In this formula Bf is the magnetic field intensity measured by a fixed observer while Be 

is the field intensity experienced by a particle's guiding center, which moves with the 

ftuctuation. 'l is t.he relativistic Lorentz factor. While this formula is only strictly appli-

cable to equatorially-mirroring electron.c;, it should provide an upper limit esti..mate for 

other pitch angles as long as the pitch an.gle distribution is isotopic or peaked at 90 e 

pitch an,gle. If we adopt the symmetric compression model of Roederer [1970J, then 

;~c = 5/2. The spectral index, g~ is taken to be 5 to 12 (Figure 4) and the fac-'J 

tor a~!J{- = -Lgr l3 where Or = a!~J is the radial gradient 'Which was observed to be 

in the range gr := -1.0 for the >2.5 MeV electron rate and Or = -4.7 for the >5.0 MeV 

rate (Table 1). TIlus we obtain 

(7) 

In the region of interest, 48 second averages of the observed magnetic field 

(N.F.Ness, personal communication) show no fluctuations larger than ~: = 0.001. 

(!~B < 1,) and an inspection of finer ti.me resolution data confirms this conclusion. 

(J.E.P. Connerney, personal commur.Jcation). Thus on the basis of this analysis no adi-

abatic magnetic ftuctuation was observed which was large enough to produce the 

observed (> 15%) decrease in electron flux intensity. 

A localized region of intense wave-particle interactions could also produce an 

absorpti()ll signature similar to that observed by scattering trapped electrons L..'1to 

Saturn's atmosphere. At L=3.1 the atmospheric loss cone extends to ..... 8° equatorial 

pitch angle and thus occupies 1% of the total solid angle. Thus at most, 1% of the par-

ticles in a flux tube can be scattered into the atmosphere in the time required for a 

particle to travel from the equator to its mirror latitude, a time interval equal to one-

quarter of the particle's bounce period, or 0.6 seconds for relativistic particles at 

L=3.1. 1n this strong pitch-angle diffusion limit, therefore, it would take a 10 second 

23 

burst of intense wave-particle activity to remove 1570 or the electrons in a flux tube. 

A problem with this hypothesis is that of confining the interaction to a region 6L 

..... 0.02 to produce a localized signature. Presumably, such confinement could be pro-

duced by spatial variations in the plasma density to create a duct in which the 

interactions occur. While whistler-mode turbulence which could precipitate energetic 

electrons was observed [Scar!, et al., 1982] these waves were observed throughout 

large regions of Saturn's inner magnetosphere. This electron signature, however, was 

a unique event. Data from the Voyager 2 Plasma-wave experiment were examined for 

any signals that could have caused a short-lived dropout in MeV electrons. None were 

observed through a large region surrounding the absorption signature [W. S. Kurth, 

personal communication]. 

6.2. Electron aL'Sorption by material in f,Urnas's orbit 

The final alternative that we consider for producing the signature is absorptio:J. 

by material in orbit with Mimas. There are several characteristics of the observations 

which make this an attractive possibility. First, tr.J.s was the only such signature 

observed by the CRS instruments inside of the orbit of Enceladus. and it occurred in 

the orbital range of Mimas. Stable orbits exists for smaller particles near the orbits of 

larger satellites [Dermott et o.L., 1980]. Secondly. the width of the observed signature, 

M '" 0.02 = 1200 km is less than the maximum width of a "ring" of particles that 

Mimas can sustain. According to the ~odel of Dermott. et a.L .• this width is 

[ ]112 [ ]1/3 

W = 40. ~ ~ Rl 1800km (8) 

where ex ~ 1.2 is a parameter. m/M = 6.7x10-B is the ratio of the mass of Mimas to the 

mass of Saturn. and a = 1.86x105 km is the semi-major axis of Mimas's orbit. Compan-

ion material is not uncommon at Saturn. Both Dione and Tethys have small co-orbital 

satellites [Smith, et ai .• 1982]' Thus it is possible that material may also exist in orbit 

with Mimas. 

24 

Characteristics of the absorption signature suggest that the absorber must have 

been relatively dose to the longitude of the spacecraft when the signature was 

observed. Any material in a Keplerian orbit of 3.1 ~, would have only been 20° further 

west of the spacE~craft during the inbOWld pass than it was during the outbound pass 

(Figure 31). Since no significant absorption signature was observed inbound, this 20° 

difIerenc.~ betweEm the approach distances inbound and outbound measures the long i·· 

tudinal extent of a signature. Thus the lifetime against diffusion must be on the order 

of the time required for electrons to drift through 20°, i.e. less than 2 hours, and the 

spacecraft must have passed within 20° longitude of the absorber's position along the 

outbound pass. The lower bound on the diffusion coefficient that results from these 

considerations is estimated below. The lack of dispersion between the >2.5 MeV and 

>5.0 MeV signatures requires a similarly close approach distance outbound, assuming 

the orbit of the absorbing material shares YJrnas's eccentricity. 

Under the hypothesis that the >17% deep electron microsignature observed by 

Voyager 2 outbound is due to absorpti(m by orbiting material, since the absorption 

signature was not observed along the inbound pass «5% absorption), another lower 

bound on the di1Tusion coefficient for MeV electrons at L=3.1 may be calculated which 

is indepEmdent of the estimate obtained earlier in section 5. From the ratios of the 

depths c)f the ir:lbound and outbound signatures, Z = erf ('1'-112) < 0.3, which requires 

'1'=4Dt/b 2 >10. The value for t is the time required for 2.5-MeVelectrons to drift 20° 

from an orbiting absorber at 3.1 Rs ' 4x103 seconds. The value for b is the half-'l'ridth of 

the signature at. half-maximum (section 2, Figure 2), 300 km. or 0.005 Rs' Combining 

these quantities we obtain another lower limit on the diffusion coefficient of 

D> 1.5x:l O-B Rs 2 s-l. It is fortuitous that this value is so close to the other lower 

bound, .D> 10-8 Rs 2 s-l which was calculated in section 5. However, the similarity 

between these results, which are based on entirely di.fi'erent considerations and thus 

are independent, gives added confidence in both the estimate of the diffusion 

25 

coefficient and in the suggestion that the outbound Voyager 2 signature was due to 

absorption by material. If. for example, the real ditiusion coefficient were as small as 

10-10 ~ 2 s-l, a significant inbound signature should have been observed. 

The depth and width of an absorption signature are related to the size of the 

absorber. The absorber cannot be significantly larger than the width of the signature. 

Conversely, if the signature is wider than the absorber, the depth of the signature 

must be correspondingly smaller. For example, if the absorber were smaller than a few 

tens of kilometers, then by the time the signature had spread to 1000 km across (via 

radial diffusion) the maximum depth of the signature could not exceed a few percent. 

Thus to have a 10% or more absorption signature extending over 1000 km would 

require an object with a diameter of 100 km or more. 

Following our initial report of these observations. Voyager 2 imaging frames were 

examined of the region where we predicted the absorber to be located. No objects 

were observed in these frames and an upper limit of 10 km was obtained for the max­

imum size of any single object in this region with an albedo close to unity [S.P. S)rn­

nott, private communication]. In order to reconcile this result ",ith the hypothesis 

that the signature was due to absorbing material, either the absorber must be very 

dark. or else the absorber must consist of a cloud of small particles which may be 

brighter. The former possibility is very unlikely because it would require a 100 krn 

object to have an albedo <0.01, making it much darker even than Phoebe or the dark 

side of Iapetus. which have albedos of ..... 0.05 in contrast to the 0.5 albedo of !limas 

[Smith. at al., 1982]' 

A cloud or swarm of small particles could fill an area (projected onto the equa­

torial plane) of a few xl Q4 km 2 and yet have a total area not larger than the area of a 

single 10 km object. In order to absorb electrons with energies of a few MeV the sizes 

of the particles in the swarm must be at least a few centimeters. Since at least 30% of 

the >5.0 MeV fiux was absorbed, in terms of this model 

26 

!!.E.!!:.. > -In(0.7) = 0.36 cosa 

(9) 

where a is the area of an individual partide in the swarm. p is the packi.ng density of 

these particles projected onto the equatorial plane. n is the number of times an elec­

tron penE~trates the cloud, and a is the electron's equatorial pitch angle (a <: 75°. cosu 

> 0.26, f(:>r electrons which mirror at or above the latitude of Voyager 2). Due to the 

combined drift Emd bounce motion. 2.5 MeV electrons would cross this cloud at the 

equatorial plane every -10 km while 5 MeV electrons would cross every ..... 40 kIn. Thus 

for a cloud extending a few hundred kilometers in longitude. n ~ 10. Combining these 

estimates, the observations would require ap~O.Ol, i.e. more than 1% of the total area 

of the cloud must be occulted by material. , 

In tE!rms of this absorption model. the spatial structure in the electron Signatures 

(Figure ;~) must retlect a spatial variation in the density of the cloud. The energy 

dependence of the electron signatures, however. is more difficult to understand. Since 

the pathtength of a particle in one pass through a slab region (thinnest normal to the 

equator) that is large compared to thE~ particle's gyroradius depends only on that 

particle's pitch angle, not on its gyroradius, and since higher-energy electrons, due to 

their larger drift velocities, would traverse such a slab fewer times, more lower-energy 

electrons (down to -1 MeV) should be absc)rbed. The measured signatures are deeper 

at higher energi.es, however .. This contradiction may be reconcilable if the higher-

energy electrons had !latter pitch angle distributions, and thus were better confined 

to the equator where the absorber is presumed to be. 

7. DiscU!mon and Snmmary 

The electron microsignature observed by the CRS instrument near V.Jm.as may be 

explainable either as the result of an intense, localized burst of waves which scatter 

electrons out ol~ the regiOn. or as the result of absorption by some additional material 

in Mimas's orbit. Both hypotheses require additional ad hoc assumptions to produce 

the absorption: a wave duct tor the former, and a cloud of finer material for the latter; 

27 

and neither set of assumptions has been directly verified by other observations. How­

ever, other observations of another microsignature which is interpreted as due to low 

energy ions [Carbary, st aI., 1983], were obtained simultaneously with the CRS elec­

tron signature. If the interpretation of these other data is correct, the ion observa­

tions discriminate against the wave-particle interaction hypothesis in favor of the 

absorption hypothesis. 

Carbary, st aI. [1983] report observing a micro signature similar to and simultane­

ously with the CRS signature, but in ions with energies of 28 - 100 keY. In addition, 

they have measurements that suggest that the absorption is greatest for local pitch 

angles near 90°. These observations discriminate against the wave-particle mechan­

ism for three reasons. First, since the gyrofrequencies of these ions and MeVelec­

trons differ by a factor of 100, the wave turbulence would need to be extremely 

broad-band to resonantly interact with both of these particle species. Secondly, since 

the bounce period for these ions is 100 times longer than the relativistic electron 

bounce period. the required interaction time would rise from 6 seconds (estimated for 

the electrons) to many minutes. Finally, waves would be expected to make the parti­

cle distribution isotropic with particles lost at small pitch angles, in the loss cone, not 

at 90° pitch angle. Alternatively, the pitch angle dependence of these ion observations 

supports the hypothesis of absorption by material. As retiected by the cosa factor in 

equation (7), particles with larger pitch angles spend relatively more time in the 

absorption region and thus would be expected to be more heavily absorbed. 

The simultaneous observation of signatures in both MeV electrons and keV ions 

also places stringent constraints on the location where the absorption must have 

occurred. Since these two populations of particles drift in opposite directions with a 

relative velocity or 60 km 5- 1 (for 5 MeV electrons and 100 keV ions) the observation of 

an absorption signature Simultaneously in both ions and electrons means that the 

spacecraft must have crossed the L-shell of the interaction region at the longitude 

28 

where the intera(~tion was occurring, and that the absorption was taking place as the 

spacecraU passed. The probability of suc:h a close encounter is ~10-4, assuming a sin­

gle cloud 100 km long. Thus either the observation was extremely lucky, or there may· 

be many such clouds or particles in orbit with Mirnas. 

A similar set of circumstances surrowlds the Pioneer 11 microsignature observa­

tions. Simpson, et al. [1980b] reported sir:nultaneous proton and electron signatures. 

Van Allen, et al. [1980b] have disputed this report. suggesting that the proton signa­

ture was spurious, i.e. that it was produced by electrons. The probability that an. 

absorption signat.ure would have been observed along the inbound pass of Pioneer 11 

may be expected to be higher than 10--4., the probability of crossing a 100 kIn object or' 

cloud randomly distributed around 3.1 Rll/, because Pioneer 11 passed near the Lagran·· 

gian point ..... 600 behind Mimas [Simpson, st al., 1980b]. Small objects may be expected 

to reside in stable orbits in this region [Dermott, et al., 19BO]. The Voyager 2 absorp" 

tion sign.ature was not observed near a stable Lagrangian point, rather, it was 

observed 2120 beh.ind (i.e. west of) l'J.m.as. Thus, if both the Voyager 2 and the Pioneer 

11 signat.ures were produced as absorption signatures due to additional material in 

orbit with Mirnas, it is improbable that the two signatures were produced by the same 

object or clump of material. 

From the perspective of the Pioneer 11 and Voyager 2 charged particle observa·· 

tions, as currently interpreted, since microsignatures were observed in 2 of the 4 

passes across the orbit or Mimas, and since the probability of an encounter with a sin .. 

gle absorber is small, there must be a significant abundance of material surrounding 

Mimas. Clearly the best way to support or refute this conclusion is through a detailed 

analysis or all available Voyager images of Mimas's orbit. Such analysis should either 

find some of the~ suspected objects or place upper limits on the sizes of any such 

absorbers that can be compared to the results of the parti.cle absorption studies. 

The other major results or the analysis presented in this report are independent 

29 

of the question of what produced these signatures. The electron spectrum near 

Mimas's orbit as displayed in Figure 3 illustrates that most of the electron flux above 

.... 100 keV is concentrated in the energy range 1 to 3 MeV. Van Allen, et al. [1980b] had 

predicted that the flux should be concentrated near 1.6 MeV by the "band-pass filte!,­

ing" action of Enceladus. The data of Figure 3 support this model. However, the 

observed spectrum is clearly broader than -0.1 MeV, the maximum width deduced by 

Van Allen, et at. [1980b], who assumed that the Pioneer 11 signature was produced by 

Y.Jmas. In their "band-pass-filter" model, Van Allen et al. further suggested that such 

a narrow spectrum would require a small ditrusion coefficient. They estimated a value 

of D ~ 10-10 ~ 2 s-l at the orbit of Enceladus which they extrapolated to D ~ 8x 10-12 to 

4X10-11 ~2 s-l at the orbit of Mimas. 

However, the lower limit derived in this paper for the radial difIusion coef!icient 

for electrons at Mimas's orbit is D,;:: 10-8 Rs2 s"l. This value is based on the absence of 

any significant absorption signature in the inbound Voyager 2 data and on the lack of 

energy dispersion in the position of the outbound signature. Both of these features 

suggest that Mimas could not have produced the signature observed on Voyager 2. A 

similar limit on D is required under the hypothesis that the signature is an absorption 

signature, in order to confine the Signature to within ..... 20 0 of the absorber. 

If this value for the d.ift'usion coefficient is applied to the Pioneer 11 observations, 

it appears unlikely that the Pioneer 11 signature could be attributed to Mimas. 

Pioneer 11 passed -60Q from Mimas during its inbound pass [Simpson et al., 1980b; Van 

Alien, eL cl .. 1980b]. The age of the signature. Le. the time since Mimas last passed the 

lrshell where the signature was observed, was 6.44 hours [Van Alien, et al., 1980b]. 

Thus with our lower limit estimate for the dif!usion coefficient, the normalized 

ditIusion time (section 5) is 7':?! 70, and the maximum depth of an absorption signature 

at any energy could be no more than 13%. The dispersive effects of the energy depen­

dence of the drift velocity would act to reduce the depth of a signature observed with 

30 

a detector with a broad energy responsl~ even further. Since Van Allen, et al. [1980b] 

observed absorption signatures with depths of 30% to 40%, these signatures could not 

have been produced by Mimas if D";;/! 10-8 R.2 s-l. 

The lower limit for the electron diffusion coefficieIlt that we have obtained -is 

significantly larger than the values inIurred from studies of the high-energy proton 

populatil:>n. Cooper [1983] has determined D~10-15L9 R/ s-I,"with an estimated uncer­

tainty of a factc)r of two, for >30-MeV protons. Thus at L = 3.1, D~2.6xl0-11 Rfj2 s-l. 

Van Allen [1983J has obtained D~2.8x10-"11 ~ 2 s-l, for >80-MeV protons at L = 2.6'7, 

with a lower limit of roughly half this value and an upper limit ..... 25 times larger. These 

results are all le~ss than 1% of the lower limit inferred in this paper for MeV electrons. 

This dit!1~rence may ultimately be reconcilable if the diffusion coefficient is inversely 

proportional to the rigidity of a particle or inversely proportional to the square of a 

particle's rnagneltic moment. It is important to note, ho"wever, that while the proton 

clifiusion coefficient may be sensitive to phenomena that are effective over time scales 

of up to years (the inferred lifetime of high-energy protons in this region), the 

phenomena responsible for the electron ditfusion analyzed in this paper operate on 

time scales of a few hours or less. 

In conclusion, we emphasize two important aspects of this analysis. First. the 

limit inflerred for the electron diffusion coefficient, D, is independent of the question (,f 

what produced the observed signature. TIils limit is one of the principal results of this 

paper. Secondly, the 1% or more opacity inferred for the cloud on the basis of the 

absorpti.on hytx)thesis is large, and a significant number of such clouds is suggested 

by combining the Voyager and Pioneer observations. While a more satisfactory expla­

nation for these microsigI:ature observations has not yet been suggested, these con­

clusions need t.1~ be either confirmed or refuted by analysis of imaging observations. 

Until that happens, the Mimas ghost will remain an enigma. 

31 

This Page Intentionally Left Blank 

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End of Document