On the basis of earth observations of the HF and UHF radio emission generated near Jupiter, the presence of energetic charged particles trapped in the planet's dipole magnetic field has been inferred. For electrons, energies of the order of 10 MeV and peak fluxes of the order of 10 to the 7th power per square centimeter per second can be derived from the data for equatorial regions about two planetary radii from the dipole. Energetic protons and lower-energy electrons and protons are also expected, but the limited data require that their fluxes be based on theory or earth analogy. Because descriptions available in the literature suggest large associated uncertainties, both nominal and limiting models for the charged-particle populations of Jupiter's belts are derived. These new engineering models describe electron and proton fluxes and their distributions in energy and position in forms suitable as space vehicle design criteria

Divine, N.

English

NASA Technical Reports Server

Jupiter Radiation Belt Engineering Model
Nell Divine
Jet Propulsion Laboratory
On the basis of earth observations of the HF and UHF radio emission
generated near Jupiter, the presence of energetic charged particles trapped in
the planet's dipole magnetic field has been inferred. For electrons, energies
of the order of 10 MeV and peak fluxes of the order of 10 7 cm -2 s -1 can be
derived from the data for equatorial regions about two planetary radii from
the dipole. Energetic protons and lower-energy electrons and protons are
also expected, but the limited data require that their fluxes be based on theory
or earth analogy. Because descriptions available in the literature suggest
large associated uncertainties, both nominal and limiting models for the
charged-particle populations of JupiterIs belts are derived. These new engi-
neering models describe electron and proton fluxes and their distributions in
energy and position in forms suitable as space vehicle design criteria.
In the planning of missions to encounter the
planet Jupiter both spacecraft design considera-
tions and trajectory selection may be strongly
affected by our understanding of the charged-
particle environment trapped in Jupiterts magnetic
field. These energetic electrons, and possibly
protons, could be hazardous for spacecraft elec-
tronics and other sensitive subsystems. The
presence of relativistic electrons has been in-
ferred from analyses of Jupiter's radio emission.
The extensive literature in this field has been
reviewed recently by Cart and Gulkis (ref. I) and
by Warwick (ref. 2), from which the following
brief summary is adapted.
RADIO DATA
The HF radiation, at wavelengths longer than
about 7 m, is sporadic; the probability that it be
observable is correlated with the sub-earth longi-
tude on Jupiter and with the Jovicentric longitude
of the first Galilean satellite, Io. The radiation's
characteristic patterns in time and frequency
coordinates permit conclusions to be drawn about
the strength and configuration of ,Tupiter's mag-
netic field, although controversy surrounds many WAVELENGTHX(cmJ
features of such interpretations. Nevertheless, 3000 1000 3o0 100 30 10 3 1.0
the upper limit shown in figure 1 near 40 MHz for m-211[/_1 i _ I 1 i i
the radiofrequency in bursts reaching the earth _ m "22
implies a magnetic field strength of 14 G some-
where just above Jupiter's atmosphere, following _E 10.23 rusk
the commonly accepted argument that the burst _ m_t
EMISSION /
mechanism yields radiation at the local electron _ i0_24 //
gyrofrequency. Thus, a magnetic dipole moment _-_ /
near 4 X 103UG-cm3, considerably stronger than 0_ [,_/D.EBCuA._T_T£R_DECAMETERBuRSTS SYNCHROTRON /
the earth's, is implied for Jupiter. The dipole is =×<_ 10-25_z///////_ y/z/////////-////_/RADIATION/
probably centered on Jupiter (although displace- _ _ /
ments up to 0. 7 radii south have been proposed; __
ref. 2), and inclined about 10 deg to Jupiter's _o HF _UHF.._ D.
10 -27
axis. The int raction of this dipole with the solar
wind leads us to anticipate a large magnetosphere, 10 -28 l I [ ] ] I
whose minimum extent (in the sunward direction) m 30 m0 300 moo _0 10,000 30,000
is about 50 Jupiter radii (ref. 1). O8SERVATIONFR[QUENCYy(MHz)
At wavelengths less than or near a few centi-
meters the UHF component shown in figure 1 is
dominated by thermal emission from the disk,
which need not be further discussed here. At
wavelengths up to about 100 cm a non-thermal
component is indicated on figure 1, having a flux
density with very little dependence on time and
frequency (generally less than 30%). Numerous
characteristics indicate that this radiation is
synchrotron radiation from relativistic electrons
contained by Jupiter's magnetic field. Strong
support for this hypothesis is provided by the
radio brightness temperature contour maps ob-
tained by aperture synthesis at 10. 6 and 21 cm by
Berge (ref. 3) and Branson (ref. 4). Most of this
radiation is produced noticeably away from the
disk of the planet, in a region elongated roughly
parallel to the equator. In addition, up to 30%
east-west linear polarization is observed. These
characteristics, plus the beaming inferred from
the flux density variations, confirm the synchro-
tron mechanism, and imply that the relativistic
electrons are most abundant near Jupiter's mag-
netic equator. The models in the following sec-
tions have been derived from these data for use as
NASA space vehicle design criteria, and are dis-
cussed more fully in ref. 5.
Figure I. Schematic radio spectrum of Jupiter, adapted from Carr and
Gulkis (ref. i)
This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory,
California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aero-
nautics and Space Administration.
556
https://ntrs.nasa.gov/search.jsp?R=19720010023 2020-03-17T03:45:09+00:00Z
RELATIVISTICELECTRONS
If the strength of the magnetic field at the
UHF flux peak and the observed bandwidth are
known, the characteristic electron energy can be
derived from numerical formulas which summa-
rize the results of synchrotron emission theory.
As some of the required data are uncertain, only
the order of magnitude of the electron energy near
the UHF flux peaks has been evaluated at about
10 MeV (ref. 1). If a reasonable distribution of
the source contributions along the line of sight is
taken, the synchrotron theory also permits the
local electron flux to be derived from the ob-
served intensity. This can be done for the source
as a whole, or in detail so that the distribution of
electron flux with position is obtained.
For JupiterWs equatorial plane, figure 2
shows the results of several such derivations; the
differences among them result from the applica-
tion of various combinations of reasonable
assumptions required in the analysis. The result
credited to Carr and Gulkis (ref. 1) is simply an
order-of-magnitude estimate, in which a flux of
107 relativistic electrons/cm 2 s occurs in a broad
region of space surrounding Jupiter. The models
of Branson (ref. 4) and Luthey and Beard (ref. 6)
are based on the observations alone, but the poor
resolution of the data is reflected by the lack of
detail in their results. The model of Eggen (ref.7}
is based on earth analogy as well as on the data,
but the details of this model result from the anal-
ogy and are unrealistic. The model described by
Warwick (ref. 2) is based on both the data and on
a physical mechanism for the population of
Jupiter's radiation belts. That mechanism is the
L-shell diffusion of solar wind electrons which
have penetrated the outer boundary of the magneto-
sphere, and predicts a position distribution pro-
portional to L -4 away from the observed peak
within two radii of the planet.
1091
I0 8
"i'
E
,0 107
Z
u
106
105
I I I I I I I I I
B = BRANSON
CG = CARR AND GULKIS
E = EGGEN
LB = LUTHEY AND BEARD
W = WARWICK
CG
2 3 4 5 6 7 8 9 10
MAGNETIC SHELL PARAMETER L
Figure 2. Flux # of relativistic electrons as functions of distance L from
the dipole (in Jupiter radii) in the plane of the magnetic equator, as
derived by the authors listed
The new engineering models reported here
are plotted in figure 3 to the same scale as in
figure 2, and it is intended that they bracket most
of the conclusions of the authors cited above. In
the figure, the central line represents the nominal
values and the shaded area indicates the range of
the models. In particular, the nominal model
resembles the L-shell diffusion model by Warwick
(ref. 2), because it was felt that the successful
application of such a model to the earth's outer
belt protons (ref. 8) warranted its application to
Jupiter as well. For simplicity in application it
is flat within 2 radii of JupiterJs dipole and pro-
portional to L -4 elsewhere. The limiting models
in figure 3 imply uncertainty factors of 3 at the
flux peak, and larger ones elsewhere, reflecting
the insecurity in the numerical details of the der-
ivation from the limited data available.
In addition to the radial dependence just dis-
cussed, the concentration of the radiation near
JupiterIs magnetic equator implies that the flux
depends strongly on latitude qb. The engineering
models include a factor proportional to
exp (-if2/103) for ff in degrees; this dependence
cuts off near latitude 30 ° in a manner consistent
with the brief latitude analysis presented by
Warwick (ref. Z}.
109
I I I I I I I I I
I08 k
u
107
g
10 6
2 3 4 5 6 7 8 9 10
MAGNETIC SHELL PARAMETER L
Figure 3. Flux ¢ _f relativistic electrons in the engineering models
{same scales as fig. 2)
557
The electron energies, derived from the field
strength and bandwidth, are near 10 MeV, but
there is considerable uncertainty associated with
all quantities involved. In order to achieve con-
sistency with the features of the model adapted
above from Warwick (ref. g), the engineering
models display( characteristic electron energies
E 0 = 6. 2 × 3 "¢1 MeV at the flux peak, and pro-
portional to L -3:e2 elsewhere (a typical L-shell
diffusiontheorydependence).Basedonthe syn-
chrotrontheoryalone,a monoenergeticelectron
populationwouldsufficeto explaintheobserva-tions. Nevertheless,sucha distributionis prob-
ablyunrealistic. Thedataapparentlyrequire
thatfewlow-energyelectrons(ref. 9), andthatfewelectronsabove30MeV(ref. 4), existnear
theflux peak. Thedifferentialenergydistribution(d@/dE)proportionalto (E/E0)exp(-E/E0) is
adoptedfor engineeringpurposes,becauseit is
oneof thesimplestwhichis nearlymonoenergetic(at thecharacteristicenergyE0)andcontainsan
exponentialtermthatresemblesonefor the
earthts belts.
ENERGETIC PROTONS
There are no Jupiter data from which proton
fluxes may reliably be inferred. The few pub-
lished models (refs. 2, 6, 7, 10, and II) proceed
from various assumptions and derive widely
divergent proton energy and flux values. Appar-
ently the most physical discussion among the
above, that of Warwick (ref. Z), applies the
L-shell diffusion mechanism cited for the elec-
trons to the trapping of solar wind protons within
Jupiter's magnetosphere. The result is a number
density everywhere equal to that of the electrons
and identical energy characteristics, where
E 0 = 29 MeV at the flux peak. In the absence of
relevant data and theoretical predictions of equi-
libria among complex source and loss mechanisms,
the uncertainties associated with the flux and
energy values are arbitrarily taken as factors of
10 at the flux peak, and greater elsewhere; for the
model, the lower limit is zero. The upper limit
model flux and energy are independent of distance
from Jupiter. These engineering models are
based on the foregoing considerations, but should
be considered extremely tentative.
In order to illustrate the possibly great range
of proton flux values, figure 4 compares the above
models with the limiting fluxes which can be
_,_n_o_.___.... _ Jupiter's magnetic field. The solid
lines in the figure represent trapping limits,
parametrized by proton kinetic energy E. The
dashed lines represent the model fluxes of protons
with E > 100 MeV. Although it has seldom been
seriously proposed that the real flux values
approach these trapping limits (see ref. 6), such
fluxes are possible, do not violate any known
observations or theoretical considerations, and
would be severely hazardous if they were to reach
spacecraft electronics.
1015
10 TM
1013
1012
1011
'_ 1010
E
O 109
i08
Z
o
C_ 107
106
105
104
103
1
I I I I I I I I
3 4 5 6 7 8 910 20 30 40 50
MAGNETIC SHELL PARAMETER L
Figure 4. Flux ¢ of energetic protons as a function of distance L from
the dipole in the plane of the magnetic equator
could have some serious consequences for space-
craft design, particularly if their uncertain
dependences of energy and flux far from the planet
were relatively flat; nominally these dependences
are expected to diminish rapidly with distance.
The field may also contain energetic protons, for
which apparently reasonable estimates and large
uncertainties are presented. Even these values
are severely hazardous for spacecraft electronics
within two planetary radii of the dipole.
AC KNG W LE DGMEN T
The assistance of Dr. James W. Warwick of
the University of Colorado is gratefully acknowl-
edged.
CONCLUSIONS
Details of the engineering models for Jupiterls
radiation belts based on the above considerations
are presented in the Appendix. The magnetic
field, securely based on the HF and UHF radio
data, is strong and primarily dipolar, having field
strengths near 14 G in the atmosphere, but it has
few in_portant impacts on spacecraft design
directly. Although the dipole is nominally located
at the center of Jupiter, it is inclined by about
10 deg and could be displaced up to 0. 7 radii south
of the center. The field is responsible for the
containment of relativistic electrons, which are
securel_ based on the UHN data. Their peak fluxes,
near 10 / cm-2 s-l, and energies, near 6 MeV,
558
REFERENCES
l.
3.
4.
5.
6.
7.
8.
9.
I0.
ii.
Carr, T. D. , and Gulkis, S.: The Magnetosphere of Jupiter, Annual
Review of Astronomy and Astrophysics, vol. 7, 1969, p. 577.
Warwick, J. W. : Particles and Fields near Jupiter, NASA CR-1685,
1970, 123 pp.
Berge, G. L.: An Interferometric Study of Jupiter's Decimeter Radio
Emission, Astrophys. J., vol. 146, 1966, p. 767.
Branson, N.J.B.A.: High Resolution Radio Observations of the Planet
Jupiter, Monthly Notices of the Royal Astronomical Society, vol. 139,
1968, p. 155.
Anon.: 1970 October draft of "The Planet Jupiter (1970)," NASA Space
Vehicle Design Criteria (Environments), to be published as NASA
SP-80XX.
Luthey, J. L. , and Beard, D. B.: The Electron Energy and Density
Distribution in the Jovian Magnetosphere, Dept. of Physics and
Astronomy, Univ. of Kansas, Lawrence, 1970, 19 pp.
Eggen, J. B.: The Trapped Radiation Zones of Jupiter, Report
FZM-4789, Fort Worth Division, General Dynamics Corp. , 1967,
44 pp.
Nakada, M. P. , Dungey, J. W. , and Hess, W. N.: On the Origin of
Outer-Belt Protons, I, J. Geophys. Res., vol. 70, 1965, p. 3529.
Gulkis, S.: Lunar Occultation Observations of Jupiter at 74 cm and
IZ8 cm, Radio Science, vol. 5, 1970, p. 505.
Haffner, J. W.: Calculated Dose Rates in Jupiter's Van Allen Belts,
AIAA J., vol. 7, 1969, p. Z305.
Koepp-Baker, N. B.: A Model of Jupiter's Trapped Radiation Belts,
Report 68 SD Z63, Missile and Space Division, General Electric
Corp., 1968, 24 pp.
APPENDIX
Electron and proton concentrations and fluxes
may be calculated from the formulas in table I
for a specific position (specified by distance R and
latitude _ with respect to Jupiter) and energy
interval (between E and E + AE) according to the
following procedure. Taking the radius of Jupiter
as Rj = 71,422 kin, calculate the magnetic shell
parameter L = R/Rj (cos 4) 2 . Evaluate the con-
centration parameter NO and the characteristic
energy E 0 from two of the top eight formulas in
table I, ignoring exponents following + signs (use
the pair appropriate to the particle kind, and
appropriate for L less or greater than-Z). Using
the last formula in table I, calculate NE, the par-
ticle concentration for energy greater than E, for
both end points of the energy interval, and differ-
ence them (next-to-last formula in table I) to
obtain (_E)E, the concentration in the energy
interval of interest. Then apply the formula in
the FLUX row to obtain the flux (A_)E in the
interval; if (AE) is not much smaller than E, the
procedure should be repeated with small intervals
and the (A¢)E values summed. Nominal interval
concentrations and fluxes result, in which prob-
ably only two significant figures should be re-
tained. Limiting ones are obtained in the same
way, except that appropriate combinations of
exponents following the ± signs in the expressions
for N O and E 0 should be taken.
559
TABLE I. Formulas for trapped charged-particle radiation near Jupiter *
Relativistic electrons Energetic protons
Number density
parameter
for 0-< L <- 2 N O = (6. 3 X 3 ±1 ) × 10 -4 exp[-c_g/103]cm-3 N O = (6. 3 X 10 -4+1 ) exp[-_g/103]cm-3
for 2-< L _ 50
Characteristic
energy
for O__L -<2
for 2_< L <-50
Flux*_ (interval
distribution with
energy)
for _E << E
Number density*_
(interval and
cumulative
distributions
with energy)
N O =
(minimum N O = 0 for 0 -< L <_ 1.6)
5.8 X 10 -3 "1 15 '4e2
e_p [_/_0 3] (-:T) cm -3
E 0 = 6.2 × 3 +1 MeV
= 1 15 `3±2
E 0 33(_) MeV
(A¢) E = c(AN) E
(_N) E
N O -
(minimum N O = 0)
5.8 × 10 -3
e_P[;3/-_0_] (__.5)4:k4 cm_3
(minimum N O = 0)
E 0 = 29 × I0 ±I MeV
"0 93.3±3
[E(E + 2mpC2)] 1/2
= c(AN)E (E + mpC 2)
For energies >1 MeV only.
_Table IIgives (AN)E and (A@) E as functions of E for 1.6 < L < 2 and d; = 0.
TABLE II. Energetic charged-particle concentrations and fluxes for individual energy intervals at the
peak of Jupiter's trapped radiation belts (1.6 < L < Z and _ = 0)
Particle Energy
kind interval,
MeV
Electrons
Protons
1-3
3-10
10-30
30-100
100-300
300-1000
1-3
3-10
10-30
30-100
100-300
300-1000
1000-3000
3000-10,000
Concentration (AN)E, cm -3
2. 2 x 10 -6
1.9 × 10 -5
9.8 x 10 -6
0.0
0.0
0.0
Non_iL_l
-5
4.6×10
2.5x 10 -4
3.0 x 10 -4
Z. 9 x 10 -5
0.0
0.0
Z. 8 × 10 -6
Z. 7 x 10 -5
1.4 × 10 -4
3.7 × 10 -4
8.9 × 10 -5
0.0
0.0
0.0
M_xln_un_
6.4 × 10 -4
1. 1 x 10 -3
1.0 x 10 -3
9. 3 × 10 -4
5.6 x 10 -5
0.0
1.4 X 10 -3
3. 7 x 10 -3
3.4 × 10 -3
3.7 X 10 -3
3.4 × 10 -3
3.7 × 10 -3
8.9 × 10 -4
0.0
Flux (A_,) E, cm -z s -1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Miulnmu_ ] _u,nlnal
6. 3 X 10 4 I. 4 X 10 6
5.7 × 10 5 7.4 × 10 6
2.9 × 10 5 9.0 × 10 6
0.0 8.7 × 10 5
0.0 0.0
0.0 0.0
0.0 5.6 × 10 3
0.0 9.6 X 10 4
0.0 8.8 x 10 5
0.0 3.6 × 106
0.0 1.3 x 106
0.0 0.0
0.0 0.0
0.0 0.0
ivlaximunl
I. 9 × 10 7
3. 3 × 10 7
3. I × 10 7
2.8 × 10 7
I. 7 X 10 6
0.0
Z. 9 X 10 6
I. 2 × 10 7
Z.O × 10 7
3.6 × 10 7
5. 5 × 10 7
8. 5 × 10 7
Z. 4 × 10 7
0.0
*Maximum (and Minimum) entries are interval-by-interval only, and do not yield a realistic cumulative
spectrum when combined; to obtain the latter the formulas given in table I must be applied using
specific values of N O and E 0.
560


Jupiter radiation belt engineering model

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