Absorption effects of the four innermost moons in the radial transport equations for electrons and protons in Jupiter's magnetosphere are presented. The phase space density n at 2 R sub J for electrons with equatorial pitch angles less than 69 deg is reduced by a factor of 4.2 x 1000 when lunar absorption is included in the calculation. For protons with equatorial pitch angles less than 69 deg, the corresponding reduction factor is 3.2 x 100000. The effect of the satellites becomes progressively weaker for both electrons and protons as equatorial pitch angles of pi/2 are approached, because the likelihood of impacting a satellite becomes progressively smaller. The large density decreases which we find at the orbits of Io, Europa, and Ganymede result in corresponding particle flux decreases that should be observed by spacecraft making particle measurements in Jupiter's magnetosphere. The characteristic signature of satellite absorption should be a downward pointing cusp in the flux versus radius curve at the L-value corresponding to each satellite

Birmingham, T. J.

Hess, W. N.

Mead, G. D.

English

NASA Technical Reports Server

- X-641-73-362
ABSORPTION/ OF TRAPPED PARTICLES
BY JUPITER'S MOONS
(NASA-TH-X-70522) ABSORPTION OF TRAPPED 74-12481
PARTICLES BY JUPITER'S MOONS (NASA)
20-p HC $3.00 CSCL 03B
Unclas
G3/30 22809 )
W. N. HESS,
T. J. BIRMINGHAM
G. D. MEAD
/
- - ~NOVEMBER ; 9' -,
\ (
GODDARD SPACE FLIGHT, CENTER,
GREENBELT, MARYLAND
.- -
https://ntrs.nasa.gov/search.jsp?R=19740004368 2020-03-23T12:34:23+00:00Z
ABSORPTION OF TRAPPED PARTICLES BY JUPITER'S MOONS
W. N. Hess
Environmental Research Laboratories
National Oceanic and Atmospheric Administration
Boulder, Colorado 80302
T. J. Birmingham
G. D. Mead
Laboratory for Space Physics
NASA/Goddard Space Flight Center
Greenbelt, Maryland 20771
November 1973
)
ABSTRACT
We have included absorption effects of the four innermost moons
in the radial transport equations for electrons and protons in Jupiter's
magnetosphere. We find that the phase space density n at 2 R. for
electrons with equatorial pitch angles <690 is reduced by a factor of
4.2 x 104 when lunar absorption is included in the calculation. For
protons with equatorial pitch angles <690 the corresponding reduction
factor is 3.2 x 106. The effect of the satellites becomes progressively
weaker for both electrons and protons as equatorial pitch angles of r/2
are approached because the likelihood of impacting a satellite becomes
progressively smaller. The large density decreases which we find at
the orbits of Io, Europa, and Ganymede result in corresponding particle
flux decreases that should be observed by spacecraft making particle
measurements in Jupiter's magnetosphere. The characteristic signature
of satellite absorption should be a downward pointing cusp in the flux
vs. radius curve at the L-value corresponding to each satellite.
ECEDING PAGE BLANK NOT FILMED
2
INTRODUCTION
The Galilean satellites of Jupiter, located deep within its
magnetosphere, may play an important role in limiting the fluxes of electrons
and protons in Jupiter's radiation belts. The effectiveness with which
a moon reduces particle fluxes in its neighborhood by its sweeping effect
depends on how rapidly particles move radially across the moon's orbit
by diffusion and acceleration processes. Mead and Hess (1973) concluded
that if radial diffusion were caused by solar wind-induced magnetic
field variations or by fluctuations in the convection electric field in
Jupiter's magnetosphere, diffusion would proceed very slowly at low altitudes,
and the inner Galilean moons would absorb essentially all radially
diffusing particles.
Recent studies by Brice and McDonough (1973), Jacques and Davis
(1972), Coroniti (1973), Birmingham et al. (1973), and Stansberry and
White (1973) have indicated, however, that if the trapped electrons
responsible for Jupiter's decimeter radiation have diffused in from the
solar wind, additional low-altitude diffusion mechanisms are needed in
order to bring the electrons down to the synchrotron-emitting region in
times comparable to their average synchrotron loss lifetimes. Brice and
McDonough have suggested that inside about 10 RJ, the diffusion is
probably caused by electric fields associated with an upper atmospheric
dynamo driven by neutral winds. This type of diffusion is estimated
to be much stronger than diffusion generated by magnetopause motions or
convection electric fields in the region R < 10 RJ, because of the
proximity of its source.
3Birmingham et al. (1973; hereafter referred to as BHNBL) have determined
a radial diffusion coefficient D by making empirical fits to the observed
10.4-cm radiation from Jupiter (Berge, 1966). A steady-state model of
the electron radiation belts was developed. This model assumed injection
of particles from the solar wind, radial diffusion, energy degradation
by synchrotron radiation, and absorption at Jupiter's surface. A
diffusion coefficient of the form
D = k Rm (1)
was assumed. The following values of the parameters were in best
agreement with the observations:
k = 1.7 ± 0.5 x 10- 9 R 2/sec (2)
m = 1.95 ± 0.5
1o = 770 MeV/Gauss
where o is the (monoenergetic) magnetic moment at the time of injection.
These values of k and m are reasonably consistent with the atmospheric
dynamo mechanism.
LUNAR ABSORPTION MODEL
In this paper we estimate the absorption effects of the moons
Amalthea (R = 2.55 R), Io (R = 5.95 R), Europa (R = 9.47 RJ), and
Ganymede (R = 15.1 Rj), by adding loss terms representing these satellites
to the BHNBL electron transport equation!
As in BHNBL, n is the number of electrons with magnetic moments between
p and p + dp (p is in units of MeV/Gauss), with longitude invariants
between 0 and AJ, contained in a (dipole) magnetic field flux tube which
crosses the jovimagnetic equatorial plane a distance R (in units of
Jovian radii) from the center of the planet and which has a cross-sectional
area of R dR d4 in that plane (d is an element of longitude). The first
term on the left side is the radial diffusion term, the second term
represents synchrotron energy loss, and the third term represents absorption
by the satellites. The source, located at Ro with the source strength N,
is represented by the term on the right. (The position of the source,
so long as it is further out than Ganymede, has no effect on the radial
shape of n at R<15.1 Rj; we have taken Ro = 35 Rj.) The four satellites,
i = 1 to 4, are centered at distances Ri from the center of the planet
and have radii ai. The step function S(R-Ri±ai) is unity over the
region Ri - ai < R < Ri + ai and zero elsewhere. The average "lifetimes"
Ti depend on the electron energy and equatorial pitch angle as well as
the satellite by which the electron is being absorbed. Implicit in
Equation 3 is the assumption that a single form of D is valid out to
the radius of Ganymede's orbit.
As in BHNBL, Equation (3) is solved by a numerical finite difference
technique with the boundary conditions that n vanish at the surface of
Jupiter [n (R=l) = Ol and at the magnetopause Jn(R=Rm) = O] and that the
sole source of electrons be that shown explicitly on the right hand side
(we thus demand that n(p > Vo) = 0 so that there is no flow of electrons
into the system through boundaries in u-space).
6RESULTS
Equation (3) has been solved for several different combinations of
parameters. In all cases we have taken po = 770 MeV/Gauss at injection.
Populations of electrons with p <1jo are formed, however, due to energy
degradation caused by synchrotron radiation. The upper curve in Figure 1
is a plot of the density of the highest-energy electrons (V = po) vs.
R for m = 1.95 and k = 1.7 x 10- 9 Rj2/sec. (Electrons with 1 =po occur
at radii other than the injection radius Ro because of the finite difference
method of solution; cf. discussion in BHNBL.)
The lower curve of Figure 1 shows the effect of lunar absorption on
electrons with equatorial pitch angles everywhere less than 690 (mirror
latitudes greater than 100). These electrons undergo Case 2 or snowplow
absorption (Mead and Hess, 1973). That is, since their mirror latitude
is always greater than the jovimagnetic latitude of the absorbing moon,
and since the relative longitudinal motion with respect to the moon during
one bounce period is less than a lunar diameter, the characteristic
absorption time T. at each moon is roughly equal to the lunar corotation1
period, i.e., the apparent (retrograde) period of revolution of each
moon in a frame of reference rotating with Jupiter's decametric rotation
period (Mead and Hess, 1973). The trapped particles are assumed to
corotate with the planet at least out to 16 Rj. This lunar corotation
period is 2.4 days at Amalthea, 0.54 days at Io, 0.47 days at Europa,
and 0.44 days at Ganymede.
7A significant absorption effect occurs at the positions of Io, Europa,
and Ganymede (due to its tiny size, Amalthea exerts a negligible effect).
The effect is seen as a discontinuity in the slope of the electron
density at each of the satellite positions, producing a downward-pointing
cusp.
Due to the 100 tilt of Jupiter's dipole with respect to its rotation
axis, electrons with equatorial pitch angles greater than 590 will have
longer average absorption lifetimes at each satellite. The Galilean
satellites oscillate between ± 100 jovimagnetic latitude in one corotation
period, and low-latitude-mirroring particles are less likely to collide
with a satellite than are high-latitude-mirroring particles (Mead and
Hess, 1973). The middle curve of Figure 1 shows the density of electrons
with an equatorial pitch angle of 870 (mirror latitude of 1.50) at
R = 1.85 Rj, the heart of Jupiter's synchrotron radiation region. These
electrons would contribute significantly to the emission observed at
Earth. The equatorial pitch angle varies from 870 to 84.90 in the
region out to 16 Rj under V and J conservation. The absorption lifetimes
for a p = 770 MeV/Gauss electron as calculated from Equation 37 of
Mead and Hess (1973) are 25 days at Amalthea, 5.8 days at Io, 5.1 days
at Europa, and 5.0 days at Ganymede. The effects of absorption are
clearly greatly reduced for these near-equatorial particles.
The effectiveness of each satellite in wiping out electrons which
mirror at latitudes greater than 100 is also evident from the first
column of Table 1. The reduction factor is the ratio of n at adjacent
points midway between satellites. The cumulative effect of the satellites
8on these same electrons is seen from the second column of Table 2. The
ratio listed here is the value of n without moons (upper curve of Fig. 1)
divided by n with moons (lower curve of Fig. 1) at the same R.
The error limits quoted in Equation (2) result from uncertainties
in fitting the Berge (19E6) data. The dependence of satellite wipe-out
on these uncertainties has been estimated by also solving Eq. (3) for
high latitude mirroring electrons for the following pairs of m and k:
1) m = 1.45, k = 1.7 x 10 sec-1; 2) m = 2.45, k = 1.7 x 10 9 sec-1
3) m = 1.95, k = 1.2 x 10 sec-1 ; and 4) m = 1.95, k = 2.2 x 10 sec-I
Results for Cases 1 and 2 are shown in Fig. 2. We show both high-p (1=770
MeV/gauss) and low-I' (1=0.48 MeV/gauss) electrons. (The dotted curves
are the m = 1.95 results without moons.) Uncertainties in n resulting
from this m variation are of the order of a factor of 20 at each
satellite for the p = 770 MeV/gauss electrons. They are even larger for
the low- electrons. In no way, however, do these uncertainties negate
the conclusion that the satellites are very effective in wiping out high
latitude mirroring electrons. Uncertainties in n due to the k-variation
are of the order of a factor of 2 at each satellite and hence considerably
smaller than those shown in Fig. 2. Values of the reduction factor at
each satellite for p = 770 MeV/gauss electrons are also listed in Table 1
for Cases 1-4.
The Galilean satellites can be similarly important in limiting the
fluxes of energetic protons. We have studied this effect by solving
Eq. (1) with the synchrotron energy loss term eliminated. (Because of
their mass, protons are far poorer synchrotron radiation emitters than
are electrons of the same p.) The values of po and D were taken to be
the same as were determined for the electrons. Figure 3 shows the results
for protons mirroring at latitudes greater than 100. The lifetimes of
these particles (0.14 days at Amalthea,0.28 days at Io,0.38 days at
Europa, 1.13 days at Ganymede) were calculated in the same way as for
electrons, the one difference being that proton energies close in to
Jupiter's surface are so large that gradient-curvature drifts strongly
dominate co-rotational ExB motions. Shown for comparison is the
lower electron curve of Fig. 1.
The generally greater effectiveness of the satellites in removing
protons, as seen in Fig. 3 and Tables 1 and 2, results from the shorter
absorption lifetimes of protons. The precipitous fall-off of the electron
density inside of Io is partly the strong effect of electron synchrotron
energy loss in this region. The cumulative effect of the satellites is
to reduce the proton density near R = 2 by a factor of 3.2 x 106 from
what it would be without moons.
DISCUSSION
Because the Galilean satellites have such a large effect on the
electron density, it is legitimate to question the use of m = 1.95 and
k = 1.7 x 10 9 sec-1 which were obtained by BHNBL without considering
satellite absorption. We have repeated the synchrotron calculation of
BHNBL with these same values of m and k and with satellite absorption
included in the electron transport equation. We find that the fit to
10
the observed radial profile of synchrotron radiation is only slightly
poorer with satellite absorption than without: the RMS residual U is
0.0049 with satellites and0.0027 without satellites. (For the same
injection strength, the intensity of sychrotron radiation is, however,
orders of magnitude weaker with satellites than without.) We have
-9 -1
therefore continued to use m = 1.95, k = 1.7 x 10 sec
The large density drops in electrons and protons at Ganymede,
Europa, and Io should manifest themselves in corresponding flux reductions
as observed by satellites traversing Jupiter's magnetosphere. The flux
4
F (E, Q) of particles differential in total energy E = ymoc and solid
angle Q is related to n by (Northrop and Teller, 1960)
2 24 2(E - mo c ) n R (4)
F=
2
r mo c ao
at a near-equatorial point R in the field of a dipole of strength ao. In
crossing the orbits of Ganymede, Europa, and Io, F in Eq. 4 is most criti-
cally affected by the change in n.
The fluxes of protons and high energy electrons ought to exhibit
the behavior of n as shown in Figures (1-3) with a downward pointing cusp
(indicating a discontinuity in an/DR) at the position of each of the
three effective satellites. The drop in flux should be most pronounced
at jovimagnetic latitudes >100 because (cf. Fig. 1) particles mirroring
near the magnetic equator have a greater chance of escaping absorption
than do those mirroring at higher magnetic latitudes.
11
Our conclusions are based on the simplest model of Jupiter's magneto-
sphere containing what we consider the essential physics. The possible
failure of spacecraft to see the flux jumps which we predict would
indicate to us that one or more of our premises are in error: 1) the
Galilean satellites may be sufficiently conducting that field distortions
allow particles to slip around and past moons rather than impact them;
2) the form of D obtained by BHNBL in the 1-4 Rj region may be invalid at
the larger R positions of the satellites; or 3) the source of energetic
charged particles may not be the solar wind but local acceleration in the
vicinity of one or more of the satellites themselves (Hubbard et al., 1973).
The era of active exploration of Jupiter's magnetosphere which is
now beginning should answer the question of the correctness of our model.
REFERENCES
Berge, G. L., An interferometric study of Jupiter's decimeter radio
emission, Astroph. J., 146, 767, 1966.
Birmingham, T., W. Hess, T. Northrop, R. Baxter, and M. Lojko, The
electron diffusion coefficient in Jupiter's magnetosphere,
J. Geophys. Res., in press, 1973.
Brice, N. M., and T. R. McDonough, Jupiter's radiation belts, Icarus,
18, 206, 1973.
Coroniti, F. V., Energetic electrons in Jupiter's magnetosphere,
Astroph. J., in press, 1973.
Hubbard, R. F., S. D. Shawhan, G. Joyce, Io as an emitter of 100 KeV
electrons, Dept. of Physics and Astronomy Res. Report 73-22,
University of Iowa, 1973 (submitted to J. Geophys. Res.).
Jacques, S. A., and L. Davis, Jr., Diffusion models for Jupiter's
radiation belt, California Institute of Technology preprint, 1972.
Mead, G. D., and W. N. Hess, Jupiter's radiation belt and the sweeping
effect of its satellites, J. Geophys. Res., 78, 2793, 1973.
Northrop, T. G. and E. Teller, Stability of the adiabatic motion of
charged particles in the earth's field, Phys. Rev., 117, 215, 1960.
Stansberry, K. G., and R. S. White, Jupiter's radiation belts, to be
published in J. Geophys. Res., 1973.
TABLE 1
Reduction Factor per Moon*
ELECTRONS PROTONS
Best Fit Best Fit
Parameters +A m -A m + A k -A k Parameters
IO N(R=7.7) 64.9 16.6 336.7 40.8 114.9 38.9N(R=4.2)
EUROPA N(R=12.3) 21.6 6.62 84.0 16.0 31.0 36.7N(R=7.7)
N(R=19)
GANYMEDE N(R=12.3) 23.4 5.75 123.1 17.2 33.8 83.3
* These values are for /- = 770 MeV/Gauss the highest magnetic moment particles
present and also they are for particles of equatorial pitch angle ae< 690 so that
these particles bounce far enough off equator to always reach the moon's orbit.
- 109954 (.A
TABLE 2
Total Reduction Factor*
ELECTRONS PROTONS
R/RJ N(no moons) N(no moons)
N(4 moons) N(4 moons)
2.0 41700 3.23 x 108
4.2 39600 1.10 x 106
7.7 1694 18000
12.3 72.0 331.0
19.0 2.40 2.70
These values are for/. = 770 MeV/Gauss the highest magnetic moment particles
present and also they are for particles of equatorial pitch angle ae<690 so that
these particles bounce far enough off equator to always reach the moon's orbit.
LIST OF ILLUSTRATIONS
Fig. 1
The phase space density of electrons with magnetic moment v = 770
Mev/gauss obtained by solving Eq. 3. The top curve does not include
lunar absorption. The middle curve is for electrons which have an
equatorial pitch angle of 870 at 1.85 R. The bottom curve is for
electrons which everywhere have an equatorial pitch angle <690.
Fig. 2
The phase space density of electrons.with equatorial pitch angles
<690. The effect of the uncertainties in m (Eq. 2) on both high and low
V particles are evident.
Fig. 3
The phase space density of protons with equatorial pitch angles
<690, with and without lunar absorption. The electron curves are
repeated for comparison.
1010
No Moons -
8108 a =87
4 Moons
Ganymede
106  ae<6910
Europa
4-104
2- 1\--102
1 5 10 15 20 25
R/Ri
Figure 1
- ' I ' ' I '' I ' ' I ' ' I ' ' -=
e4 M V104 - = 770gauss
_I 2 _ _
102- - / -
010o-0 gauss
ms mi = 2.45
108 m =1.95 --
m = i.45
mi
106 .MeV
= 0.4 8 0-=gauss
10
10 4 I:: l l I I I 1 : ::::::::: ::5::1:::l:::l::5::5::F::t :-:!::::::T ~
108
S 5 10 15 20 25 30
R/Rj
Figure 2
MI094
1010
P No Moons
8- e
10
4 Moons
106 "-Ganymede
e
- Europa
410
102  Amalthea101-
1 5 10 15 20 25
R/Rj
Figure 3


Absorption of trapped particles by Jupiter's moons

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