Saturn‘s neutral torus density
as inferred from energetic particle diffusion
observed by Cassini/LEMMS
Abstract
P. Kollmann, N. Krupp, E. Roussos (MPS)
K.K.-H. Glaß
Glaßmeier (TU Braunschweig),
Braunschweig), S. M. Krimigis (APL)
Finding the dominant loss process
During each orbit around Saturn, Cassini observes a decrease in the flux
of protons with about 100 keV in the region of Saturn’s neutral gas torus
which is situated within the inner magnetosphere. Amount and shape of
this decrease can be used to determine the density of the torus.
Introduction
• Cassini/MIMI/LEMMS
measures fluxes and directions of ions and
electrons between several 10 keV and MeV.
• Flux of protons of about 100 keV drops significantly at L<10RS. This
can be attributed to the interaction with neutral particles (neutral torus)
and ice grains (E-ring).
Neutral particles
• interact via charge exchange
• The charged particle created in this process has thermal energies and
is not considered anymore.
Ice grains
• reduce the energy of impacting protons
• Even if the protons are not stopped in the grain, they are lost to the
population with energy E0. On the other hand, protons with E0 are
produced from protons with higher energies that impact on a grain.
Results II
• The interaction with ice provides an additional source term which can
not be found in literature.
• Estimates based on values from literature reveal that the effect of
neutral particles dominates over the effect of ice grains.
E-ring
dependencies of sink term in diffusion equation
term due to interaction with neutral particles
f0 /
Figure 1: Picture of Saturn in visible wavelengths. The E-ring is visible
due to backlight illumination.
Proton distribution at any
given time is governed by
• losses (due to neutrals
and ice)
• radial diffusion
• injections (peak in Fig. 1
is an obvious signature of
the present injections)
It is assumed that the
average distribution is
• representative
• dominated only by losses
and diffusion
can be described by an
diffusion equation
Figure 2: Ion fluxes measured with Cassini/LEMMS during one orbit.
The diffusion equation provides a tool to determine the density of the
material which is creating the losses. Injections can still be added as a
source term.
v
(E) n f0
f 0 /(104 sec)
charge exchange cross section
˜ 10-20 m-2 @ 100keV
Paranicas et al., Icarus, 2008
density n of neutral particles (oxygen atoms)
n˜ 109 m-3
Melin et al., PSS, 2009 (UVIS)
proton phase space density f0
term due to interaction with ice grains
( f0
f1 ...) /
v
(E) n ( f0
f1 )
f 0 /(106 sec)
geometric cross section
˜ 10-12 m-2
Kempf et al., Icarus, 2008 (CDA)
density n of ice grains (1 m size)
n˜ 10-1 m-3
Kempf et al., Icarus, 2008 (CDA)
phase space density f0 of protons with initial energy E0(L)
phase space density f1 of protons with initial energy E1 which
reduces to E0 after passing one grain
f1 ˜ 10-1 f0 @ 100keV
LEMMS
The upper equations are for equatorial mirroring particles. For field aligned
particles the ratio of the maximum ring latitude and the mirror latitude has to be
included as an additional factor. This factor decreases the sink terms.
Figure 4: Equations and numbers showing that the interaction of protons
with neutral particles dominates over the interaction with ice grains.
Phase space densities from model
The diffusion equation can be numerically solved using
• neutral density and diffusion coefficient, which have to be assumed
• two boundary conditions, which can be taken from the observations
(preliminary) Results III
Figure 5:
Comparison
of measured
and observed
phase space
densities.
Phase space densities from observation
• energy and pitch angle are not conserved during radial diffusion
measured fluxes can not be analyzed directly
• first and second adiabatic invariants are approximately conserved
calculation of phase space densities at constant first and second
adiabatic invariant
Results I
Field
aligned
protons
(equatorial pitch angles ˜ 0°)
spend far less time in the
torus
than
the
more
equatorial mirroring protons
(equatorial pitch angles
˜ 90°). This decreases their
probability to interact with
the torus and therefore they
reach closer distances to
Saturn before being lost.
Latter is visible in Fig. 3.
Figure 3: Phase space
densities for different sets
of adiabatic invariants
averaged over more than
100 orbits.
The model of Fig. 5 assumes
• oxygen as the only present species
• diffusion constant in same order of magnitude as Roussos, PhD, 2007
• torus with constant thickness. Its density decreases exponentially in
radial direction
This results in an average density at L=4RS of n=108.9 m-3 which is in
same order of magnitude as Melin et al., PSS, 2009.
Outlook
The assumptions for the numerical calculations will be varied until a good
and robust match between the model and the observation is achieved.
This will finally provide information of the neutral torus density as well as
for the radial diffusion coefficient.