**DPS 2001 meeting, November 2001**

*Session 50. Solar System Dust*

Oral, Chair: F. Spahn, Friday, November 30, 2001, 5:50-6:40pm, Regency GH
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## [50.04] On stochastic forces in circumplanetary dust dynamics

*F. Spahn, A.V. Krivov, Miodrag Sremcevic, U. Schwarz, J. Kurths (U. Postdam, Germany)*

Dust particles in orbit around planets are affected by
stochastic perturbations beyond numerous deterministic
forces. There are, for instance, fluctuations of the
magnetic field or the grain charge. Here we investigate the
dynamics of a dust stream perturbed by a stochastic magnetic
field \vec B', which is modeled by a Gaussian white noise.
Without an electric field the Lorentz force does no work,
and the velocity is a stationary stochastic variable:
\langle \Delta \vec v\,^{2}\,\rangle = {\rm constant} \propto
D (brackets denote an ensemble average, D is a diffusion
constant), like for Brownian particles in equilibrium. This
leads to a normal diffusion in the configuration space: L^{2}
= \langle \Delta \vec r\,^{2} \, \rangle \propto t (L is a
random walk distance, t is time).

To check whether this behavior holds true in a planetary
environment, numerical experiments have been performed. We
have chosen dust grains (0.3 micrometer in radius), escaping
from Jupiter's satellite Europa and integrated numerically
their trajectories over their typical lifetime (100 years).
In one set of runs, the grains experienced a
``deterministic'' corotating dipole magnetic field \vec
B_{0}. In another one, the same grains were additionally
exposed to a Gaussian magnetic field \vec B' such that
\langle \vec B'\rangle \, = \, 0 and \langle \, B_{i}'
(t_{1}) \, B'_{j} (t_{2}) \, \rangle \, = \, B_{0}^{2} \, \delta_{ij}
\, \delta (t_{1} - t_{2}). We confirmed that L^{2} \propto t,
leading to a spread in an orbital element space by almost
200% over 100 years, which directly translates to the
dimensions of the ring formed by the grains. Our results
show a potential importance of stochasticity effects.
Analyses of the magnetic field data measured by the Galileo
magnetometer at Jupiter, providing the statistical
properties of \vec B', are in progress.

This work was funded by Deutsches Zentrum für Luft- und
Raumfahrt (DLR).

The author(s) of this abstract have provided an email address
for comments about the abstract:
frank@agnld.uni-potsdam.de

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