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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: L2 = \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 B0. 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 \, Bi' (t1) \, B'j (t2) \, \rangle \, = \, B02 \, \deltaij \, \delta (t1 - t2). We confirmed that L2 \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