  The time evolution of the strength of the Earth's virtual axial dipole moment
(VADM) is analyzed by relating it to the Fokker-Planck equation, which
describes a random walk with VADM-dependent drift and diffusion coefficients.
We demonstrate first that our method is able to retrieve the correct shape of
the drift and diffusion coefficients from a time series generated by a test
model. Analysis of the Sint-2000 data shows that the geomagnetic dipole mode
has a linear growth time of 13 to 33 kyr, and that the nonlinear quenching of
the growth rate follows a quadratic function of the type [1-(x/x0)^2]. On
theoretical grounds, the diffusive motion of the VADM is expected to be driven
by multiplicative noise, and the corresponding diffusion coefficient to scale
quadratically with dipole strength. However, analysis of the Sint-2000 VADM
data reveals a diffusion which depends only very weakly on the dipole strength.
This may indicate that the magnetic field quenches the amplitude of the
turbulent velocity in the Earth's outer core.
