The density and clustering of magnetic nulls in stochastic magnetic fields

Many processes in astrophysical plasmas, such as magnetic reconnection and current sheet formation, are sensitive to the topology of the magnetic field. Magnetic nulls are special in a topological sense because they are connected to an infinite number of field lines. Complicated magnetic field geometries may have many nulls and many null-null lines. This work examines the statistical properties of zeros in a random divergence-free vector field model. An analytic expression for the density of nulls is obtained as a function of the dissipation and integral length scales of the random field and the exponent of the energy spectrum of the field. For a broad class of spectra which are similar to the spectra of turbulent cascades magnetic nulls form self-similar clusters. The fractal dimension of the set of nulls is computed as a function of the power law index of the random field. Complicated magnetic topologies may possess tangled webs of nulls and null-null lines. These webs of nulls may be the sites of current sheet formation and heating, and they may modify the properties of particle transport in turbulent plasma media. (C) 1999 American Institute of Physics. [S1070-664X(99)01111-8].