Spectral Properties and Length Scales of Two-dimensional Magnetic Field Models

Two-dimensional (2D) models of magnetic field fluctuations and turbulence are widely used in space, astrophysical, and laboratory contexts. Here we discuss some general properties of such models and their observable power spectra. While the field line random walk in a one-dimensional (slab) model is determined by the correlation scale, for 2D models, it is characterized by a different length scale, the ultrascale. We discuss properties of correlation scales and ultrascales for 2D models and present a technique for determining an ultrascale from observations at a single spacecraft, demonstrating its accuracy for synthetic data. We also categorize how the form of the low-wavenumber spectrum affects the correlation scales and ultrascales, thus controlling the diffusion of magnetic field lines and charged test particle motion.