  The Sun's magnetic field is structured over a range of scales that span
approximately seven orders of magnitudes, four of which lie beyond the
resolving power of current telescopes. Here we have used a Hinode SOT/SP deep
mode data set for the quiet-sun disk center in combination with constraints
from the Hanle effect to derive scaling laws that describe how the magnetic
structuring varies from the resolved scales down to the magnetic diffusion
limit, where the field ceases to be frozen-in. The focus of the analysis is a
derivation of the magnetic energy spectrum, but we also discuss the scale
dependence of the probability density function (PDF) for the flux densities and
the role of the cancellation function for the average unsigned flux density.
Analysis of the Hinode data set with the line-ratio method reveals a collapsed
flux population in the form of flux tubes with a size distribution that is
peaked in the 10-100 km range. Magnetic energy is injected into this scale
range by the instability mechanism of flux tube collapse, which is driven by
the external gas pressure in the superadiabatic region at the top of the
convection zone. This elevates the magnetic energy spectrum just beyond the
telescope resolution limit. Flux tube decay feeds an inertial range that
cascades down the scale spectrum to the magnetic diffusion limit, and which
contains the tangled, "hidden" flux that is known to exist from observations of
the Hanle effect. The observational constraints demand that the total magnetic
energy in the hidden flux must be of the same order as the total energy in the
kG flux tubes. Both the flux tubes and the hidden flux are found to be
preferentially located in the intergranular lanes, which is to be expected
since they are physically related.
