We derive a first order linear differential equation
describing the shape of the probability density
function of magnetic field strengths in the quiet
Sun (PDF). The modeling is very schematic. It considers
convective motions which continuously supply
and withdraw magnetic structures. In addition, a
magnetic amplification mechanism increases the field
strength up to a threshold that cannot be exceeded.
These three basic ingredients provide PDFs in good
agreement with the PDFs produced by realistic numerical
simulations of magneto convection, as well as with quiet
Sun PDFs inferred from observations. In particular, the
distribution is approximately lognormal, and it produces
an excess of magnetic fields (i.e., a 'hump' in the
distribution) right before the maximum field strength.
The success of this simple model may indicate that
only a few basic ingredients shape the quiet Sun PDF.
Our approach provides a concise parametric representation
of the PDF, as required to develop automatic methods of
diagnostics.