  We present a physics-based statistical theory of a force-free magnetic field
in the corona above a turbulent accretion disk. The field is represented by a
statistical ensemble of loops tied to the disk. Each loop evolves under several
physical processes: Keplerian shear, turbulent random walk of the disk
footpoints, and reconnection with other loops. To build a statistical
description, we introduce the distribution function of loops over their sizes
and construct a kinetic equation that governs its evolution. This loop kinetic
equation is formally analogous to Boltzmann's kinetic equation, with loop-loop
reconnection described by a binary collision integral. A dimensionless
parameter is introduced to scale the (unknown) overall rate of reconnection
relative to Keplerian shear. After solving for the loop distribution function
numerically, we calculate self-consistently the distribution of the mean
magnetic pressure and dissipation rate with height, and the equilibrium shapes
of loops of different sizes. We also compute the energy and torque associated
with a given loop, as well as the total magnetic energy and torque in the
corona. We explore the dependence of these quantities on the reconnection
parameter and find that they can be greatly enhanced if reconnection between
loops is suppressed.
