  In this article, we study Beltrami equilibria for plasmas in near the horizon
of a spinning black hole, and develop a framework for constructing the magnetic
field profile in the near horizon limit for Clebsch flows in the single-fluid
approximation. We find that the horizon profile for the magnetic field is shown
to satisfy a system of first-order coupled ODEs dependent on a boundary
condition for the magnetic field. For states in which the generalized vorticity
vanishes (the generalized `superconducting' plasma state), the horizon profile
becomes independent of the boundary condition, and depend only on the thermal
properties of the plasma. Our analysis makes use of the full form for the
time-independent Ampere's law in the 3+1 formalism, generalizing earlier
conclusions for the case of vanishing vorticity, namely the complete magnetic
field expulsion near the equator of an axisymmetric black horizon assuming that
the thermal properties of the plasma are symmetric about the equatorial plane.
For the general case, we find and discuss additional conditions required for
the expulsion of magnetic fields at given points on the black hole horizon. We
perform a length scale analysis which indicates the emergence of two distinct
length scales characterizing the magnetic field variation and strength of the
Beltrami term, respectively.
