  Hydrodynamic stability has been a longstanding issue for the cloud model of
the broad line region in active galactic nuclei. We argue that the clouds may
be gravitationally bound to the supermassive black hole. If true, stabilisation
by thermal pressure alone becomes even more difficult. We further argue that if
magnetic fields should be present in such clouds at a level that could affect
the stability properties, they need to be strong enough to compete with the
radiation pressure on the cloud. This would imply magnetic field values of a
few Gauss for a sample of Active Galactic Nuclei we draw from the literature.
We then investigate the effect of several magnetic configurations on cloud
stability in axi-symmetric magnetohydrodynamic simulations. For a purely
azimuthal magnetic field which provides the dominant pressure support, the
cloud first gets compressed by the opposing radiative and gravitational forces.
The pressure inside the cloud then increases, and it expands vertically.
Kelvin-Helmholtz and column density instability lead to a filamentary
fragmentation of the cloud. This radiative dispersion continues until the cloud
is shredded down to the resolution level. For a helical magnetic field
configuration, a much more stable cloud core survives with a stationary density
histogram which takes the form of a power law. Our simulated clouds develop
sub-Alfvenic internal motions on the level of a few hundred km/s.
