  Hot accretion tori around a compact object are known to be susceptible to a
global hydrodynamical instability, the so-called Papaloizou-Pringle (PP)
instability, arising from the interaction of non-axisymmetric waves across the
corotation radius, where the wave pattern speed matches the fluid rotation
rate. However, accretion tori produced in various astrophysical situations
(e.g., collapsars and neutron star binary mergers) are likely to be highly
magnetized. We study the effect of magnetic fields on the PP instability in
incompressible tori with various magnetic strengths and structures. In general,
toroidal magnetic fields have significant effects on the PP instability: For
thin tori (with the fractional width relative to the outer torus radius much
less than unity), the instability is suppressed at large field strengths with
the corresponding toroidal Alfven speed $v_{A\phi}\go 0.2r\Omega$ (where
$\Omega$ is the flow rotation rate). For thicker tori (with the fractional
width of order 0.4 or larger), which are hydrodynamically stable, the
instability sets in for sufficiently strong magnetic fields (with $v_{A\phi}\go
0.2 r\Omega$). Our results suggest that highly magnetized accretion tori may be
subjected to global instability even when it is stable against the usual
magneto-rotational instability.
