Magnetic field creates strong superradiant instability

It is well known that massless scalar fields, scattering near the Kerr black hole, are stable and have the well-known super-radiance effect, while a massive field has superradiant instability of some modes with a tiny growth rate, what makes this instability insignificant for real black holes. We find that massless (neutral) scalar fields, otherwise stable, are superradiantly unstable if a rotating black hole is immersed in an external magnetic field. In addition, we show that magnetic fields may significantly increase the growth rate of superradiant instability of both massless and massive fields. This effect occurs because magnetic field adds an "effective mass" term $2 B |m|$ to the scalar field potential for a Kerr black hole. Considerable increase of the instability growth rate may make impact on radiation processes around large astrophysical, primordial or mini black holes.