A small cylindrical anisotropic plasma volume with central vacuum cavity surrounding an electro-magnetic source is considered and the influence of this volume on radiation characteristics of the source is studied. Conditions for the resonance radiation are found and properties of this radiation are investigated as a function of the intensity of the axial magnetic field for different relative dimensions of the inner cavity. It is shown that, with allowance for the depleted ion sheath around the radiator, the radiation induced by the magnetic field in the wave zone in vacuum in the direction of the dipole axis may exceed the radiation induced in the perpendicular direction.