The role of deviation of magnetic field direction on the beaming angle: Extending of beaming angle theory

In the beaming angle theory, the magnetic field direction is assumed perpendicular to the normal boundary, and the prediction of this theory, from beaming angle is base on the Jones' formula. We investigate the effect of deviation the magnetic field direction respect to normal boundary direction. In this study, we present new conditions that under these conditions two modes, extraordinary and ordinary modes waves can match. Also, we show for these cases the beaming angle does not correspond to Jones' formula. This effect leads to the angles larger and smaller than the angle estimated by Jones' formula. This effect on the mode conversion process becomes important in a case where local fluctuations in the direction of the density gradient vector or the magnetic field direction are observed. By comparing the beaming angle from observations with the beaming angles resulting from different ∆Φ, we showed a ∆Φ about 3 to 5° are necessary in consistence with observation.