Conical effect in diffraction radiation

Diffraction radiation from a charge as radiation from a superluminal source in a vacuum

“…As shown in Ref. [15], the DR angular distribution is mainly defined by the exponential factor in formula (10). It can be readily seen that for the perpendicular geometry b x 0 the argument of this exponential function attains the minimum value À4phagbl provided the condition cos c b À1 cos c 0 Y 12a which, with account for variables (11), takes the form…”

“…Figure 1a depicts a typical geometry of diffraction radiation when the charge velocity vector is oriented at some angle to the target edge. As shown in Refs [14,15], DR in such a geometry is emitted in the form of a cone, characteristic of CR, with the opening half-angle y ch determined by the angle between particle's momentum and target edge (the y axis in Fig. 1a).…”

“…Condition (12b) was already obtained as early as in Ref. [9]; however, only Refs [14,15] found that it leads to a so-called conical effect in diffraction radiation and Smith± Purcell radiation.…”

“…The phase factor (15) for the bunch depends on both the coordinate y (along the edge) and the distance z between the bunch electrons. Different from the single charge diffraction radiation considered earlier, with the characteristics of superluminal CR governed by the charge velocity bc and target inclination angle c 0 , the characteristics of coherent diffraction radiation from ultrashort bunches also depend on the angle w 0 between the minor axis of the ellipsoid describing the charge distribution in the bunch and its velocity (Fig.…”

“…Based on the approach proposed in [7], the form factor for a bunch described by a three-dimensional Gaussian function with the parameters s x Y s y Y s z , turned over the angle w 0 relative to the z H axis (see Fig. 7) with phase (15), can be expressed analytically:…”