ZGOUBI USERS' GUIDE - HEP

3.2 Spectral-angular radiated densities [11] 31Then, given the observer position §The calculation of ž w$ ž"!"§wÉ = normalized velocity vector of the particle ŠÌqw"§Éw"ÉqwÉwqŠ> ! @ O R (.) > $ @ (*) > ! @(*)ÉwÉ"qw @ (.) > ! @ "ZYTrajectory0→R(t)←n(t)Xr(t)ObserverXFigure 5: A scheme of the reference frame in zgoubi together with the vectors entering in the definition ofthe electric field radiated by the accelerated particle:Ä " : horizontal plane; : vertical axis.1 = particle position in the fixed frame " Ä "m" ;(time-independent) = position of the observer in the§ ! !" Ä "m" frame;= position of the particle with respect to the observer; 1 1 . = (normalized) direction of observation = x;ž x tƒ(3.2.2) The Évectors and 1acceleration is calculated from (eq. 1.2.1) ž &(eq. 1.2.2) that describe the motion are obtained from the ray-tracing (eqs. 1.2.4). The (3.2.3)in the fixed frame, it is possible to calculate IL x x(3.2.4) w{1 and ž ÉOwing to computer precision the crude computation of w žÉ may lead tož ƒÉ and qž ƒÉ and qž ƒsince the preferred direction of observation is generally almost parallel É to (exactly parallel in the sense of computerprecision), É