ZGOUBI USERS' GUIDE - HEP

30 3 SYNCHROTRON RADIATION¾ÍôVTïÌ¢ÍñžqŠÁR©ž 4ŠñqÊñ>§ŠqwÉÉŠ «ÉAbout\values ofcomputed from eq. 3.1.3 [36],Rare tabulated in\, first ais generated uniformly, then Ê Ê Ìisqdrawn either by simple inverse linear interpolation of the tabulatedvalues\ B @ZG\ ¬if),or, ifÊhonnestly spread over a range Ê ÌÌKîzgoubi source file (see figure). In order to getÍÊ Êrandom value \ðï ÍòñÊ‡Ì ÊM >eô3õ÷ö$øïó\ B @G(corresponding tofrom eq. 3.1.4 that directly gives ÍýüÊ Ê‡ÌÊ‡Ì Êwith precision no less than 1û at.1.0.80.6ZGOUBIPö Y7 >eù T/ú ¿\ B @GUpon request of SR loss tracking, several optical elementsthat contain dipole magnetic field component (e.g.,MULTIPOL) provide a printouot of various quantities relatedto SR emission, as drawn from classical theoretical expressions,such as for instance,- energy loss per particle : :þÅ , ( ¡ is0.40.2ε/εc0 1 2 3 4 5Cumulative èIéëê¸ß[ê;ì[í distribution .the dipole field, exclusive of any other multipole componentor non-linearity in the magnet; :›Å is the total deviation as calculatedfrom ¡ , the magnet length, and the reference rigidity ¡ ! 1 ! (as defined with, e.g., OBJET)- energy ÊeÌ> T4T ¡ ¢ ˜ T$ÿLö, with ¡ ! 1 ! ¡£- energy of radiated photons , ¤ 7 M ù TÊ[Ì,’ ï K\ B NN¨§ Ê §¦¥- r.m.s. energy of radiated photons q ÊeÌ,- number of radiated photons per particle £ :¢ ï.ÊThis is done in order to facilitate verifications, since on the other hand statistics regarding those values are drawnfrom the tracking and printed upon use of the dedicated keyword SYNPRNL. ˜ > z¡Finally, upon user’s request as well, SR loss can be limited to particular classes of optical elements, for instancedipole fields alone, or dipole + quadrupole magnets, etc. These tricks are made available in order to permit deeper insight,or easier comparison with other codes, for instance.3.2 Spectral-angular radiated densities [11]The ray-tracing procedures provide the ingredients necessary for the determination of the electric field radiated by theparticle subject to acceleration, as shown in Fig. 5 (section 3.2.1). This allows calculation 4 of spectral-angular densitiesradiated by particles in magnetic fields (section 3.2.2).3.2.1 Calculation of the radiated electric fieldThe expression for the radiated electric field © " as seen by the observer in the long distance approximation is [12] ž ž I ¨ « © " wT(3.2.1) ¨…ƒž whereis the time in which the particle motion is described and is the observer time. Namely, when at positionwith respect to the observer [or as well at position 1 in the ( ! " Ä "m" ) frame] the particle emits a signalwhich reaches the observer at time , such that where is the delay necessary for the signal to travelfrom the emission point to the observer, which also leads by differentiation to the well-known relation w 4 These procedures are for the moment implemented in the post-processor zpop