ZGOUBI USERS' GUIDE - HEP

74 4 DESCRIPTION OF THE AVAILABLE PROCEDURES%©žÉ˜ ÇÇŠ2ŠŠŠŠ§ÄÉÇ©$Š©/Ç ˜ i §2 ¡., ¥ > ¡., ¡-, > > ¡., ¡., ¥oÉžŠ>Š>© Š¥ ÉŠ>sCAVITE: Accelerating cavityCAVITE provides an simulation of a (zero length) accelerating cavity; it can be used in conjunction with keywordsREBELOTE and SCALING for the simulation of multiturn tracking with synchrotron acceleration (see section 4.6.7). Itmust be preceded by PARTICUL for the definition of mass and charge .If ’ÁÀ‹Âaà : CAVITE is switched off.If ’ÁÀ‹Âaà ·: CAVITE simulates the R.F. cavity of a synchrotron accelerator. Normally the keyword CAVITE appearsat the end of the optical structure (the periodic motion ¤ q over , NPASS + 1 turns is simulated by means of thekeyword REBELOTE, option K = 99 while R.F. and optical elements timings are simulated by means of SCALING —see section 4.6.7). The synchrotron motion of any of the IMAX particles of a beam is obtained by solving the followingmapping$ > w $]7Š wÅ Æ @µ‚¨(*)È$ 7where $= R.F. phase;> w $]7 $= kinetic energy; > w5% 7 %variation ofbetween two traversalsenergy gain at a traversal of CAVITE% > w5% 7É ¥= length of the synchronous closed orbit (to be calculated by prior ray-tracing,see the bottom NOTE)= orbit length of the particle between two traversals= velocity of the (virtual) synchronous particle= velocity of the particle= peak R.F. voltage= particle electric charge.The R.F. frequencyis a multiple of the synchronous revolution frequency, and is obtained from the input data,µ‚¨§followingwhere= harmonic number of the R.F= mass of the particle= velocity of light.µ‚¨ > ¥32The current rigidityING followingSCALE(TIMING)). If SCALING is not used,description (see OBJET for instance).The É velocity of a particle is calculated from its current rigidity¡-, of the synchronous particle is obtained from the timing law specified by ¥ means of¡ ! 1 !SCAL-SCALE(TIMING) (see SCALING for the meaning and calculation of the scale factor¡., ¥ ƒis assumed to keep the constant value given in the object1 ! ! ¡ ¥ ¡., 32The velocity É ¥of the synchronous particle is obtained in the same way fromi 32É ¥ > ¡., The kinetic energies and rigidities involved in these formulae are related byi > ¥