ZGOUBI USERS' GUIDE - HEP

112 4 DESCRIPTION OF THE AVAILABLE PROCEDURES·4¥4444ºŠ¥o¢wŠ4o -Š4>, à wÁwŠƒ¡Ã¨ ' «ŠŠ ·É²Ã 7É4qwÉ>ô¥4ŠÊÉŠ=7SEPARA: Wien Filter - analytical simulationSEPARA provides an analytic simulation of an electrostatic separator. Input data are the ¨ length of the element, theand charge of the particles are entered by means of the keywordPARTICUL.electric field ¢ and the magnetic field ¡ . The mass The subroutines involved in this simulation solve the following system of three equations with three unknown variables, , (while §¨ ), that describe the cycloidal motion of a particle in ¢ , ¡ static fields (Fig. 34).w ¹§ wr1 · à ŠÉÊ s· à ŠÉw ² >Ã>¹ wà 1 (*)Ê s· (*)- where, is the path length in the ¹ separator, and> ·Q² &are initial conditions. = velocity of É light, = velocity of the particle, e¬S and ¡ )² > ºò ².,Á , ¥ , are the initial coordinates of the particle in the zgoubi reference frame. É Here and are assumedconstant, which is true as long as the change of momentum due to the electric field remains negligible all along theÁseparator.The index ¤¦´>Á , ² 7in the input data allows switching to inactive element (thus equivalent to ESL), horizontal or verticalfor wanted particles are related byseparator. Normally, ¢ , ¡ and the value of Éó(*)- 4&` Q 4¢ o ˜ ¡ sÉ>óFigure 34: Horizontal separation between a wanted particle,undergoes a linear motion while % %, and an unwanted particle,‰ undergoes a cycloidal motion.‰ .