ZGOUBI USERS' GUIDE - HEP

4.4 Optical Elements and related numerical procedures 93where ˜- are the potential at the £U˜Mfwelectrodes (and normally ˜ qFigure 26: Electrostatic N-electrode mirror/lens, circular slits, in the case £©w¢o©OwsELMIRC: Electrostatic N-electrode mirror/lens, circular slits [22]The device works as mirror or lens, horizontal or vertical. It is made of £ 2-plate electrodes and has mid-plane symmetry 6 .Electrode slits are circular, concentric with radii 1 q , 1 @ , ..., 1 N-1, O is the mirror/lens gap. The model for the mid-plane( C\) radial electrostatic potential is (after Ref. [22, p.443])11 ˜}˜å(*)'éw61¡¨è ¡ )bDc >\refers to the incident beam energy).is the currentradius.The mid-plane field ¢ -derivatives are first derived by differentiation, then ¢ and itsŸ"[ and derivativesare obtained from Taylor expansions and Maxwell relations. Eventually a transformation to the rotating frame provides ¢§#"kS"e1 2 "/w91]¢qw91 ·q"$§#"$ ˜1]¢O ˜ ï 1 · ïand derivatives as involved in eq. 1.2.13.Stepwise integration starts at entrance (defined byreference rotating framehas reached the value AT. Normally, and(possibly sensibly, so that and have negligible effect in terms of trajectory tails).Positioning of the element is performed by means of KPOS (see section 4.6.5).Use PARTICUL prior to ELMIRC, for the definition of particle mass and charge.) of the first electrode and terminates when rotation of theshould both exceedTrajectoryRMRETE > 0rY-AT/2AT/2R1XSymmetryaxisRSR2TS < 0V1V2V3ZMid-planeD, in horizontal mirror mode. U6 NOTE : in the present version of the code, the sole horizontal mirror mode is operational, and ë is limited to 3.