ZGOUBI USERS' GUIDE - HEP

!!%" && 131 NUMERICAL CALCULATION OF MOTION AND FIELDS1.1 zgoubi FrameThe reference frame of zgoubi is presented in Fig 1. Its origin is in the median plane on a reference curve which coincideswith the optical axis of optical elements.1.2 Integration of the Lorentz EquationThe Lorentz equation, which governs the motion of a particle of charge , relativistic massand magnetic fields and , is written and velocity in electric (1.2.1) ←VTrajectoryZMPY0←WReferenceXTFigure 1: Reference frame and coordinates ( , , , ¥ ) in zgoubi .!§ : in the plane of the reference curve in the direction of motion, ! § §#"$ §#"$ § ¥ : in the plane of the reference curve, normal to ,: orthogonal to the plane,: projection of the velocity, , in the plane,= angle between and the -axis,= angle between and .Taking¡-,& ('where ¡-, is the rigidity of the particle, this equation can be rewritten" &*) (' "+ &(1.2.2)