ZGOUBI USERS' GUIDE - HEP

A cylindrically symmetric field can be described by an axial 1-D field map of its longitudinal > >component ¢}Ž>^ R¢rŽ MM¢ Ž >>qTTPR ^ G¢ Ž PPMR ^ U”M1.5 Calculation of ¢ and its derivatives 25Z (k)Yk=1(j)j=1i=-1j=-10,0,0i=1X(i)k=-1Figure 4: A 3-D 27-point grid is used for interpolation ofsecond order. The central node of the gridvicinity of the actual position of the particle.¡ š and its derivatives up toœ \ is at the closest1.5 Calculation of ¢ and its derivativeszgoubi §©"$Œ"[ calculates and its derivatives in various ways, depending whether field maps or analytical representa-¢tions of optical elements are used. The basic means are the following [4].1.5.1 Extrapolation from 1-D axial field map7$‘ >§#"$ a\ is obtained at any point along the § -axis by a polynomial interpolation from the map mesh (see section 1.4.1). Then the field components Ž ¢C\isassumed to be §#"$ C\ §#"$ zero (e.g. in ELREVOL). ¢„Ž, at the position of the §#"$ particle, are obtained from Taylor expansions to the §#"/ ’ ¢ §©"/fifth order in(hence, up to the fifth order derivative ^§#" \ ), assuming cylindrical symmetry, while the radial component ¢v’ ^ § ¢ Ž §#" \ w§#"/\ O §©"¢ Ž T\ §#"¢ Ž M¢ Ž ^ §^ §¢ ’ ¢ Ž(1.5.1)§#"/ w@ ^§#" \ -§#" \ G ^§©" \ w^ §^ §^ §