ZGOUBI USERS' GUIDE - HEP

4 ´ ´""4§> ´4 >4>1.4 Calculation of ¡ from Field Maps 23YXXB ooXYXYB ooXYXY(A)(B)Y∆αB ooXYX∆R(C)Figure 3: Mesh in theon the node which is closest to the actual position of the particle.A: 9-point interpolation grid.B: 25-point interpolation grid.C: Mesh in §©"$ the plane in polar coordinates.§©"$ plane in Cartesian coordinates. The grid is centered1.4.3 Arbitrary 2-D Map, no SymmetryThe map is supposed to describe the¡ Ž ¡ – ¡|• field in §©"$ the plane at ¡ Ž d bigelevation, – d big, ¡ • d bhgat each node¡ š(of a 2-D mesh.¡ k"The value of and its derivatives at the projectionof the actual positionpoints grid centered at the node¡means of a polynomial interpolation from a U U§#"$Œ"[. It provides the componentsof a particle is obtained by§#"kS"eš(which is closest to the position["§#"$ > 4(1.4.11)7k7¡r½ 4k47ˆ44‡7where ¡ ½ stands for any of the three components ¡|Ž , ¡ – or ¡ • . Differentiating then gives the derivatives§#"kS"e§ ´ ´§© ´