diff --git a/doc/usermanuals/DD4hep/chapters/basics.tex b/doc/usermanuals/DD4hep/chapters/basics.tex index 65fbf6af6fee4db7c855aa06023c0ac174b85144..6e1bfcd775ddd247f745b00bf35f28257d16c891 100644 --- a/doc/usermanuals/DD4hep/chapters/basics.tex +++ b/doc/usermanuals/DD4hep/chapters/basics.tex @@ -1663,12 +1663,12 @@ Magnetic Dipoles are defined as follows: Magnetic Multipole Fields are developed according to their approximation using the multipole coefficients. The dipole is assumed to be horizontal as it is used for bending beams in large colliders i.e. the dipole field lines are vertical. -The different momenta are given by: +The different field components are given by: \begin{eqnarray*} -B_n^{\mathrm{norm}}(x)&=& \frac{cp}{e} \sum_{m=1}^{\frac{n}{2}} \frac{(-1)^{m-1} C_n y^{2 m-1} x^{n-2 m}}{(2 m-1)! (n-2 m)!} \quad, \\ -B_n^{\mathrm{norm}}(y)&=& \frac{cp}{e} \sum_{m=0}^{\frac{n-1}{2}} \frac{(-1)^m y^{2 m} C_n x^{-2 m+n-1}}{(2 m)! (-2 m+n-1)!} \quad, \\ -B_n^{\mathrm{skew}}(x)&=& \frac{cp}{e} \sum_{m=0}^{\frac{n-1}{2}} \frac{(-1)^m y^{2 m} S_n x^{-2 m+n-1}}{(2 m)! (-2 m+n-1)!} \quad, \\ -B_n^{\mathrm{skew}}(y)&=& \frac{cp}{e} \sum_{m=1}^{\frac{n}{2}} \frac{(-1)^m y^{2 m-1} S_n x^{n-2 m}}{(2 m-1)! (n-2 m)!}\quad. +B_{x}^{\mathrm{norm}} &=& \frac{cp}{e} \sum_{m=1}^{\frac{n}{2}} (-1)^{m-1} \; C_n \frac{ x^{n-2 m} \; y^{2 m-1} }{ (n-2 m)!(2 m-1)! } \quad, \\ +B_{y}^{\mathrm{norm}} &=& \frac{cp}{e} \sum_{m=0}^{\frac{n-1}{2}} (-1)^m \; C_n \frac{ x^{n-2 m-1} \; y^{2 m} }{ (n-2 m-1)! (2 m)! } \quad, \\ +B_{x}^{\mathrm{skew}} &=& \frac{cp}{e} \sum_{m=0}^{\frac{n-1}{2}} (-1)^m \; S_n \frac{ x^{n-2 m-1} \; y^{2 m} }{ (n-2 m-1)! (2 m)! } \quad, \\ +B_{y}^{\mathrm{skew}} &=& \frac{cp}{e} \sum_{m=1}^{\frac{n}{2}} (-1)^m \; S_n \frac{ x^{n-2 m} \; y^{2 m-1} }{ (n-2 m)! (2 m-1)! }\quad. \end{eqnarray*} With $C_n$ being ``normal multipole coefficients'' and $S_n$ the ``skew multipole coefficients''. The maximal moment used is the octopole moment. The lower four moments are used to describe the magnetic field: