Multipole Field Errors

Multipole field errors can be assigned to all multipole-like elements:

• RBEND,
• SBEND,
• QUADRUPOLE,
• SEXTUPOLE,
• OCTUPOLE,
• MULTIPOLE,

The main field and the error field are evaluated separately and then added. Error field components can be absolute or relative values. Relative errors are referred to the amplitude of the nominal component of order ORDER = $n$ (default = 0), taken at the radius RADIUS = $R$ (default = 1).

Given the factors

$$\psi_k = (k + 1) * \texttt{ROT[k]}, \qquad c_k = \cos \psi_k... ... \sin \psi_k, \qquad f_k = \texttt{RADIUS[k]}^(k-n) * n! / k!.$$

the field components $\delta K_{kn}$ (normal) and $\delta K_{ks}$ (skew) are computed as follows from the input data:

$$\begin{array}{lclclclcl} \delta K_{kn} &=& c_k \mathtt{DK[k... ...R[k]} &=& \mathtt{DKS[k]} &=& f_k \mathtt{DKSR[k]} \end{array}$$

The first line gives the normal components, the second line the skew components.