A Magnetic Sector Field

A magnetic sector field is defined by the command: 6 M(AGNETIC) S(ECTOR_FIELD) <radius of deflection $\rho_{B0}$ in meter> <angle of deflection $\phi_0$ in degrees> <half air gap G₀ in meter> <n_B1> <n_B2> <n_B3> <n_B4> <n_B5> ; [example: M   S   1.0   90   0.05   0.51 ;]

The magnetic flux density in this sector field equals

$$\begin{eqnarray*} B(x,y=0) &=& B_0[1-n_{B1} \left( \frac{x}{\rho_{B0}}\right) -... ...)^4 - n_{B5}\left(\frac{x}{\rho_{B0}}\right)^5 - \ldots ] \; . \end{eqnarray*}$$

In calculation mode 1 (C M 1) the matrix coefficients are only calculated up to second order for inhomogenous sector fields. For higher orders one has to use differential algebra (calculation mode 2 or 3). For first- and second-order calculations n_B1 is defined for -1<n_B1<1. For higher-order calculations n_B1 is defined only for 0<n_B1<1.