An Electrostatic Sector Field

An electrostatic sector field is defined by the command: 7 E(LECTROSTATIC) S(ECTOR-FIELD) <radius of deflection $\rho_{E0}$ in meter> <angle of deflection $\phi_0$ in degrees> <half electrode gap G₀ in meter> <n_E1> <n_E2> <n_E3> ; [example: E   S   1.0   90   0.03   1 ;] [E   S   1.0   90   0.01   0   0   0 ;]

where the toroidicity of the mid-equipotential surface of the sector field is determined by R_E (see Fig. 4.17 in Ref. 7) with

$$\frac{\rho_{E0}}{R_E} = n_{E1} + n_{E2} \left( \frac{x}{\rho... ...\frac{n_{E3}}{2} \left( \frac{x}{\rho_{E0}} \right)^2 + \ldots$$

For first- and second-order calculations n_E1 is defined for -2<n_E1<2. For third-order calculations n_E1 is defined only for 0<n_E1<2. Special cases are:

• cylindrical electrodes: n_E1=n_E2=n_E3=0
• spherical concentric electrodes: n_E1=-n_E2=n_E3=1
• toroidal electrodes, i.e. electrodes which intersect the xz- as well as the yz-planes in circles: $n_{E1} \neq n_{E2} \neq n_{E3} \neq 0$