Fringing Fields for Magnetic Sector Fields

Fringing fields for magnetic sector fields are defined by the command: 5 F(RINGING) F(IELD) <table#> <entrance or exit angle $\varepsilon$ in degrees> <curvature $\rho_{B0}/R$ of effective field boundary> ; [example: F   F   2   10.0   1.0   0.4853 ;] [F   F   1   0   0 ;] .

The fringing-field integrals are taken from GIOSFF.DAT, if this mode is active; the coefficients are taken from GICOFF.DAT otherwise. Note that

• $\zeta$ is a coordinate perpendicular to the effective field boundary,
• G₀ is the half air gap,
• the integral I₅ must be taken from $\zeta_a$ to the effective field boundary, i.e. to $\zeta$ =0,
• and the integrals I₁ and I₂ must be taken from $\zeta_a$ outside to $\zeta_b$ inside the main-field region.

Note that $\varepsilon$ (see Fig. 4.8 in Ref. 7) is positive if the normal to the field boundary is further away from the center of curvature of the optic axis than the incoming or outgoing beam. Note further, that $\rho_{B0}/R$ (see Fig. 8.6 in Ref. 7) is positive for a convex field boundary and negative for a concave one.