Fig. 1. Sketch map of beam position monitor

Fig. 2. Two-dimensional electrostatic problem (a) and discretization of the boundary Г by a finite number N of small line segments (b)

Fig. 3. Cross section diagram of the HEPS storage ring BPM^[15-16] on circular pipe (a), HEPS booster BPM on elliptical pipe (b), and BEPC II BPM^[17] on octagonal pipe (c)

Fig. 4. Cross sectional diagram of the HEPS storage ring BPM (a), induced charge distributions for the storage ring and booster BPM (b), and induced charge distributions for the BEPCII octagonal pipe BPM (c) (color online)

Fig. 5. Mapping of a round pipe with two-electrode (a) and four-electrode (b) algorithms

Fig. 6. Sensitivity coefficient matching for an oval pipe (a) and octagonal pipe (b) by the boundary element method

Fig. 7. Contour maps of k for the two-electrode (a) and four-electrode (b) algorithms

Fig. 8. Contour maps of horizontal sensitivity coefficient k_x (a) and vertical sensitivity coefficient k_y (b) for an oval pipe

Fig. 9. Contour maps of horizontal sensitivity coefficient k_x (a) and vertical sensitivity coefficient k_y (b) for an octagonal pipe