Electrostatic Bender Fields, Optics, Aberrations, with Application to the Proton EDM Ring

Electrostatic bender optics are derived up to second order (third order in fields and the Hamiltonian) and applied to the proposed EDM proton ring. The results for linear optics agree with those already presented by V.\ Lebedev (Nov.\ 18, 2013). Second order optics is not sensitive to the shape of the fringe fields and formulas are given. It is shown that the proposed electrode shape that linearizes the vertical electric field is no advantage to this order.