ZGOUBI USERS' GUIDE - HEP

4.4 Optical Elements and related numerical procedures 91˜˜@@˜˜777@@ qO Ã>7Ä0 O1 4ch Ãch Ã Ä w>O7>@@EL2TUB: Two-tube electrostatic lensThe lens is cylindrically symmetric about the -axis.The length and potential of the first (resp. second) electrode are and and ). The distance between thetwo electrodes is , and their inner radius is (Fig. 24). -axis cylindrical symmetry is assumed. The model for theelectrostatic potential along the axis is [21]> wthÃ=Ä4 ª ˜1 ˜§ ˜@ «if O †\ž ž ˜> w†\§ ˜ª3 ˜@ «if O ‡( = distance from half-way between the electrodes; = 1.318; th = hyperbolic tangent; ch = hyperbolic cosine) fromwhich the field ¢ Ä and its derivatives are derived following the procedure described in section 1.5.2 (note thatà §#"kS"e1 4they don’t depend on the constant term ª ˜«which disappears when differentiating).Use PARTICUL prior to EL2TUB, for the definition of particle mass and charge. ˜R 0V1V2XX1DX2Figure 24: Two-electrode cylindrical electric lens.