AN OPTICAL MODEL FOR OFF-AXIS QUADRUPOLES

The description in terms of standard optical elements of the Interaction Region (IR) quadrupoles where the electron and positron beams travel off-axis in a common vacuum chamber has been a problem since the first design of DAΦNE. In this note a new approach is described, which takes into account the magnetic measurements performed on the quadrupole. Particles are tracked through the measured field along the nominal trajectory and with small displacements and angles to obtain the transfer matrix of the quadrupole. Then the resulting matrix is fitted by a proper combination of standard optical elements such as drift spaces and bending dipoles with gradient. The results of the procedure performed on one of the permanent magnet quadrupoles of the KLOE interaction region are presented. 2. Application to the lattice proposed for the DAΦNE upgrade The IR lattice for an upgrade of DAΦNE by means of large crossing angle, small betatron functions at the Interaction Point (IP) and the “crabbed waist ” scheme [1] consists of a short vacuum chamber common to both beams surrounded by a first vertically focusing permanent magnet quadrupole on each side of the IP, followed by separated channels with 4 small horizontally focusing quads. The total crossing angle is 50 mrad (25 mrad per beam) and th