• L. Wang, L. Lee, G.V. Stupakov
  SLAC, Menlo Park, California

A new method, using the parabolic equation (PE), for the calculation of both high-frequency and small-angle taper (or collimator) impedances is developed in [1]. One of the most important advantages of the PE approach is that it eliminates the spatial scale of the small wavelength from the problem. As a result, the numerical solution of the PE requires coarser spatial meshes. We developed a new code based on Finite Element Method (FEM) which can handle arbitrary profile of a transition. As a first step, we completed and benchmarked a two-dimensional code. One of the important advantages of the code is its fast execution time.

• K.L.F. Bane, L. Lee, C.-K. Ng, G.V. Stupakov, L. Wang, L. Xiao
  SLAC, Menlo Park, California

PEP-X, a next generation, ring-based light source is designed to run with beams of high current and low emittance. Important parameters are: energy 4.5 GeV, circumference 2.2 km, beam current 1.5 A, and horizontal and vertical emittances, 150 pm by 8 pm. In such a machine it is important that impedance driven instabilities not degrade the beam quality. In this report we study the strength of the impedance and its effects in PEP-X. For the present, lacking a detailed knowledge of the vacuum chamber shape, we create a straw man design comprising important vacuum chamber objects to be found in the ring, for which we then compute the wake functions. From the wake functions we generate an impedance budget and a pseudo-Green function wake representing the entire ring, which we, in turn, use for performing instability calculations. In this report we consider in PEP-X the microwave, transverse mode-coupling, multi-bunch transverse, and beam-ion instabilities.