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This paper presents a tolerance Budget for accelerators dictated by the linear transverse dynamics of particle motion. The linearized equations satisfied by the particle motion when errors in the lattice are present are given along-with the solution to these equations. The forms of these errors giving rise to the linearized equation are stated. These results are used to derive a tolerance budget for the Advanced Photon Source (APS) injector synchrotron. This manuscript has been authored under contract nuiiber W31-109-ENG-38 with the U.S. Department of Energy. Accordingly, the U S. Govenmient retains a non-exclusive, royalty-free liceiise t o publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Govenurient purposes.

This note describes the low-energy-transfer-line designed for the APS. The low energy transfer line constitutes two transport lines. One of these lines runs from linac to the positron accumulator ring ,also called "PAR", and is 23.7138 m long. The second part of the low energy transport line runs from the "PAR" bo the injector synchrotron and is about 30.919 rn long. The above length includes two quadrupoles, a bend magnet and a septum magnet in the injector synchrotron (see fig. 1 and table 2).The positron bunches of emittance e~ = l.lmm -mrad arriving at the end of the linac at 450 MeV have twiss parameters as given by N&siri 1The transfer line (see also Yoon and Crosbie2 ) from linac to "PAR" is made up of ten quadrupoles and one bending magnet B4 (see fig.1). The bending magnet bends the beam by 0.2 radians towards the septum magnet m the "PAR". The five quadrupoles in the region between the bend magnet and the septum magnet in the "PAR" give a phase shift of 2a radians, in order to get dispersion free bunch at the end of the septum magnet.The twiss parameters at the end of the linac given above are matched with the twiss parameters and the dispersion functions at the end of the septum magnet, in the "PAR" lattice structure. These parameters at the end of the "PAR" septum are given by az = -0.94910, pz = 2.1261, ay = -0.02429, py = 8.2401,~z = 0.0, q'x = 0.0The matching procedure was carried out using computer code "COMFORT". It should be mentioned that the 2.9 m of distance between the last quadrupole and the septum magnet in the "PAR" is more or less forced on us because of the considerations of the