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Relativistic electron bunches in linear colliders are characterized by 6D phase spaces. In most linear accelerators, the longitudinal phase space distribution does not interact significantly with the transverse distributions. This assumption allows the use of a 2D design model of the longitudinal phase space. The design of linear colliders is typically based on manipulations in the longitudinal phase space. The two dimensional single bunch tracking code LiTrack (Bane/Emma 2005) allows to simulate bunch-compression up to 3rd order and RF acceleration with wake fields. This code is implemented in Matlab with a graphic user interface front end. In order to improve the ability to simulate a two-stage bunch compression system, which consist of a RF accelerating section, a higher harmonic RF section and a dipole magnet chicane, an extension to the LiTrack code is proposed. An analytical model of this two-stage bunch compression system is defined using the energy and the momentum derivatives up to 3rd order of the system. As a consequence, the energy of the system can now be specified directly, for the simulation criteria the peak current and the symmetry of the charge distributions and be specified via parameters. This extended model allows the definition of bunches with an arbitrary energy, phase space correlation, longitudinal emittance, charge distribution and resulting peak current. A minimal longitudinal emittance is generally considered as a quality factor of the bunch, where the bunch energy, peak current and a symmetric charge distribution are represented as constraints. Under these conditions, a constrained optimization problem is defined to minimize the longitudinal emittance with a predetermined bunch-energy and peak-current with respect to the charge distribution symmetry. For the solution of this problem, LiTrack is extended with a optimization solver based on a SQP formulation to find an optimal bunch corresponding to the newly introduced constraints.
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