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Plasma based particle accelerators driven by either lasers are the future of the particle accelerators technology, due to the fact, that this technology can overcome the limit of the standard accelerators given by the physicalchemical properties of the material used for the construction as well as by the huge size and the financial costs. Nevertheless, a stable synchronization of the electron bunch and of the plasma wakefield in the range of few femtoseconds is necessary in order to optimize the acceleration. Therefore, for SINBAD a shot to shot synchronization system is planned, that should be able to synchronize the electron bunch with the plasma exciting laser pulse with a time resolution of less than 1 fs. In a first step, stable Terahertz (THz) pulses should be performed by optical rectification of high energy laser pulses in a nonlinear crystal. These pulses allow an energy modulation of the electron bunch in order to achieve the required resolution This paper focuses on the first step of the feedback system, i.e. the generation of THz pulses using a periodically poled lithium niobate crystal LiNbO3 (PPLN) and we investigate the in uence of the optical properties of the material on the stability and efficiency of this process. We present systematic calculations of the optical properties of the crystal and of their in uence on the efficiency and on the optimum crystal length for the generation of THz pulses. We compare different models and approximation for the dielectric function (full Sellmeier equation or linear approximation, FC implementation or neglecting, different description of the FC saturation, depletion of the pump) and different modeling of the generation dynamic (full second order calculation or first order slope varying approximation) in order to obtain a detailed diagnostic for the THz generation and to optimize our feedback system.
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