In this paper, novel optimization methodologies of sub-relativistic guided interaction structures for dielectric laser particle acceleration (DLA) are presented. In particular, we focus on co-propagating geometries based on slot waveguides in continuous wave (CW) operation, where the particle flow and the direction of propagation of the accelerating field are co-linear. Since the velocity of sub-relativistic particles varies along the acceleration path, proper tapering of the waveguide geometry is required to achieve an extended acceleration region, and, thus a large energy gain. The design of an optimal taper ensuring particle-wave synchronicity and maximum energy gain is pursued through a physics-based approach, and these results are compared, for validation, with the outcomes of a downhill simplex method searching algorithm. Additionally, the application of a simplified 2D model of the accelerating slot waveguide is investigated and profitably used to get qualitative results useful for fast structure optimization. Indeed, this approach can hold significant potential for the development of novel accelerating structures, as it enables a thorough and fast exploration of the design space.
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