Nasr, M.H. Tantawi, S.G. JACoW Publishing Geneva, Switzerland 978-3-95450-184-7 10.18429/JACoW-IPAC2018-THPMK048 English 4391-4394 THPMK048 Contribution to a conference proceedings 2018 2018-06 https://doi.org/10.18429/JACoW-IPAC2018-THPMK048 http://jacow.org/ipac2018/papers/thpmk048.pdf One promising approach in boosting accelerators efficiency is dual-mode simultaneous operation. In our work, the topic of dual-mode acceleration is studied from a wider perspective with new approaches and tools. We present a new type of accelerator structures that operates simultaneously with two modes and two frequencies. The frequencies are not constrained to be harmonically related, but rather have a common sub-harmonic. These designs will utilize a newly developed parallel-feeding network that feeds each individual accelerating cell independently using a distributed feeding network. As a result, the design problem converges to a single-cell design with identical cells. The cells are designed for maximum efficiency using new geometrical optimization that utilizes nonuniform rational B-spline (NURBS) with a series of control points. We will present a study on the topic for S-band simultaneous operation with C-band or X-band.