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In this talk I provide an update on the RF research for future colliders in the U. S. , through the prism of Snowmass and P5 report. During Snowmass, we considered various applications of RF technology to the proposed future colliders and other accelerator- and non-accelerator-based experiments. P5 narrowed down the choices of future machines. The colliders include circular and linear e^+ e^- Higgs factories, and longer-term options such as muon and hadron high energy colliders. I will start with Snowmass and P5 recommendations. As it is impossible to cover all possible RF R&D topics, I will discuss only three critical topics relevant to future colliders: efficiency of RF power sources, cold normal conducting RF, and cavities for ionization channel of muon collider. Progress on SRF accelerating cavities for future colliders will be covered in a separate talk. The choice of topics reflects my preference and in some cases ignorance, which I think is inevitable when one tries to cover such a broad subject.
S. Belomestnykh (Tue,) studied this question.