Looking for future high energy accelerators we point at a very strong interaction between relativistic electrons and powerful electromagnetic fields existing in the vicinity of a dielectric cylinder in conditions of resonantly excited whispering gallery modes (WGM). A particular example of the WGM resonance, corresponding to angular index n=22, shows that the accelerating fields are almost 100 times stronger than these in the incident wave. That yields an acceleration rate of about 5 GeV/m with the incident microwave radiation beam of the wavelength lambda=1 cm and a moderately high intensity of P=1 MW/cm2.
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Władysław Żakowicz (2005) studied this question.
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