Investigation of the second harmonic influence on focusing of moderate energy protons in travelling wave accelerating structure

For proton acceleration in the traveling wave mode with backward n=-1 spatial harmonic the faster main harmonic n=0, having a larger amplitude, influences on proton beam focusing. In the report an additional focusing by the faster main harmonic n=0 is estimated in acceleration of proton beam with energy above 15 MeV assuming the traveling wave accelerating structure in the S band frequency range.