“…and even in the vacuum electronic devices, such as, linear/particle accelerators [11,12], backward-wave oscillators (BWOs) [13], magnetrons [14], coupledcavity and helix travelling-wave tubes (TWTs) [15][16][17][18][19], cyclotron masers [20,21], gyrotron sources [21][22][23][24] and amplifiers [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], etc.. In these devices, one may see the periodic beam-wave interaction structures holding either azimuthal or axial periodicity [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]…”