We construct a cubically nonlinear theory of plural interactions between harmonics of the growing space charge wave（SCW） during the development of the two-stream instability. It is shown that the SCW with a wide fre...We construct a cubically nonlinear theory of plural interactions between harmonics of the growing space charge wave（SCW） during the development of the two-stream instability. It is shown that the SCW with a wide frequency spectrum is formed when the frequency of the first SCW harmonic is much lower than the critical frequency of the two-stream instability.Such SCW has part of the spectrum in which higher harmonics have higher amplitudes. We analyze the dynamics of the plural harmonic interactions of the growing SCW and define the saturation harmonic levels. We find the mechanisms of forming the multiharmonic SCW for the waves with frequencies lower than the critical frequency and for the waves with frequencies that exceed the critical frequency.展开更多
We developed a cubic non-linear theory describing the dynamics of the multiharmonic spacecharge wave（SCW）, with harmonics frequencies smaller than the two-stream instability critical frequency, with different relati...We developed a cubic non-linear theory describing the dynamics of the multiharmonic spacecharge wave（SCW）, with harmonics frequencies smaller than the two-stream instability critical frequency, with different relativistic electron beam（REB） parameters. The self-consistent differential equation system for multiharmonic SCW harmonic amplitudes was elaborated in a cubic non-linear approximation. This system considers plural three-wave parametric resonant interactions between wave harmonics and the two-stream instability effect. Different REB parameters such as the input angle with respect to focusing magnetic field, the average relativistic factor value, difference of partial relativistic factors, and plasma frequency of partial beams were investigated regarding their influence on the frequency spectrum width and multiharmonic SCW saturation levels. We suggested ways in which the multiharmonic SCW frequency spectrum widths could be increased in order to use them in multiharmonic two-stream superheterodyne free-electron lasers, with the main purpose of forming a powerful multiharmonic electromagnetic wave.展开更多
文摘We construct a cubically nonlinear theory of plural interactions between harmonics of the growing space charge wave（SCW） during the development of the two-stream instability. It is shown that the SCW with a wide frequency spectrum is formed when the frequency of the first SCW harmonic is much lower than the critical frequency of the two-stream instability.Such SCW has part of the spectrum in which higher harmonics have higher amplitudes. We analyze the dynamics of the plural harmonic interactions of the growing SCW and define the saturation harmonic levels. We find the mechanisms of forming the multiharmonic SCW for the waves with frequencies lower than the critical frequency and for the waves with frequencies that exceed the critical frequency.
基金supported by the Ministry of Education and Science of Ukraine under Grant No.0117U002253
文摘We developed a cubic non-linear theory describing the dynamics of the multiharmonic spacecharge wave（SCW）, with harmonics frequencies smaller than the two-stream instability critical frequency, with different relativistic electron beam（REB） parameters. The self-consistent differential equation system for multiharmonic SCW harmonic amplitudes was elaborated in a cubic non-linear approximation. This system considers plural three-wave parametric resonant interactions between wave harmonics and the two-stream instability effect. Different REB parameters such as the input angle with respect to focusing magnetic field, the average relativistic factor value, difference of partial relativistic factors, and plasma frequency of partial beams were investigated regarding their influence on the frequency spectrum width and multiharmonic SCW saturation levels. We suggested ways in which the multiharmonic SCW frequency spectrum widths could be increased in order to use them in multiharmonic two-stream superheterodyne free-electron lasers, with the main purpose of forming a powerful multiharmonic electromagnetic wave.
