The time evolution of the beam-plasma instability and the ensuing emission of transverse waves is studied using a set of self-consistent equations of weak turbulence theory, considering that the electron beam is along a direction with a finite pitch angle relative to the direction of the ambient magnetic field, therefore characterizing a ring-beam electron velocity distribution. The results obtained show that the finite beam pitch angle leads to an enlarged plateau in the beam region of the electron velocity distribution, and to a more complex structure in the spectra of Langmuir and ion-sound waves than obtained with beams with zero pitch angle. The associated turbulence in the spectrum of ion-sound waves is increased in the case of beams with finite pitch angle, in comparison with the case of beams with same speed and zero pitch angle. The spectrum of transverse waves generated by nonlinear processes has similar characteristics for all values of beam pitch angle, but it is observed that the emission at harmonics of the fundamental frequency is higher for moderate values of beam pitch angle than in the case of beam traveling along the parallel direction.

使用一组弱湍流理论的自洽方程研究了束等离子体不稳定性和随后的横波发射的时间演变，考虑到电子束沿着一个方向，相对于方向的倾角有一个有限的俯仰角。环境磁场，因此表征环形束电子速度分布。获得的结果表明，有限的波束俯仰角导致平台扩大在电子速度分布的射束区域，朗缪尔波和离子声波的光谱结构比零俯仰角射束更复杂。与具有相同速度和零俯仰角的束的情况相比，在具有有限俯仰角的束的情况下，离子声波谱中的相关湍流增加。非线性过程产生的横波频谱对于所有波束俯仰角值都具有相似的特性，但可以观察到，对于中等波束俯仰角值，基频谐波处的发射高于波束沿其传播的情况。平行方向。