Quasilinear Development and Mutual Influence of Langmuir and Weibel Turbulence in Plasma with an Electron Beam

In order to analyze the joint development of two-stream (Langmuir) and filamentation (Weibel) kinetic instabilities in plasma with an electron beam, a quasi-linear approach has been developed that takes into account the integral nonlinear interaction of spatial modes (harmonics) caused by a change in the spatially averaged particle velocity distribution function. On this basis, within the framework of the initial two-dimensional problem for a number of plasma and beam parameters, a numerical study of the evolution of the spectra of Langmuir (plasma) and Weibel (magnetic) turbulence was carried out. It has been established that developing turbulence of the magnetic field can significantly deform the region of electron velocity distribution resonant with Langmuir waves, strongly influencing the formation and especially the attenuation of these waves. Electric field turbulence, in turn, is capable of significantly isotropizing the distribution of electron velocities and thereby changing the increments, the nature of evolution, and the saturation level of filamentary harmonics of electric current. The characteristic properties of the joint dynamics of the spectra of magnetic and electric fields are found, the features of saturation and attenuation of both turbulent fields are established, and the necessary conditions for their mutual influence are discussed.