Harmonic generation and superthermal tail formation during beam-plasma interaction

Summary form only given, as follows. The quasi power-law spectrum associated with the Langmuir turbulence is explained in terms of the generation of harmonics of the Langmuir mode, which are nonlinear eigenmodes of a turbulent plasma. It is shown that the saturated wave spectrum is made of multiple harmonic peaks, which form a quasi power-law profile. The formation of energetic electrons can readily be explained if the nonlinear correction to the particle kinetic equation is included. The new kinetic equation has an extra hyper-diffusion term in addition to the customary diffusion term. The hyper-diffusion term, which is represented by a fourth-order velocity derivative, is dictated by a nonlinear wave-particle resonance condition. It is shown that the presence of the new hyper-diffusion term leads to the superthermal tail in the distribution.