Harmonics of electromagnetic and electrostatic plasma waves

Abstract

This paper shows that there are two types of nonlinear harmonics in a turbulent plasma. Until recently, it was not clear whether the electromagnetic second-harmonic mode ͓P. H. Yoon, Phys. Plasmas 2, 537 ͑1995͔͒ and the electrostatic harmonic at 2 pe ͓P. H. Yoon, Phys. Plasmas 7, 4858 ͑2000͔͒ were separate branches of nonlinear dispersion relation or whether one was a more general solution which includes the other as a special case. This paper shows that the former is true, namely, the two modes are independent solutions. This reconciles previous, apparently contradictory, predictions by showing that electromagnetic harmonic is a long-wavelength mode, while the electrostatic harmonic is characterized by short wavelengths.

Multiple harmonic plasma emission

“…The theories by Yoon (1995) and Yoon et al (2005) cannot yet be extended to discuss such backscattered harmonic modes. Thus, no satisfactory theory exists to account for the apparent backscattering of these modes.…”

“…Consequently, these modes cannot be discussed on the basis of the customary textbook theory. Such harmonic EM waves with short wavelengths and with frequency ∼nω pe have been analyzed by Yoon (1995) and Yoon et al (2005). These modes are EM counterparts of the ES nonlinear eigenmodes discussed earlier.…”

“…These modes are EM counterparts of the ES nonlinear eigenmodes discussed earlier. Consequently, Yoon (1995) and Yoon et al (2005) have provided essential explanations for the existence of these modes. However, the analyses by Yoon (1995) and Yoon et al (2005) are primarily concerned with the superluminal regime of the nonlinear EM harmonics, ω/k > c, so strictly speaking the EM harmonics in the subluminal regime, ω/k < c, have not been studied in detail.…”

Weak turbulence theory for collisional plasmas

“…The formalism was later expanded to include effects due to processes related to spontaneously emitted fluctuations, which come from discrete-particle effects, both for wave equations and for particle equations [17]. Further extension occurred when electromagnetic waves were incorporated into the formalism, initially without the discrete-particle effects [18], but later by incorporating effects representing spontaneously emitted thermal fluctuations [19,20]. The foundational equations that resulted from these developments were applied for actual applications, mostly related to quantitative analyses of nonlinear processes associated with the beam-plasma instability.…”

Two dimensional kinetic analysis of electrostatic harmonic plasma waves

“…[32][33][34][35][36] While alternative interpretations for the occurrence of these emissions are possible, more recent simulation studies confirm the ubiquitous excitations of harmonic L mode during beamplasma instability process. [37][38][39] A hitherto unanswered question concerning the possible occurrence of both electrostatic and electromagnetic harmonics was addressed in another paper, 40 which lead to the conclusion that both modes are independent solutions. 40 Indeed, in related works in which two-dimensional (2D) electromagnetic particle-in-cell simulation code was employed, Refs.…”