Progress in the kinetic theory of electrostatic harmonics of plasma waves

Abstract

The electron geodesic acoustic mode Phys. Plasmas 19, 092113 (2012) Spatio-temporal evolution of the L→I→H transition Phys. Plasmas 19, 092306 (2012) Effect of trapping in a degenerate plasma in the presence of a quantizing magnetic field Phys. Plasmas 19, 092304 (2012) Roles of polarization force and nonthermal electron on dust-acoustic waves in an inhomogeneous dusty plasma with positively charged dust This paper performs numerical analysis to verify the theoretical predictions of Yoon ͓"Effects of spontaneous fluctuations in the generalized weak turbulence theory," Phys. Plasmas 12, 042306 ͑2005͔͒, according to which the higher harmonics of the electron plasma frequency, generated during the course of electron beam-plasma interaction start to grow initially with fast quasilinear growth rate, which is roughly n times higher than the fundamental Langmuir mode growth rate, n being the harmonic number, but the rapid initial growth soon slows down to the level of fundamental mode growth rate. It is also shown that when the initial wave levels for the harmonics are relatively high, then the overall dynamics is largely dictated by the slow nonlinear growth rate, but when the initial wave levels associated with the harmonic components are artificially suppressed, then the fast quasilinear growth stage is prolonged.

Beam-Plasma Interaction and Nonlinear Effects

“…For the real part, we ignore nonlinear mode-coupling term. Keeping nonlinear terms in the real part leads to the so-called "nonlinear frequency shift" [11][12][13] and the "electrostatic harmonics" generation [14,15], each of which is interesting in its own right, but we do not have the space to deal with those problems. The simplified real part of (15), Ree(fc,a;) < E'^ >kLo= 0 determines the eigenmode solution, that is, the dispersion relation.…”

Two dimensional kinetic analysis of electrostatic harmonic plasma waves

“…The term with c Ln q represents the quasilinear effect, and the term with Ln q represents the effect of wave-particle scattering. 11,42 For the evaluation of various objects defined in Eqs. (5) and (6), we utilize a n q;q 0 ¼ fðn À 1Þq 2 ½q 0 Á ðq À q 0 Þ þ nq 02 ½q Á ðq À q 0 Þ þnðn À 1Þjq À q 0 j 2 ðq Á q 0 Þg 2 Â ½n 2 ðn À 1Þ 2 qq 0 jq À q 0 j À2 ;…”

“…11 and Equation (7) in Ref. 42. The set of equations which has been obtained for the amplitudes of electrostatics waves in an unmagnetized plasma, comprising L, S, and harmonic modes, must be solved along with the dynamical equations for the particle distribution functions…”

“…11, discreteparticle effects were incorporated in Ref. 42, but the analysis still pertained to 1D approximation.…”

Two-dimensional time evolution of beam-plasma instability in the presence of binary collisions

“…For a detailed derivation of the above equations without the term that represents the collisional effects, the reader is referred to Yoon (2000Yoon ( , 2005Yoon ( , 2006. The collisional term is essentially the Landau collision integral, which is well known in the literature (e.g., Lifshitz & Pitaevskii 1981;Karney 1986;Jeffrey et al 2014, see also Appendix A).…”