Nonlinear Effects in Plasma

Abstract

Doctor of Physicomathematical Sciences. Prior to 1956 his scientific interests centered on quantum electrodynamics. From 1957 to 1960 he elaborated the theory proposed by Wexler for coherent methods of charged particle acceleration. Since 1959 he has studied plasma physics and astrophysics. Tsytovich has been responsible, in particular, for investigations of the properties of relativistic plasma, the physics of turbulent plasma, and nonlinear effects in plasma.The original Russian text, first published by Nauka Press in Moscow in 1967, has been corrected by the author for this edition. The present translation is published under an agreement with Mezhdunarodnaya Kniga, the Soviet book export agency.

Second Harmonic Emission during Solar Flares

“…An estimate for this timescale (Tsytovich 1970) results an order of magnitude longer than the isotropization timescale for the most intense beams (three most intense beams on Table 1). Then, for those cases, the angle distribution of Langmuir waves can be considered isotropic.…”

“…The typical timescales of this problem are the quasilinear relaxation timescale, (Tsytovich 1970), and the q p 0 4 (n e /n b )(nu e )~1 collisional timescale, In these expressions,…”

“…There are at least two decay processes that could play this role : (a) scattering of Langmuir waves by ions, and (b) the electrostatic (ES) decay process L % L@ ] S (S : ion-acoustic wave), both of which have been discussed in the literature (see, for example, Tsytovich 1970). Each individual decay is constrained by the conservation of momentum and energy, which poses restrictions on the allowed decays.…”

“…For the kinematically allowed decays, the rate of occurrence of L % L@ ] S can be estimated by computing the rate of generation of S waves, considering both the direct and inverse processes. Using the probability of the decay under analysis (see Tsytovich 1970, Appendix 3), a detailed estimate shows that the decay is fastest for the cases (i.e., equally fast for both cases) of backscattering (L and L@ possessing wavevectors almost antiparallel) and small-angle scattering (L and L@ possessing wavevectors forming a small angle).…”

“…In particular, these energetic beams are known to generate plasma turbulence by the so-called bump on-tail instability (Tsytovich 1970). Langmuir turbulence, in turn, generates photons at the second harmonic of the local plasma frequency as a result of the coalescence process where L and L@ denote Langmuir waves of L ] L@ ] T (2u e ), di †erent momentum and T denotes a transverse wave at twice the plasma frequency (Kaplan & Tsytovich 1973).…”