By Thierry Passot, Pierre-Louis Sulem
This e-book is of curiosity to researchers in astrophysics and the planetary sciences. It surveys the present wisdom at the propagation of nonlinear waves and the improvement of a turbulent dynamics in magnetohydrodynamic flows. The authors emphasize how the theoretical knowing of MHD waves and turbulence is expounded to the outline of media the place the presence of an ambient magnetic box is understood to play a necessary function. those results are vital within the physics of assorted house plasmas resembling the magnetosphere, the sun wind, the sunlight corona, the interplanetary and interstellar media, and so on. The authors deal with primary points as printed via asymptotic research, numerical simulations, and observations within the sunlight wind.
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Extra info for Nonlinear MHD waves and turbulence
5] by means of a modiﬁed WKB approach. In the weak ducts, both the transformation coeﬃcient and the leakage rate are exponentially small. The expression for the leakage rate looks very similar to the tunneling coeﬃcient in quantum mechanics  and therefore this eﬀect was called tunneling transformation [5,6]. Further developments of this approach were described in Refs. [15,16,11]. One should point out that in the ducts produced by solitons the conditions of the WKB approximation are not fulﬁlled .
The theory is extended to the whistler spiral wave beams which, according to the NLS equation, must be liable to the self-focusing. It is shown that when the wave beam becomes suﬃciently narrow, the self-focusing is replaced by the defocusing because of big radiation losses. These predictions are conﬁrmed by numerical experiments. Possible generalizations to other gyrotropic media are brieﬂy discussed. 1 Introduction Among many kinds of waves in space plasmas, the whistler waves play very important role.
The reason is that in addition to the angular momentum of the m th harmonic there is a “spin” angular momentum, associated with the right-handed polarization of the ﬁeld described by F¯m . ¯ m and E ¯z by means of Eqs. (93) Solving Eq. (105), we then can calculate G and (96). Equation (105), in the dimensional units, can be written as  iVg ∂ F¯m 1 (m−1) + S Λ(r) F¯m − δω F¯m = 0, ∂z 2 (106) where Vg = ∂ω ∂kz 0 , S= ∂2ω 2 ∂k⊥ 0 , δω = N0 ∂ω ∂N 0 ν. (107) 2 and ( )0 means Here ω = ω(k, kz , N ) is the function (20) with k 2 = kz2 + k⊥ that after diﬀerention one should put k⊥ = 0, N = N0 .