By A. I. Morozov, L. S. Solov’ev (auth.), Acad. M. A. Leontovich (eds.)
In the curiosity of pace and financial system the notation of the orig inal textual content has been retained in order that the move fabricated from vectors A and B is denoted via [AB], the dot product by way of (AB), the Laplacian operator by means of ~. and so on. it may well even be worthy mentioning that the temperature is often expressed in power devices within the Soviet literature in order that the Boltzmann consistent should be lacking in a variety of frequent expressions. In concerns of terminology, every time pos sible a number of varieties are used while a time period is first brought, e. g. , magnetoacoustic and magnetosonic waves, "probkotron" and replicate desktop, and so forth. it really is was hoping during this option to support the reader to narrate the phrases used right here with these in latest translations and with the normal nomenclature. quite often the method of literature quotation utilized in the bibliographies follows that of the yankee Institute of Physics "Soviet Physics" sequence. aside from the cor rection of a few seen misprints the textual content is that of the unique. we want to exhibit our gratitude to Academician Leontovich for kindly delivering the most recent corrections and additions to the Russian textual content. v CONTENTS Steady-State Plasma circulation in a Magnetic box A. I. Morozov and L. S. Solov'ev advent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 bankruptcy 1. Acceleration Mechanisms , • • • • • • • • • • . 2 §1. Microscopic photo of Plasma Acceleration . . . . . . . . . . . . . . . . . . . 2 §2.
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Additional info for Reviews of Plasma Physics / Voprosy Teorii Plazmy / Вопросы Теории Плазмы
Sample text
These equations can be generalized to the case in which the system shows helical symmetry. Omitting the calculations, we write the result [26] [see Eq. £. ~ ~ + ~ . £. £. 33) Here ~ is a function of the two coordinates r and e, e = cp- az, a = 21r /L. f3 = 1 + a 2r 2, and Lis the pitch of the helix. § 2. Axisymmetric Flow across an Azimuthal Magnetic Field An important case of MHD flow is the flow across an azimuthal magnetic field with velocity v = v 11 and field H = HfP. The equations describing flow of this type can be found from Eqs.
37) must be solved together for p and ~; the functions U(0 and B(O and the equations of the boundary surfaces must be given. If the field Hr,o is known we can write the current density j in terms of H r,o by means of . _ (rH In the first approximationp we can replace p in Eq. 115) by p0 (z). Equating the flow velocity v (z) to the critical velocity c s. we find the equation of the surface at which the critical velocity is reached: v 2 (z) (l+y) ---(2--y) B 2 r 2 p0 (z)=(y-l)U. 116) Since v(z) is an increasing function, while p 0(z) is a decreasing function, the critical surface is located at progressively larger values of z as the radius increases (Fig. lOa). B. In the other limiting case, (3 « 1, a cold plasma, in the zeroth approximation in the parameter (3, the density is p 0(r, z) = (U - v 2/2) jr2B 2• We now write c~ as c~= U- v2 /2 + ('\'- 2)W (p).