By A. I. Morozov, L. S. Solov’ev (auth.), Acad. M. A. Leontovich (eds.)
In the curiosity of pace and economic 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 by way of [AB], the dot product by way of (AB), the Laplacian operator via ~. and so forth. it could even be worthy stating that the temperature is usually expressed in power devices within the Soviet literature in order that the Boltzmann consistent might be lacking in a variety of frequent expressions. In concerns of terminology, every time pos sible a number of varieties are used whilst a time period is first brought, e. g. , magnetoacoustic and magnetosonic waves, "probkotron" and replicate computer, and so on. it truly is was hoping during this strategy to support the reader to narrate the phrases used the following with these in latest translations and with the traditional nomenclature. in most cases the process of literature quotation utilized in the bibliographies follows that of the yank 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 show our gratitude to Academician Leontovich for kindly supplying 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 creation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 bankruptcy 1. Acceleration Mechanisms , • • • • • • • • • • . 2 §1. Microscopic photograph of Plasma Acceleration . . . . . . . . . . . . . . . . . . . 2 §2.
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Example text
124) Here V(z) and R(z) are slowly varying but otherwise arbitrary functions of the variable z. By specifying these functions we find various configurations of the surfaces, ~ (r, z) = const. 124) that in this approximation p = p(z). , we assume that among the streamlines ~ (r, z) = const there is a straight line r = R. The correspond- MOROZOV AND SOWV'EV \ "" " o' \ '-... ........... -/ / / / / I r=R Fig. 11 ing pattern of streamlines is shown in Fig. 11, where the velocity V(z) is plotted along the z axis.
32 MOROZOV AND SOWV'EV Accordingly, in this case (r == const) we find a property of an ordinary gasdynamic nozzle: The sound velocity and the flow velocity are equal at the critical cross section. 58) that the signal velocity cannot be crossed at the minimum of f. For high-velocity flows we are primarily interested in the case c). » c~. 63a), we find f = const;p V l-pjp 0 • (2. 70) These equations show that if the velocity increases monotonically in the channel, then p and H decrease monotonically.
78) 4np 0 Thus, with p ,... __ 4;-~p ~ cfo_ (. _ll__ \ v- 1 y-1 Po ) (2. DV'EV we have Hmax ~ Ho l/ Pmax. 80) An exact expression for the maximum magnetic field is given in [22]. § 4. , ~ = ~ (r, ez), p = p (r, ez), where e is a small parameter. Neglecting terms in Eqs. _ 2 (-I-. ~)2 +pr2B2=U. 82) As noted above, B and U are arbitrary functions of ~ alone. 82) only contain partial derivatives with respect to r. In general, solution of this system of equations depends on the two arbitrary functions c 1 (z) and c 2 (z), so that ~ = ~ (r, c 1, c 2), p = p(r, c 1, c 2).