Download Plasma Electrodynamics. Linear Theory by A. I. Akhiezer, I. A. Akhiezer, R. V. Polovin, D. Ter Haar PDF

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By A. I. Akhiezer, I. A. Akhiezer, R. V. Polovin, D. Ter Haar

From the intro: houses of plasmas as a particular nation of topic are to a huge quantity made up our minds via the truth that there are among the debris which represent the plasma electromagnetic forces which act over macroscopic distances. methods happening in a plasma are accordingly in most cases observed via the excitation of electromagnetic fields which play a basic position within the means those techniques advance. The electromagnetic interactions which expand over macroscopic distances appear to begin with within the incidence within the plasma of collective oscillations within which a lot of debris takes half at the same time. The life of those particular collective electromagnetic oscillations is simply as a lot a attribute of a plasma as a particular country of subject as, for example, the crystalline ordering is for the forged nation of subject. This explains where occupied in plasma physics by way of plasma electrodynamics, that's, the idea of electromagnetic fields in a plasma-and, within the first example, the idea of electromagnetic oscillations of a plasma-and the speculation of macroscopic electric and magnetic homes of a plasma. Such difficulties because the concept of magnetic traps, the matter of plasma heating through exterior fields or currents, and the idea of instabilities in a non-uniform plasma belong additionally to the sector of plasma electrodynamics in its widest experience. we will no longer think about those difficulties within the current book-not simply because they don't seem to be vital; on the contrary, they're of significant significance. We limit ourselves to an exposition of the speculation of the electromagnetic houses of a uniform plasma as this idea is the root of the complete of plasma electrodynamics

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Sample text

180«» 270« FIG. 1. Phase polars. r + : fast phase polar; V_: slow phase polar; Va* Alfvén phase polar. The magnetic field is along the abscissa axis. We have given in Fig. ^), a slow magneto-sound wave (vj), and an Alfvén wave (v^) for the case when Vj^ > c^. If Vj^ < c^, the polar for the Alfvén wave will go through the point A rather than through the point B. 10'), respectively equal to OA = Min (I;A, Cs), OB = Max (v^, c^l OC = Vi^l-^cl). 10') that for 0 ^ θ the phase velocity of the fast magneto-sound wave is an increasing function of θ while the phase velocity of the slow wave is a decreasing function of Θ.

7. 1) This velocity is called the group velocity of the 7th kind of wave. It is clear that the group and phase velocities of one-dimensional wavepackets are the same because the dispersion laws of the magneto-hydrodynamic waves are linear. However, the group and phase velocities of two- or three-dimensional packets are no longer the same. Let us first of all consider a two-dimensional packet. 2) νφ) sin Θ+ ν\θ) cos Θ, where ν\θ) is the derivative of V(ß) with respect to Θ. These relations can be represented graphically in a C/^, t/^-plane.

To do this we express the electrical field in terms of the magnetic field: £ = -l[«AA]+li = -i[«AB]+¿c„rlA. 11> t Here and henceforth we shall not distinguish between the vectors Β and Η and use the notation B. 29 PLASMA ELECTRODYNAMICS Substituting now this equation into the last of eqns. 12) where 4πσ ' This is now the required equation, satisfied by the magnetic field. For given u{r, t) this equation, together with the equation div Ä = 0 , uniquely determines B. We note that the quantity has the same dimensions as the kinematic viscosity ν = η/ρ^; it is called the magnetic viscosity.

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