An Introduction to Plasma Physics by W. B. Thompson (Auth.)

By W. B. Thompson (Auth.)

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They also use the plasma balance equation to determine the specific ionization rate λ and compare this with a direct calculation of ηρ(σν} for ionization, using experimental values for the ionization cross section. Current (A) 0-5 1 2 8 Te°K 27,500 29,000 26,600 19,500 λ (IO"4 sec-i) 7-29 7-48 7-15 6-3 ng

7) c For convenience, we will now assemble the equations of magnetohydrodynamics in the first form, at the same time making the assumption which is valid for all slow motions, that the displacement current can be neglected. We have the hydrodynamic equations [D/Dt = (d/dt) + v . V, is the substan­ tial time derivative] D —p + p div v = 0 Dt D\ 1 p — = -V^ + -jx B Dt c Dt ~ c~ ΙΓ Maxwell's equations 1 4π 4π - curl B = μ c 1 dB curl E = c dt divB = 0 div E = III' IV V 4π£ VI' € and the two "equations of state" D —(pp-r) = 0 or divv = 0 VII' and ) = G(E + -XB\ or E+-xB=0 VIII' 48 AN INTRODUCTION TO PLASMA PHYSICS It is possible to transform these equations and effect a very significant compression by eliminating E and j , leaving p, v, p and B as variables.

E. to right of line τ = IO -5 sec, interaction is present (Dolder and Hide, Nature, 118, 1116, 1958). % fi o lOOO to z CALCULATED loo tr υ io **· 4 DISTANCE β FROM 12 COIL TO 16 INDUCED O " ^ 2 0 cms CURRENT FIG. 4. Magnitude of magnetohydrodynamic interaction. By measuring distor­ tion in magnetic field, current distribution in plasma may be determined as a function of distance from inducing coil. Measured values are shown, with theoret­ ical curve for a fully ionized gas. (Dolder, op. ). MAGNETOHYDRODYNAMICS 4.

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