By Günter Ecker
ISBN-10: 0122297504
ISBN-13: 9780122297502
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Additional resources for Theory of Fully Ionized Plasmas
Example text
MICROSCOPIC QUALITIES OF THE COULOMB SYSTEM 53 depends only on the absolute value of r = ^r,· — qrt of the particles (/) and (j). 75) Using this we have Σ J (». ^ τ * ) *» **■- - ? 76) The interaction potential energy ^ · according to its definition also depends only on the absolute value of the distance vector r. 77) simply by shifting the origin of the coordinate system to qvi. 80) i V = t Vt. 81) being the nabla operator in the ^-configuration space. 80) to the average energy of the ^-configuration <^>(e) - 1 ΪΦυ + Σ | Φυ Pi8+pisü'9 lTj) dk r ' J + ClN'8) ( 4 · 82 ) The first term on the right-hand side of this equation represents the 54 I.
40) and find for the average potential Φ\1} the differential equation 477 \ Jexpi-^«)/©)^ (4 41) · This is the basic Poisson-Boltzmann equation which here has been justified within the single-particle approximation. 6. THE POISSON-BOLTZMANN EQUATION The Poisson-Boltzmann equation is quasilinear since its highest derivative is linear. The mathematically interesting features are identical with those of the Poisson equation. In general, it would be necessary to find numerical solutions of the Poisson-Boltzmann equation.
6. THE POISSON-BOLTZMANN EQUATION The Poisson-Boltzmann equation is quasilinear since its highest derivative is linear. The mathematically interesting features are identical with those of the Poisson equation. In general, it would be necessary to find numerical solutions of the Poisson-Boltzmann equation. 42). Before doing this we would like to stress that so far we have always considered an arbitrary multicomponent system. Without loss of generality we consider in the following a two-component system with 46 I.
Theory of Fully Ionized Plasmas by Günter Ecker
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