Equivalence of the Landau and Fokker-Planck Collision Terms

Author:

Enoch Jacob

Publisher

AIP Publishing

Subject

General Engineering

Reference5 articles.

1. W. P. Allis,Encyclopedia of Physics(Springer-Verlag, Berlin, 1956), vol. XXI, p. 429.

2. Landau states in his original paper thatwis an even function of Δi and Δiʹ. His definition ofwhowever is not the same as the definition ofwin the present paper. Let Landau’swbe denoted by wL. Then w(pi,piʹ,Δi,Δiʹ) = wL(pi+(Δi∕2),piʹ+(Δiʹ∕2),Δi,Δiʹ). When pi+(Δi∕2) and piʹ+(Δiʹ∕2) are replaced pi and piʹ, respectively, in the expression for wL, without modifying thenewdependence of wL on the Δ; wL is, indeed, an even function of the Δ. It must be noted, however, that wL(pi,piʹ,Δi,Δiʹ) is no longer the collision rate as calculated in the usual fashion, but differs from the latter by terms of order Δi, Δiʹ, and higher-order terms. It turns out, however, that the use ofwinstead of wL will merely change the value of the collision term by terms of order cubic in the Δ which are neglected anyway throughout.

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