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Quasi-static evolution of a dissipative plasma column in vacuum

Published online by Cambridge University Press:  13 March 2009

C. Lo Surdo
C. Lo Surdo
Affiliation:
Associazione Euratom-ENEA sulla Fusione, Centro Ricerche Energia Frascati, C.P. 65-00044 Frascati, Rome, Italy
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Abstract

We consider the following problem: how far, in what sense and with what practical applications might the analysis of the quasi-static evolution of a (strictly) dissipative plasma column in vacuum be carried out independently of computational means (however necessary at a later stage) in the framework of a conveniently simplified, yet significant, mathematical model. We show that the the (two-region) evolution problem of concern can be reduced to the (numerical) solution of just three nonlinear non-autonomous evolution equations in three unknowns, say Ẋ = Ẋ(X, t), with X ≡ (X1, X2, X3), where the corresponding mapping (X, t)↣ Ẋ can be made effective at the cost of inverting a non-canonical Fredholm operator of the second kind that is completely defined for the given X = X(t) and t. The assumption of sufficiently slow evolution allows us to work with the static-equilibrium momentum equation. Under axial (or cylindrical) symmetry, we know that the ‘radial’ equilibrium condition leads to a semi-linear elliptic equation in the meridional (or (x, y)) plane. The Fredholm operator arises from the inversion of the Laplacian appearing in that equation.

Type
Research Article
Information
Journal of Plasma Physics , Volume 43 , Issue 2 , April 1990 , pp. 217 - 237
Copyright
Copyright © Cambridge University Press 1990

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References

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