Mathematical and Numerical Methods for the Nonlinear Hyperbolic Propagation Problem $\frac{\partial^{2}\Gamma}{\partial t^{2}} = \frac{\partial }{\partial z} \lbrace \frac{\partial \Gamma}{\partial t} \frac{\partial \Gamma}{\partial z} \rbrace$ : A Preliminary Treatment of Collective Space Charge Effects in Accelerator Physics

Funk, U.; Vaccaro, V. G.; Wüstefeld, G.; Stanco, L.; Mika, K.; Krüger, U.

Book/Report

FZJ-2018-01855

Mathematical and Numerical Methods for the Nonlinear Hyperbolic Propagation Problem $\frac{\partial^{2}\Gamma}{\partial t^{2}} = \frac{\partial }{\partial z} \lbrace \frac{\partial \Gamma}{\partial t} \frac{\partial \Gamma}{\partial z} \rbrace$ : A Preliminary Treatment of Collective Space Charge Effects in Accelerator Physics

Funk, U.FZJ* ; Krüger, U.FZJ* ; Mika, K.FZJ* ; Stanco, L. ; Vaccaro, V. G. ; Wüstefeld, G.FZJ*

1982
Kernforschungsanlage Jülich, Verlag Jülich

Jülich : Kernforschungsanlage Jülich, Verlag, Berichte der Kernforschungsanlage Jülich 1772, 168 p. (1982)

Please use a persistent id in citations: http://hdl.handle.net/2128/17667

Report No.: Juel-1772

Abstract: In the first part of this report a physical model is presenten, which describes the deforming of a bunch in a storage ring influenced only by its own space charge field. A system of two differential equations for the density and the monentum of the particles is set up, which is independent of any special machine parameter. Due to the sign of the inductance of the chamber walls and the sign of the dispersion of the revolution frequency, we distinguish between a de-bunching and a self-bunching situation. The de-Bunching corresponds to a nonlinear hyperbolic propagation problem well-known in gas dynamics, and the self-bunching to a nonlinear elliptic initial value problem. [..]

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