Formation of Patterns in Intense Hadron Beams. The Amplitude Equation Approach

Details Formation of Patterns in Intense Hadron Beams. The Amplitude Equation Approach Formation of Patterns in Intense Hadron Beams. The Amplitude Equation Approach

2000-01-31

arxiv.org/abs/physics/0001073v1

Physics

Accelerator Physics

LaTeX, 12 pages

Scientific paper

We study the longitudinal motion of beam particles under the action of a single resonator wave induced by the beam itself. Based on the method of multiple scales we derive a system of coupled amplitude equations for the slowly varying part of the longitudinal distribution function and for the resonator wave envelope, corresponding to an arbitrary wave number. The equation governing the slow evolution of the voltage envelope is show to be of Ginzburg-Landau type.

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