Single Bunch Stability to Monopole Excitation | Zendy

Boris Podobedov | Zendy

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Single Bunch Stability to Monopole Excitation

Author(s) -

Boris Podobedov

Publication year - 1999

Language(s) - English

Resource type - Reports

DOI - 10.2172/10000

Subject(s) - magnetic monopole , physics , electrical impedance , stability (learning theory) , vlasov equation , excitation , resonator , perturbation theory (quantum mechanics) , perturbation (astronomy) , nonlinear system , fokker–planck equation , quantum electrodynamics , classical mechanics , mathematical analysis , partial differential equation , electron , quantum mechanics , mathematics , optics , machine learning , computer science

We study single bunch stability with respect to monopole longitudinal oscillations in electron storage rings. Our analysis is different from the standard approach based on the linearized Vlasov equation. Rather, we reduce the full nonlinear Fokker-Planck equation to a Schroedinger-like equation which is subsequently analyzed by perturbation theory. We show that the Haissinski solution [3] may become unstable with respect to monopole oscillations and derive a stability criterion in terms of the ring impedance. We then discuss this criterion and apply it to a broad band resonator impedance model

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