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Modeling longitudinal bunched beam dynamics in hadron synchrotrons using scaled fourier-hermite expansions

Groß, Kerstin ; Lens, Dieter Etienne Mia (2022):
Modeling longitudinal bunched beam dynamics in hadron synchrotrons using scaled fourier-hermite expansions. (Publisher's Version)
In: IPAC2013: Proceedings of the 4th International Particle Accelerator Conference, pp. 2513-2515,
Darmstadt, Joint Accelerator Conferences Website, IPAC2013: the 4th International Particle Accelerator Conference, Shanghai, China, 12.-17.05.2013, ISBN 978-3-95450-122-9,
DOI: 10.26083/tuprints-00020333,
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Item Type: Conference or Workshop Item
Origin: Secondary publication service
Status: Publisher's Version
Title: Modeling longitudinal bunched beam dynamics in hadron synchrotrons using scaled fourier-hermite expansions
Language: English
Abstract:

To devise control strategies and to analyze the stability of systems with feedback, a set of few ordinary differential equations (ODEs) describing the underlying dynamics is required. It is deduced by combining two approaches not used in that context before: (I) Numerical Fourier-Hermite solutions of the Vlasov equation have been studied for over fifty years [1, 2]. The idea to expand the distribution function in Fourier series in space and Hermite functions in velocity is transferred to the dynamics of bunched beams in hadron synchrotrons in this contribution. The Hermite basis is a natural choice for plasmas with Maxwellian velocity profile as well as for particle beams with Gaussian momentum spread. The Fourier basis used for spatially nearly uniform plasmas has to be adapted to bunched beams where the beam profile is not uniform in phase. (II) This is achieved analogously to the deduction of the three term recursion relations to construct orthogonal polynomials, but applied to Fourier series with the weight function taken from the Hamiltonian. The resulting system of ODEs for the expansion coefficients of desired order - dependent on the number of functions retained - is roughly checked against macro particle tracking simulations.

Book Title: IPAC2013: Proceedings of the 4th International Particle Accelerator Conference
Place of Publication: Darmstadt
Publisher: Joint Accelerator Conferences Website
Classification DDC: 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften
Divisions: 18 Department of Electrical Engineering and Information Technology > Institut für Automatisierungstechnik und Mechatronik > Control Methods and Robotics (from 01.08.2022 renamed Control Methods and Intelligent Systems)
Event Title: IPAC2013: the 4th International Particle Accelerator Conference
Event Location: Shanghai, China
Event Dates: 12.-17.05.2013
Date Deposited: 19 Jan 2022 09:24
Last Modified: 19 Jan 2022 09:24
DOI: 10.26083/tuprints-00020333
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-203330
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/20333
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