Approximating accelerator impedances with resonator networks

Journal Article · Mon May 13 00:00:00 EDT 2024 · Journal of Instrumentation

DOI:https://doi.org/10.1088/1748-0221/19/05/t05008· OSTI ID:2283704

Vaughn, Brian J. ^[1]

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1. Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

It is common in the accelerator community to use the impedance of accelerator components to describe wake interactions in the frequency domain. However, it is often desirable to understand such wake interactions in the time domain in a general manner for excitations that are not necessarily Gaussian in nature. Here, the conventional method for doing this involves taking the inverse Fourier Transform of the component impedance, obtaining the Green's Function, and then convolving it with the desired excitation distribution. This method can prove numerically cumbersome, for a convolution integral must be evaluated for each individual point in time when the wake function is desired. An alternative to this method would be to compute the wake function analytically, which would sidestep the need for repetitive integration. Only a handful of cases, however, are simple enough for this method to be tenable. One of these cases is the case where the component in question is an RLC resonator, which has a closed-form analytical wake function solution. This means that a component which can be represented in terms of resonators can leverage this solution. As it happens, common network synthesis techniques may be used to map arbitrary impedance profiles to RLC resonator networks in a manner the accelerator community has yet to take advantage of. In this work, we will use Foster Canonical Resonator Networks and partial derivative descent optimization to develop a technique for synthesizing resonator networks that well approximate the impedances of real-world accelerator components. We will link this synthesis to the closed-form resonator wake function solution, giving rise to a powerful workflow that may be used to streamline beam dynamics simulations.

• Research Organization: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: AC02-07CH11359
• OSTI ID: 2283704
• Report Number(s): FERMILAB-PUB--24-0011-AD; arXiv:2402.01937; oai:inspirehep.net:2751220
• Journal Information: Journal of Instrumentation, Journal Name: Journal of Instrumentation Journal Issue: 05 Vol. 19; ISSN 1748-0221
• Publisher: Institute of Physics (IOP)
• Country of Publication: United States
• Language: English

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