IPAC2021 - List of Authors (Frank, J.)

Paper	Title	Page
TUPAB213	Important Drift Space Contributions to Non-Linear Beam Dynamics	1914
	J. Frank, M. Arlandoo, P. Goslawski, J. Li, T. Mertens, M. Ries HZB, Berlin, Germany
	This paper presents an in-depth analysis of the non-linear contributions of drift spaces in beam dynamics for the creation of Transverse Resonance Island Buckets (TRIBs). TRIBs have been successfully generated in BESSY II and MLS at the Helmholtz-Zentrum Berlin für Materialien und Energie GmbH (HZB). They offer the possibility of generating a second stable orbit and, by populating the orbit with a different electron bunch pattern, allow to effectively have two distinct radiation sources in the same machine individually tailored to different user needs. We demonstrate the generation of TRIBs by order of non-linearity on simple lattice configurations by only treating the drift space as the non-linear element. Moreover, we also insert other non-linear magnets to show how they modify the already generated TRIBs from the drift spaces. We conclude by giving a qualitative analysis of the occurring effects, which provides a guideline as to when the linear approximation is insufficient and the non-linear contribution has to be taken into account.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB213
About •	paper received ※ 12 May 2021 paper accepted ※ 31 August 2021 issue date ※ 29 August 2021
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TUPAB214	Alpha Buckets in Longitudinal Phase Space: A Bifurcation Analysis	1917
	J. Frank, M. Arlandoo, P. Goslawski, T. Mertens, M. Ries HZB, Berlin, Germany
	At HZB’s BESSY II and MLS facilities we have the ability to tune the momentum compaction factor α up to second non-linear order. The non-linear dependence α(δ) brings qualitative changes to the longitudinal phase space and introduces new fix points α(δ)=0 which produce the so-called α-buckets. We present with this paper an analysis of this phenomena from the standpoint of bifurcation theory. With this approach we were able to characterize the nature of the fix points and their position in direct dependence on the tunable parameters. Furthermore, we are able to place stringent conditions onto the tunable parameters to either create or destroy α-buckets.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB214
About •	paper received ※ 12 May 2021 paper accepted ※ 17 June 2021 issue date ※ 26 August 2021
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TUPAB215	Novel Non-Linear Particle Tracking Approach Employing Lie Algebraic Theory in the TensorFlow Environment	1920
	J. Frank, M. Arlandoo, P. Goslawski, J. Li, T. Mertens, M. Ries, L. Vera Ramirez HZB, Berlin, Germany
	With this paper we present first results for encoding Lie transformations as computational graphs in Tensorflow that are used as layers in a neural network. By implementing a recursive differentiation scheme and employing Lie algebraic arguments we were able to reproduce the diagrams for well known lattice configurations. We track through simple optical lattices that are encountered as the main constituents of accelerators and demonstrate the flexibility and modularity our approach offers. The neural network can represent the optical lattice with predefined coefficients allowing for particle tracking for beam dynamics or can learn from experimental data to fine-tune beam optics.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB215
About •	paper received ※ 12 May 2021 paper accepted ※ 31 August 2021 issue date ※ 21 August 2021
Export •	reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

Paper

Title

Page

Important Drift Space Contributions to Non-Linear Beam Dynamics

1914

J. Frank, M. Arlandoo, P. Goslawski, J. Li, T. Mertens, M. Ries
HZB, Berlin, Germany

This paper presents an in-depth analysis of the non-linear contributions of drift spaces in beam dynamics for the creation of Transverse Resonance Island Buckets (TRIBs). TRIBs have been successfully generated in BESSY II and MLS at the Helmholtz-Zentrum Berlin für Materialien und Energie GmbH (HZB). They offer the possibility of generating a second stable orbit and, by populating the orbit with a different electron bunch pattern, allow to effectively have two distinct radiation sources in the same machine individually tailored to different user needs. We demonstrate the generation of TRIBs by order of non-linearity on simple lattice configurations by only treating the drift space as the non-linear element. Moreover, we also insert other non-linear magnets to show how they modify the already generated TRIBs from the drift spaces. We conclude by giving a qualitative analysis of the occurring effects, which provides a guideline as to when the linear approximation is insufficient and the non-linear contribution has to be taken into account.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB213

About •

paper received ※ 12 May 2021 paper accepted ※ 31 August 2021 issue date ※ 29 August 2021

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

TUPAB214

Alpha Buckets in Longitudinal Phase Space: A Bifurcation Analysis

1917

J. Frank, M. Arlandoo, P. Goslawski, T. Mertens, M. Ries
HZB, Berlin, Germany

At HZB’s BESSY II and MLS facilities we have the ability to tune the momentum compaction factor α up to second non-linear order. The non-linear dependence α(δ) brings qualitative changes to the longitudinal phase space and introduces new fix points α(δ)=0 which produce the so-called α-buckets. We present with this paper an analysis of this phenomena from the standpoint of bifurcation theory. With this approach we were able to characterize the nature of the fix points and their position in direct dependence on the tunable parameters. Furthermore, we are able to place stringent conditions onto the tunable parameters to either create or destroy α-buckets.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB214

About •

paper received ※ 12 May 2021 paper accepted ※ 17 June 2021 issue date ※ 26 August 2021

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

TUPAB215

Novel Non-Linear Particle Tracking Approach Employing Lie Algebraic Theory in the TensorFlow Environment

1920

J. Frank, M. Arlandoo, P. Goslawski, J. Li, T. Mertens, M. Ries, L. Vera Ramirez
HZB, Berlin, Germany

With this paper we present first results for encoding Lie transformations as computational graphs in Tensorflow that are used as layers in a neural network. By implementing a recursive differentiation scheme and employing Lie algebraic arguments we were able to reproduce the diagrams for well known lattice configurations. We track through simple optical lattices that are encountered as the main constituents of accelerators and demonstrate the flexibility and modularity our approach offers. The neural network can represent the optical lattice with predefined coefficients allowing for particle tracking for beam dynamics or can learn from experimental data to fine-tune beam optics.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB215

About •

paper received ※ 12 May 2021 paper accepted ※ 31 August 2021 issue date ※ 21 August 2021

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)