Selected applications of resonant phenomena in fourth-generation light sources

Abstract

This thesis is focused on the design of the future fourth-generation light source PETRA IV and its booster ring. It investigates the utilization of linear and non-linear resonant phenomena to shape and control the electron beam—a subject that has traditionally played a secondary role in beam dynamics studies of electron storage rings, but becomes more important in the last generation of synchrotron light sources. The main research topic is to develop techniques to mitigate detrimental side effects of the unprecedented ultra-low emittances for storage rings expected at PETRA IV. At extremely low emittances, the electron beam exhibits significantly reduced transverse dimensions, leading to increased charge density, which translates into increased probability of Coulomb interactions between electrons inside the bunch. These ultimately lead to beam quality and lifetime degradation. A promising approach to mitigating these adverse effects is to shape the beam such that the transverse emittances are equalized. This thesis evaluates three mechanisms for the generation of transverse emittance control: vertical dispersion waves, AC dipole excitation and emittance sharing— thereby leveraging resonant phenomena to reshape the beam properties in the last two cases. Among these, the exploitation of the difference resonance (𝑞 𝑥 − 𝑞 𝑦 = 0) to induce emittance sharing is identified as the most favorable approach, owing to its straightforward operational implementation and well-established theoretical foundation. The impact on beam dynamics performance with a beam with equal emittances is evaluated with numerical simulations. The key findings are: first, the Touschek limited beam lifetime increases by a factor of two. Second, intra-beam scattering-induced emittance deterioration is reduced, allowing the emittance to remain below 20 pm rad even for high single-bunch currents up to 𝐼 = 2.5 mA. Furthermore, PETRA IV features a sufficiently large dynamic aperture to support off-axis injection for both charge top-up and initial filling. Consequently, the injection efficiency under machine operation at the coupling resonance is assessed. Simulation results indicate that the strong amplitude dependence introduced by nonlinear effects in the electron dynamics enables an injection efficiency exceeding 99%. Experimental studies are conducted at the PETRA III electron storage ring at DESY and the Extremely Brilliant Source (EBS) at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. The experimental results reveal for both machines an injection efficiency below 20%, which deviates significantly from both simulation predictions (>99%) and a previously reported value in the literature (≈70%) at the Standford Positron Electron Accelerating Ring (SPEAR) in California, USA. This discrepancy underscores the necessity for dedicated optimization campaigns targeting nonlinear beam dynamics to achieve acceptable off-axis injection efficiency. Furthermore, it highlights the need for continuous refinement of existing models to accurately describe high-amplitude electron dynamics, particularly in the presence of strong nonlinear elements. Additionally, an unexpected resonant phenomenon is encountered during the course of this thesis. Namely, the generation of quasi-stable transverse resonance islands is observed during PETRA IV simulation campaigns. Although these islands emerge when the machine is operated near the coupling resonance, no direct correlation with the vertical tune setting is found. Instead, dedicated simulations reveal that their formation is attributed to strongamplitude detuning induced by nonlinear elements, which are introduced to mitigate the impact of nonlinear aberrations in the electron beam optics. More specifically, the amplitude detuning drives the horizontal tune to cross the third-order resonance for off-axis injected particles, making this resonance crossing the primary mechanism responsible for the formation of the islands. To validate and further characterize these quasi-stable resonance islands, dedicated experimental campaigns are conducted at the ESRF-EBS electron storage ring. The experimental results reveal a lifetime 𝜆 =6.74 s ±(0.23 stat. + 0.03 sys. ) s of trapped particles in the resonance islands. This study represents the first observed instance of a nonlinear resonant phenomenon being triggered while the machine’s working point is found far from the nominally excited resonance. The full potential of these resonance islands remains an open question for future research, which will focus on further characterization and strategies to enhance electron capture lifetime. Finally, a resonant slow extraction scheme that makes use of the generation of third order resonance islands is proposed. This novel variation of the resonant extraction can deliver extraction efficiencies in excess of 90% with electrostatic septa already available at other research facilities. The concept has been evaluated in the context of the future booster ring DESY IV and can potentially serve the high energy physics community that primarly exploits the beams offered at DESY in the test beam facility.