Elaborated Modeling of Synchrotron Motion in Vlasov-Fokker-Planck Solvers

Solving the Vlasov-Fokker-Planck equation is a well-tested approach to simulate dynamics of electron bunches self-interacting with their own wake-field. Typical implementations model the dynamics of a charge density in a damped harmonic oscillator, with a small perturbation due to collective effects. This description imposes some limits to the applicability: Because after a certain simulation time coherent synchrotron motion will be damped down, effectively only the incoherent motion is described. Furthermore – even though computed - the tune spread is typically masked by the use of a charge density instead of individual particles. As a consequence, some effects are not reproduced. In this contribution, we present methods that allow to consider single-particle motion, coherent synchrotron oscillations, non-linearities of the accelerating voltage, higher orders of the momentum compaction factor, as well as modulations of the accelerating voltage. We also provide exemplary studies – based on the KIT storage ring KARA (KArlsruhe Research Accelerator) - to show the potentiality of the methods

Studies of the Micro-Bunching Instability in the Presence of a Damping Wiggler

At the KIT storage ring KARA (Karlsruhe Research Accelerator), the momentum compaction factor can be reduced leading to natural bunch lengths in the ps range. Due to the high degree of longitudinal compression, the micro-bunching instability arises. During this longitudinal instability, the bunches emit bursts of intense coherent synchrotron radiation in the THz frequency range caused by the complex longitudinal dynamics. The temporal pattern of the emitted bursts depends on given machine parameters, like momentum compaction factor, acceleration voltage, and damping time. In this paper, the influence of the damping time is studied by utilizing the CLIC damping wiggler prototype installed in KARA as well as by simulations using the Vlasov-Fokker-Planck solver Inovesa

Studies of the Micro-Bunching Instability in the Presence of a Damping Wiggler

At the KIT storage ring KARA (Karlsruhe Research Accelerator), the momentum compaction factor can be reduced leading to natural bunch lengths in the ps range. Due to the high degree of longitudinal compression, the micro-bunching instability arises. During this longitudinal instability, the bunches emit bursts of intense coherent synchrotron radiation in the THz frequency range caused by the complex longitudinal dynamics. The temporal pattern of the emitted bursts depends on given machine parameters, like momentum compaction factor, acceleration voltage, and damping time. In this paper, the influence of the damping time is studied by utilizing the CLIC damping wiggler prototype installed in KARA as well as by simulations using the Vlasov-Fokker-Planck solver Inovesa

Studies of Longitudinal Dynamics in the Micro-Bunching Instability Using Machine Learning

The operation of synchrotron light sources with short electron bunches increases the emitted CSR power in the THz frequency range. However, the spatial compression leads to complex longitudinal dynamics, causing the formation of micro-structures in the longitudinal bunch profiles. The fast temporal variation and small scale of these micro-structures put challenging demands on their observation. At the KIT storage ring KARA (KArlsruhe Research Accelerator), diagnostics have been developed allowing direct observation of the dynamics by an electro-optical setup, and indirect observation by measuring the fluctuation of the emitted CSR. In this contribution, we present studies of the micro-structure dynamics on simulated data, obtained using the numerical Vlasov-Fokker-Planck solver Inovesa, and first applications on measured data. To deal with generated data sets in the order of terabytes in size, we apply the machine learning technique k-means to identify the dominant micro-structures in the longitudinal bunch profiles. Following this approach, new insights on the correlation of the CSR power fluctuation to the underlying longitudinal dynamics can be gained