Data-driven Iterative Learning for Model Predictive Control of Heating Systems

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Convexity Properties of the Model Predictive Control Problem for Subclasses of Multilinear Time-Invariant Systems

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Arrival Time Stabilization at Flash Using the Bunch Arrival Corrector Cavity (BACCA)

For pump-probe and seeding experiments at free electron lasers, a femtosecond precise bunch arrival time stability is mandatory. To stabilize the arrival times a fast longitudinal intra bunch-train feedback (L-IBFB) using bunch arrival time monitors is applied. The electron bunch energy prior to a bunch compression chicane is modulated by superconducting radio frequency (SRF) cavities to compensate fast arrival time fluctuations of the subsequent bunches. A broadband normal conducting RF cavity was installed in front of the first bunch compression chicane at FLASH. The L-IBFB uses the normal conducting cavity for small but fast energy corrections together with the SRF cavities for larger and slower corrections. Current measurements show arrival time stabilities of the electron bunches towards 5 fs (rms) at the end of the linac, if the normal conducting cavity acts together with the SRF cavities in the L-IBFB system

Longitudinal Intra-Train Beam-Based Feedback at FLASH

The longitudinal intra-train beam-based feedback has been recommissioned after major upgrades on the synchronization system of the FLASH facility. Those upgrades include: new bunch arrival time monitors (BAMs), the optical synchronization system accommodating the latest European XFEL design based on PM fibers, and installation of a small broadband normal conducting RF cavity. The cavity is located prior to the first bunch compressor at FLASH and allows energy modulation bunch-by-bunch (1 us spacing) on the per mille range. Through the energy dependent path length of the succeeding magnetic chicane the cavity is used for ultimate bunch arrival time corrections. Recently the RF cavity operated 1 kW pulsed solid-state amplifier was successfully commissioned. First tests have been carried out incorporating the fast cavity as actuator together with SRF stations for larger corrections in our intra-train beam-based feedback pushing now arrival time stabilities towards 5 fs (rms). The latest results and observed residual instabilities are presented

Beam Arrival Stability at the European XFEL

Free electron laser facilities, such as the European XFEL, make increasingly high demands on the longterm temporal stability and uniformity of the electron bunches, as pump-probe experiments meanwhile aim for timing stabilities of few femtoseconds residual jitter only. For a beam-based feedback control of the linear accelerator, electro-optical bunch arrival-time monitors are deployed, achieving a time resolution better than 3 fs. In a first attempt, we recently demonstrated a beam-based feedback system, reducing the arrival time jitter of the electron bunches to the 10 fs level with stable operation over hours. For pump-probe experiments it is crucial to equally verify this new level of precision in the FEL pulse arrival time with independent methods. In this work, we are discussing first results from examining the facility-wide temporal stability at the European XFEL, with attention to the contributions of various sub-systems and on the different time scales

Few-Femtosecond Facility-Wide Synchronization of the European XFEL

The first facility-wide evaluation of the optical synchronization system at the European XFEL resulted in excellent arrival time stability of the electron bunches at the end of the 2 km long linac, being measured with two individual adjacent femtosecond-resolution bunch arrival time monitors. While each of the monitors is independently linked by a stabilized optical fiber to a master laser oscillator, with one being installed in the injector area and one in the experimental hall, these two reference lasers are tightly synchronized through another few-km long fiber link. Thus, not only the accelerator performance is being benchmarked, but equally the optical synchronization infrastructure itself. Stability on this level can only be achieved by locking the RF for cavity field control to the optical reference and requires an unprecedented synchronization of the master laser oscillator to the main RF oscillator, enabled by a novel RF/optical phase detector. Finally, with the seeders of the experiment’s optical lasers synchronized to the master laser oscillator, first experiments at two independent scientific instruments proved an X-ray/optical timing jitter of few tens of femtoseconds