Regulation of electron bunch arrival time for a continuous-wave linac: Exploring the application of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi mathvariant="script">H</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> mixed-sensitivity problem

Regulating the arrival time of electron bunches is a crucial step to improve temporal resolution accelerator-based pump-probe experiments. In this regard, an beam regulation method called beam-based feedback, has been shown work well for stabilizing longitudinal properties on pulsed accelerator machines. Essentially, resembles typical design proportional regulator, where plant represented by response matrix, and inversion such matrix produces regulator. recent years, however, linear accelerators that operate in continuous-wave mode have received increasing attention. One key features machines improved statistics measured data, which enables high-resolution spectral analysis noise acting beam. This new insight allows us reinterpret as disturbance rejection goal, based frequency data. work, we show feedback principal performance limitation becomes apparent analyzing To situation, propose regulator incorporates dynamical model formulated context so-called ${\mathcal{H}}_{2}$ mixed-sensitivity problem. The designed demonstrated excellent agreement between measurements carried out at ELBE showed potential approach.