Bayesian optimization of the beam injection process into a storage ring

We have evaluated the data-efficient Bayesian optimization method for the specific task of injection tuning in a circular accelerator. In this paper, we describe the implementation of this method at the Karlsruhe Research Accelerator with up to nine tuning parameters, including the determination of the associated hyperparameters. We show that the Bayesian optimization method outperforms manual tuning and the commonly used Nelder-Mead optimization algorithm in both simulation and experiment. The algorithm was also successfully used to ease the commissioning phase after the installation of new injection magnets and is regularly used during accelerator operations. We demonstrate that the introduction of context variables that include intrabunch scattering effects, such as the Touschek effect, further improves the control and robustness of the injection process.

Figure 1

Example of a parameter scan measurement of the septum magnet voltage, where all other accelerator tuning parameters are kept constant during the scan. The GP hyperparameters $\{l_i,{\sigma }^2\}$ are fitted to the measured data points (crosses) via a log-likelihood fit. The solid line depicts the GP posterior mean and the shaded region shows the 95% confidence level.

Figure 2

In the injection scheme, electron bunches are injected from a synchrotron via an injection line into the storage ring. The relative positions of the magnets and their location are illustrated as they are placed at the storage ring KARA at KIT. See Ref. [23] for further details. The tuning parameters of the magnets and rf cavities, not shown in this figure, are used as optimization parameters.

Figure 3

Comparison of (a) a two-dimensional grid scan (grid size 400) of the injection efficiency with (b) the GP posterior mean predicted based on 20 BO evaluation steps, shown in red crosses. The tuning parameters are the strengths of the horizontal corrector magnet and the septum magnet, given in deflection angles. The BO can approximate the simple structure of parameter space in a small number of evaluation steps.

Figure 4

Optimization results in an AT simulation model using UCB (green, solid) and EI (blue, dashed) acquisition functions for the (a) three- and (b) six-dimensional problems. The lines depict the best-evaluated injection efficiency in each run, averaged over ten independent runs. The shaded areas are the one $\sigma$ spread. Within 50 and 100 steps for three- and six-dimensional problems, respectively, all the optimization runs converged to the optimum setting. The required steps for convergence increase with the input dimensions and both acquisition functions have a similar performance.

Figure 5

Example of a nonlocalized orbit defined by the magnet strengths found by the BO algorithm (navy, solid), in comparison to the reference orbit (gray, dashed) with design values, where the injection bump orbit is fully localized. The orbit oscillation outside of the injection bump is not taken into consideration by BO, as it causes no beam loss.

Figure 6

Experimental optimization result of the injection efficiency using BO with two different acquisition functions and Nelder-Mead algorithm (red, dotted). UCB (green, solid) and EI (blue, dashed) have similar results and are both able to optimize the injection efficiency within a reasonable number of evaluations. For a nine-dimensional problem, NM is clearly slower than BO.

Figure 7

Convergence behavior of BO with UCB (green, triangle) and EI (blue, square) acquisition functions and Nelder-Mead (red, circle) on the nine-dimensional problem showing the distance $\mathrm{\Delta }x$ between two consecutive sampled points in the scaled parameter space. Due to the noisy evaluation of the objective function, Nelder-Mead optimizes mostly locally and often needs to be restarted, whereas BO optimizes globally and does not require a restart.

Figure 8

Beam injection up to 100 mA using BO result (navy) compared to the manual tuning result (grey) obtained from an operation day. The dashed lines are the accumulated current of BO and manual tuning result. BO was roughly twice as fast as the manual tuning, greatly reducing the required beam injection time.

Figure 9

Two runs with the highest (purple, solid) and lowest (yellow, dashed) optimized injection efficiency achieved are plotted out of all five BO runs with UCB acquisition using the new power supplies. The evolution of the input parameters and the resulting objective function are shown over the optimization steps, where the vertical limit is the total allowed optimization range, respectively. The bottom plot shows the measured injection functions (markers) with the cumulative best results (lines). The dotted line depicts the 90% quantile of the injection efficiency obtained by manual operation in a month prior to the shutdown period. Even the BO run with the worst performance achieved a comparable result as the manual baseline.

Figure 10

Optimization results of BO (navy, solid) and contextual BO (cyan, dashdot) on the six-dimensional problem. Each line is the averaged injection efficiency from three runs. By using the stored current as a context variable, CBO optimizes faster and obtains a consistently higher injection efficiency than normal BO after about ten steps.