Online Bayesian optimization for a recoil mass separator

The Separator for Capture Reactions (SECAR) is a next-generation recoil separator system at the Facility for Rare Isotope Beams (FRIB) designed for the direct measurement of capture reactions on unstable nuclei in inverse kinematics. To maximize the performance of this system, stringent requirements on the beam alignment to the central beam axis and on the ion-optical settings need to be achieved. These can be difficult to attain through manual tuning by human operators without potentially leaving the system in a suboptimal and irreproducible state. In this work, we present the first development of online Bayesian optimization with a Gaussian process model to tune an ion beam through a nuclear astrophysics recoil separator. We show that this method achieves small incoming angular deviations ($<1\mathrm{mrad}$) in an efficient and reproducible manner that is at least 3 times faster than standard hand-tuning. Additionally, we present a Bayesian method for experimental optimization of the ion optics, and show that it validates the nominal theoretical ion-optical settings of the device, and improves the mass separation by 32% for some beams.

Figure 1

COSY Infinity ion optics calculation (x-plane only) of a proton-capture reaction on ${{}^{20}\mathrm{Ne}}^{8+}$. SECAR elements are shown up to the first mass separation slits. The recoils (${{}^{21}\mathrm{Na}}^{8+}$) are shown in black for different outgoing energies and angles, recoils of charge $Q=9+$ are shown in red, and unreacted ${{}^{20}\mathrm{Ne}}^{8+}$ of similar magnetic rigidity is shown in blue.

Figure 2

Mean $\mu$ (a), standard deviation $\sigma$ (b) and acquisition function (c) for a 2D steerer optimization run. The observations are shown in (a) and (b) by dots shaded by time of observation, with the darkest shade being the most recent observation. The next sample point is shown in (c) by the white cross indicating the minimum of the LCB acquisition function.

Figure 3

Best steering distance reached as a function of number of GP iterations, for 2D and 4D optimizations.

Figure 4

Beam spot seen at FP1 before (a–d) and after (e–h) steerers optimization with a Ne beam. Beam movement due to unbalanced quadrupole forces decreased from an average of 7 mm to an average of 0.2 mm. All axes are in pixels, and 16 pixels correspond to 5 mm.

Figure 5

Objective function defined in Eq. (3) reached as a function of number of GP iterations, for 8D (seven quadrupole and one hexapole magnets) and 9D (seven quadrupole and two hexapole magnets) optimizations within $\pm 4\%$ $dE/E$.

Figure 6

(a) Nominal and (b) after the GP optimization of the width at FP2 for the ${}^{133}\mathrm{Cs}$ commissioning run (see Table 2). Red dots indicate 5 mm. X-axis scale is in pixels, where 31 pixels is 5 mm.