Simulations, analysis, and measurements are performed on the BNL Booster’s third integer resonance extraction to the NSRL line, which uses a constant optics slow extraction method. In this method, ring dipoles and quadrupoles are changed synchronously for a coasting beam, which aids in maintaining a fixed separatrix orientation through the spill. Simulations show that the outgoing beam has a very small dispersion, independent of the periodic dispersion value at the septum. We show using a first-order normal form approximation that transforms to the Kobayashi Hamiltonian, how the dynamics of such a spill lead to a dispersion-free outgoing beam, which is critical to the uniformity requirements of the NSRL. Finally, we measure the dispersion of the beam by varying the flattop energy of the coasting beam in the booster before engaging the spill and show that the magnitude of dispersion is reduced by over a factor of 5 from the periodic value in the ring.

Drifting optimal settings and changing working conditions force accelerator operators to keep re-tuning control systems. At BNL, the RHIC injector complex accelerates many different ion species by varying a multitude of control knobs. In this report, we investigate the use of Bayesian optimization (BO) of the Booster-to-AGS (BtA) transfer line to maximize the beam brightness in the AGS. The most suitable magnets were chosen by an investigation of the betatron phase advance to facilitate an efficient BO process, using up to 4 steering magnets and up to 3 quadrupoles. To quantify the beam intensity, we used an integrated current transformer, while the beam emittance was estimated via an Ionization Profile Monitor (IPM). It was demonstrated that the chosen magnets effectively recovered a high intensity beam from a poorly tuned configuration, using an Xopt implementation of BO, without increasing the beam profile. A new electron-collecting IPM is being configured with better systematics and lower noise compared to the current ion-collecting IPM, which can further improve this process.

Alternating Gradient Synchrotron (AGS) and its Booster serve as part of the injector compound for RHIC and the future EIC at Brookhaven National Laboratory. Injection and early acceleration processes set maximum beam brightness for the collider rings. Such processes have many control parameters and are traditionally optimized empirically by operators. In an effort to streamline the injection processes with machine learning (ML) techniques, we develop and test a Bayesian Optimization (BO) algorithm to automatically tune the Linac to Booster (LtB) transfer line magnets to maximize beam brightness after injection into the Booster. We present experimental results that demonstrate BO can be applied to optimize Booster injection efficiency.

A new method is formulated for calculating the invariant spin field (ISF) at a phase space point by leveraging the property that spins which are distributed along the ISF achieve maximum time-averaged polarization. To quantify this, we construct the time-average of spin rotation matrices beginning at a certain phase space point. It is recognized that the ISF vector at that point achieves the matrix-norm, meaning that the ISF corresponds to the first right-singular vector of that matrix. We show the relation of this method with traditional stroboscopic averaging, such that these methods are two sides of the same coin. This approach offers a new perspective in invariant spin field calculations.

Spin motion in particle accelerators obeys the Thomas-Bargmann-Michel-Telegdi (T-BMT) equation. Due to the structure of the T-BMT equation, the spin-transfer quaternion of a magnet is generally a nonlinear function of the entrance coordinates even if the phase-space motion is linear. This nonlinear function can be written as a Dyson expansion, for example as employed in the program SPRINT, which normalized the first-order expansion of the spin-transfer quaternion. Alternatively, this nonlinear function can be written as a Magnus expansion. This paper points out that in cases where the phase-space coordinates change little, as is generally the case for accelerator elements, the Magnus expansion is a much more appropriate method to describe the nonlinear spin motion because this expansion terminates after the first term when the phase-space coordinates are constant. We will demonstrate, with several examples, that an approximation based on the Magnus expansion leads to very good agreement with time-consuming numerical integration, and to significantly better agreement than obtained with historical codes like SPRINT.

Simulations, analysis, and measurements are performed on the BNL Booster’s third integer resonance extraction to the NSRL line, which uses a constant optics slow extraction method. In this method, ring dipoles and quadrupoles are changed synchronously for a coasting beam, which aids in maintaining a fixed separatrix orientation through the spill. Simulations show that the outgoing beam has a very small dispersion, independent of the periodic dispersion value at the septum. We show using a first-order normal form approximation that transforms to the Kobayashi Hamiltonian, how the dynamics of such a spill lead to a dispersion-free outgoing beam, which is critical to the uniformity requirements of the NSRL. Finally, we measure the dispersion of the beam by varying the flattop energy of the coasting beam in the booster before engaging the spill and show that the magnitude of dispersion is reduced by over a factor of 5 from the periodic value in the ring.

The Hadron Storage Ring of the Electron-Ion Collider will feature 6 Siberian snakes placed at the start of each arc to coherently cancel spin precession from diametrically opposite arcs in the ring. To avoid spin-orbital resonances, the alternating sum of the rotation axes of all snakes is 90 degrees, ensuring the closed-orbit spin tune is ½ and sufficiently far away from betatron tunes and integer tunes. This choice does not account for amplitude-dependent spin tune (ADST) shift, which introduces high-order spin orbit resonances in the vicinity of strong first-order resonances. By varying betatron phase advances across each of the 6 arcs, we minimize the strength of first-order spin-orbit resonances as well as ADST shift. In the case of uncooled helium-3, we find it is necessary to minimally vary the vertical orbital tune as well but are able to completely avoid depolarization throughout the ramp with time-dependent phase advances.