ML4FCC

Introduction

Accelerator performance is characterized by the size of the area in phase space where the beam particles feature bounded, i.e. stable, dynamics under long-term tracking (~10 h, or 108 revolutions). The dynamics is defined by the static and variable non-linear electric and magnetic field elements that comprise the machine, also known as the lattice. Knowledge of the boundary between the stable and the chaotic regimes, called the Dynamic Aperture (DA), and maximization of the latter are vital during the design phase and eventually for successful machine operation since particles located in the unstable regime will be lost from the beam and reduce its lifetime. Such losses limit the collider’s luminosity reach and hence have a critical impact on its physics performance. The best way to assess the DA at present is by means of particle tracking simulations [6]. Typically, simulations can cover only up to 106 revolutions around the ring (1-minute in real time). While the physics of the involved processes is well understood, the mathematical formulation is a non-linear dynamics problem that is highly dependent on the initial conditions.

A key aspect of accelerator design is to maximize the stable area, or DA, while respecting a plethora of other objectives, by properly adjusting the 10’000s of electro-magnetic elements using a large number of high-level parameters. This requires efficient search algorithms of the available parameter space. The main objectives of this project are hence twofold: first, to identify and develop a suitable ML model of the stable phase space area as a function of the machine input parameters by training on a large number of tracking simulations; and second, to develop an active learning framework that provides a targeted, efficient, yet exhaustive search for optimal accelerator designs in terms of parameter settings and / or lattice configurations to potentially revolutionize accelerator design. Parallelization of the algorithms will be relevant to best use the available high-performance clusters at EPFL. Potentially, the DA ML model could also be employed to focus only on tracking the particles in relevant areas of the phase space. This would free up computational resources to extend the essential simulations beyond current limitations and improve the accuracy of the highly relevant particle beam lifetime estimates. In addition, we believe a paradigm shift is possible for this kind of simulation studies by exploring parameter space in a smart way and by avoiding redundant. The LHC also provides a large amount of experimental data that is currently processed within the PACMAN project [7] and will be valuable for comparison and evaluation of the accelerator design framework proposed here.

Problem‍

• A future hadron collider shall be designed for maximum performance,
• Tolerances and specifications of magnets must be determined (cost impact),
• Survival time of circulating particles as a function of deviation from beam centre is a key element,
• Is computationally expensive: 10^6 turns, several 10k elements per turn.

Solution

• Determine stability of starting amplitudes,
• Use machine learning to explore and interpolate the phase space (amplitudes) and accelerator parameter space (tuning),
• ML will speed up process by orders of magnitude.

Impact‍

• Maximise performance of this expensive research infrastructure under planning,
• Magnet specifications as best cost/benefit ratio.