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We consider the nonlinear transverse motion in a circular particle accelerator. A key parameter for accelerator performance is the so-called dynamic aperture. This quantity is defined as the volume in phase space of the stable initial conditions. The accurate numerical computation of such a volume is very CPU-time consuming.

In this paper we present some original parallel algorithms to speed up the evaluation of the dynamic aperture. A detailed analysis of different algorithms implemented is carried out. Furthermore, we studied the dependence of the CPU-time on the phase space parameters as well as the load balancing of the proposed techniques.

The Super Tau-Charm Facility (STCF) is a proposed dual-ring electron–positron collider in China, designed to operate at a center-of-mass energy (CME) range of 2–7GeV with symmetric beam energies. The collider aims for a luminosity exceeding $5\times 10^{34}{\mathrm{\text{cm}}}^{-2}{\mathrm{\text{s}}}^{-1}$ at the beam energy of 2.0GeV. This work presents the preliminary lattice design for the STCF collider ring, specifically optimized for the 2.0GeV beam energy. To improve the nonlinear dynamics performance, the optimization of lattice is carried out by adjusting the strengths of sextupole and octupole magnets following the tuning of phase advances.

In this paper, we describe newly developed tools for the study and analysis of the dynamics in FFAG accelerators based on transfer map methods unique to the code COSY INFINITY. With these new tools, closed orbits, transverse amplitude dependencies and dynamic aperture are determined inclusive of full nonlinear fields and kinematics to arbitrary order. The dynamics are studied at discrete energies, via a high-order energy-dependent transfer map.

The order-dependent convergence in the calculated maps allows precise determination of dynamic aperture and detailed particle dynamics. Using normal form methods, and minimal impact symplectic tracking, amplitude- and energy-dependent tune shifts and resonance strengths are extracted. Optimization by constrained global optimization methods further refine and promote robust machine attributes.

Various methods of describing the fields will be presented, including representation of fields in radius-dependent Fourier modes, which include complex magnet edge contours and superimposed fringe fields, as well as the capability to interject calculated or measured field data from a magnet design code or actual components, respectively.

In this paper, we introduce the layout and lattice design of Circular-Electron-Positron-Collider (CEPC) partial double ring scheme and the lattice design of Super-Proton-Proton-Collider (SPPC). The baseline design of CEPC is a single beam-pipe electron positron collider, which has to adopt pretzel orbit scheme and it is not suitable to serve as a high luminosity $Z$ factory. If we choose partial double ring scheme, we can get a higher luminosity with lower power and be suitable to serve as a high luminosity $Z$ factory. In this paper, we discuss the details of CEPC partial double ring lattice design and show the dynamic aperture study and optimization. We also show the first version of SPPC lattice although it needs lots of work to do and to be optimized.

We report an efficient dynamic aperture (DA) optimization approach using multi-objective genetic algorithm (MOGA), which is driven by nonlinear driving terms computation. It was found that having small low order driving terms is a necessary but insufficient condition of having a decent DA. Then direct DA tracking simulation is implemented among the last generation candidates to select the best solutions. The approach was demonstrated successfully in optimizing NSLS-II storage ring DA.

In this paper, we introduced the parameter choice and the first version lattice design for a 61 km and 100-km Super Proton–Proton Collider (SPPC). We started the lattice design and the beam dynamics study from last year and showed the preliminary dynamic aperture result of these two SPPC lattice versions. We also showed the layout, the lattice design and the dynamic aperture study of a CEPC partial double ring, an advanced partial double ring and a fully partial double ring schemes.

In September 2012, Chinese scientists proposed a Circular Electron Positron Collider (CEPC) in China at 240 GeV center-of-mass energy for Higgs studies. The booster provides 120 GeV electron and positron beams to the CEPC collider for top-up injection at 0.1 Hz. The design of the full energy booster ring of the CEPC is a challenge. The ejected beam energy is 120 GeV and the injected beam energy is 6 GeV. In this paper we describe two alternative schemes, the wiggler bend scheme and the normal bend scheme. For the wiggler bend scheme, we propose to operate the booster ring as a large wiggler at low energy and as a normal ring at high energy to avoid the problem of very low dipole magnet fields. For the normal bend scheme, we implement the orbit correction to correct the earth field.

In the tracking of the future circular Higgs factories, significant reduction of dynamic aperture due to the synchrotron radiation has been observed. This paper will analyze the synchrotron radiation effects including the closed orbit and optics distortion, radiation damping and quantum excitation for the lattice of CEPC.

The CEPC booster needs to provide electron and positron beams to the collider at different energy with required injection efficiency. At Higgs energy, only the on-axis injection from booster to collider can be fulfilled in CDR. With a consideration of keeping the off-axis injection scheme for safety and reliability, a new booster design based on TME lattice is considered to reduce the emittance by three times after CDR. The new booster design has reached an emittance of 1.3 nm at 120 GeV and the DA without errors is even better than CDR. The geometry of new booster is designed carefully in order to share the same tunnel with collider. The design status of CEPC new booster including parameters, optics, dynamic aperture and geometry is discussed in this paper.

I review some accelerator physics topics for circular as well as linear colliders, considering both lepton and hadron beams.

In this paper, we introduce the layout and lattice design of Circular-Electron-Positron-Collider (CEPC) partial double ring scheme and the lattice design of Super-Proton-Proton-Collider (SPPC). The baseline design of CEPC is a single beam-pipe electron positron collider, which has to adopt pretzel orbit scheme and it is not suitable to serve as a high luminosity Z factory. If we choose partial double ring scheme, we can get a higher luminosity with lower power and be suitable to serve as a high luminosity Z factory. In this paper, we discuss the details of CEPC partial double ring lattice designand show the dynamic aperture study and optimization. We also show the first version of SPPC lattice although it needs lots of work to do and to be optimized.

We report an eficient dynamic aperture (DA) optimization approach using multi-objective genetic algorithm (MOGA), which is driven by nonlinear driving terms computation. It was found that having small low order driving terms is a necessary but insufficient condition of having a decent DA. Then direct DA tracking simulation is implemented among the last generation candidates to select the best solutions. The approach was demonstrated successfully in optimizing NSLS-II storage ring DA.

In this paper, we review diffusion phenomena in stochastically perturbed Hamiltonian systems, with the aim of defining the framework to use Nekhoroshev-like estimates as prototypes for the form of the diffusion coefficient. A discussion of the features of this framework is carried out. More importantly, the results of numerical simulations based on the proposed models are compared against the experimental data from recent measurements performed at the CERN Large Hadron Collider (LHC) of the extent of phase space where bounded motions occur. The main conclusions are presented and discussed in detail together with future steps.

I review some accelerator physics topics for circular as well as linear colliders, considering both lepton and hadron beams.