Electron cloud effects have become one of the main performance limitations for circular particle accelerators operating with positively-charged beams. Among other machines worldwide, the CERN Super Proton Synchrotron (SPS), as well as the Large Hadron Collider (LHC) are affected by these phenomena. Intense efforts have been devoted in recent years to improve the understanding of electron cloud (EC) generation with the aim of finding efficient mitigation measures. In a different domain of accelerator physics, non-linear resonances in the transverse phase space have been proposed as novel means of manipulating charged particle beams. While the original goal was to perform multi-turn extraction from the CERN Proton Synchrotron (PS), several other applications have been proposed. In this paper, the study of EC generation in the presence of charged particle beams with multimode horizontal distribution is presented. Such a peculiar distribution can be generated by different approaches, one of which consists in splitting the initial Gaussian beam distribution by crossing a non-linear resonance. In this paper, the outcome of detailed numerical simulations is presented and discussed.
This paper gives an introduction of longitudinal beam dynamics for circular accelerators. After briefly discussing some types of circular accelerators, it focuses on particle motion in synchrotrons. It summarizes the equations of motion, discusses phase-space matching during beam transfer, and introduces the Hamiltonian of longitudinal motion.
A new algorithm for calculating the spin tune and the n-axis for circular accelerators is presented. The method resembles the one employed in the existing program code SODOM in that one-turn numerical spin maps at equally spaced orbit angle variables are used but it is more efficient than the latter. Furthermore, it is applicable at large openning angles of the n-axis, whereas the existing SODOM only converges for small angles.
Recent progress in particle accelerator tracking has shown that the field representation is one of the major limits of the prediction accuracy especially for machines, whose aperture is fully filled by the beam and thus higher the artefacts created by higher order modes have to be thoroughly understood. The standard tool for field presentation today are cylindrical circular multipoles due to their straight forward correspondence to the Cartesian coordinates. In this paper we extend the standard approach to other coordinate systems, show how these can be measured next to their realisation in me…
The resonant laser cooling of circular accelerator beams of relativistic charged particle is studied. It is shown that in the approximation of the given external electromagnetic wave amplitude (small gain free electron laser) the emittance of a beam of charged particles decreases. In the field of particle energy about 100 in the mass energy units the beam energy losses are negligible. The discovered effect can be used for cooling of charged particle beams in various accelerators. The significant cooling rates are possible to achieve by placing of the cooling device in the appropriate points of…
By considering delta function sextupole, octupole, and decapole perturbations and using difference action-angle variable equations, we find some useful analytical formulae for the estimation of the dynamic apertures of circular accelerators due to single sextupole, single octupole, single decapole (single 2$m$ pole in general). Their combined effects are derived based on the Chirikov criterion of the onset of stochastic motions. Comparisons with numerical simulations are made, and the agreement is quite satisfactory. These formulae have been applied to determine the beam-beam limited dynamic a…
In the usual parameter regime of accelerator physics, particle ensembles can be treated as classical. If we approach a regime where $ε_xε_yε_s \approx N_{particles}λ_{Compton}^3\$, however, the granular structure of quantum-mechanical phase space becomes a concern. In particular, we have to consider the Pauli exclusion principle, which will limit the minimum achievable emittance for a beam of fermions. We calculate these lowest emittances for the cases of bunched and coasting beams at zero temperature and their first-order change rate at finite temperature.
Coherent transverse oscillations of a bunch in a ring accelerator are considered. Three different models of the bunch are used: a hollow bunch in a square potential well, a square bunch in a parabolic potential well, and a parabolic bunch in a parabolic well. The bunch space-charge field, wakefield, and chromaticity are taken into account in all the cases. The bunch eigenmodes and various instabilities are studied. The results are compared and analyzed to establish the range of applicability of the models. Role of the Landau damping due to dependence of the SC field on the longitudinal coordin…
The leading Lie generators, including the chromatic effects, due to hard-edge fringe field of single multipole and solenoid are derived from the vector potentials within a Hamiltonian system. These nonlinear generators are applied to the interaction region of PEP-II to analyze the linear errors due to the feed-down from the off-centered quadrupoles and solenoid. The nonlinear effects of tune shifts at large amplitude, the synchro-betatron sidebands near half integer and their impacts on the dynamic aperture are studied in the paper.
Circular particle accelerators at the energy frontier are based on superconducting magnets that are extremely sensitive to beam losses as these might induce quenches, i.e.\ transitions to the normal-conducting state. Furthermore, the energy stored in the circulating beam is so large that hardware integrity is put in serious danger, and machine protection becomes essential for reaching the nominal accelerator performance. In this challenging context, the beam halo becomes a potential source of performance limitations and its dynamics needs to be understood in detail to assess whether it could b…
Electron cloud interaction with high energy positive beam are believed responsible for various undesirable effects such as vacuum degradation, collective beam instability and even beam loss in high power proton circular accelerator. An important uncertainty in predicting electron cloud instability lies in the detail processes on the generation and accumulation of the electron cloud. The simulation on the build-up of electron cloud is necessary to further studies on beam instability caused by electron cloud. China Spallation Neutron Source (CSNS) is the largest scientific project in building, w…
The efficiency of the beam extraction and collimation systems in circular accelerators with the use of the channeling effect in a bent crystal is determined. The dependences of the extraction efficiency on the geometrical parameters of the crystal (its length, thickness, and bending angle), the azimuthal location of the system components, and the offset of the septum or scraper are presented. The influence of crystal imperfections (amorphous layers, misorientation, and torsion) on the efficiency of the systems is considered, and their tolerances are proposed. It is shown that an extraction eff…
This paper is a summary report of the ICFA Beam Dynamics Workshop 'Accelerators for a Higgs Factory: Linear vs. Circular' (HF2012). It discusses four types of accelerators as possible candidates for a Higgs factory: linear e+e- colliders, circular e+e- colliders, muon collider and photon colliders. The comparison includes: physics reach, performance (energy and luminosity), upgrade potential, technology maturity and readiness, and technical challenges requiring further R&D.
We give an overview of our current/future analytical and numerical work on the spin polarization in high-energy electron storage rings. Our goal is to study the possibility of polarization for the CEPC and FCC-ee. Our work is based on the so-called Bloch equation for the polarization density introduced by Derbenev and Kondratenko in 1975. We also give an outline of the standard approach, the latter being based on the Derbenev-Kondratenko formulas.
We consider acceleration of protons in a cavity with such dimensions as length l = 10 m, width b = 20 m, height a = 1.01 m, located between two bending (180)degree magnets with isochronous magnetic field. The cavity is loaded with rows of drift plates (tubes), being excited by a wave of E110 type at the frequency fo = 148.5 MHz, excitation power P1 = 5.65 MW. Additionally, the cavity is fed with the power P2 = 8 MW, transmitted into a beam of protons with such parameters as the final energy 0.8 GeV, pulse beam current I = 10 mA, pulse width 25 microseconds, repetition rate 10 Hz. We discuss th…
Energy-frontier accelerators provide powerful tools performing high precision measurements confirming the fundamental of the physics and broadening new research horizons. Such machines are either driven by circular or linear accelerators. The circular machines, having the center-mass (CM) energy values reaching 200 GeV (for leptons) and above, experience beam energy loss and quality dilution, for example, due to synchrotron radiation, limiting the overall CM energy achievable and requiring a constant energy top-up to compensate the loss and the beam quality dilution. Linear colliders overcome …
Many advanced techniques have been developed, tested and implemented in the last decades in almost all circular accelerators across the world to measure the linear optics. However, the greater availability and accuracy of beam diagnostics and the ever better correction of linear magnetic lattice imperfections (beta beating at 1% level and coupling at 0.1%) are reaching what seems to be the intrinsic accuracy and precision of different measurement techniques. This paper aims to highlight and quantify, when possible, the limitations of one standard method, the harmonic analysis of turn-by-turn b…
The transverse instability of a bunch in a circular accelerator is elaborated in this paper. A new tree-modes model is proposed and developed to describe the most unstable modes of the bunch. This simple and flexible model includes chromaticity and space charge, and can be used with any bunch and wake forms. The dispersion equation for the bunch eigentunes is obtained in form of a third-order algebraic equation. The known head-tail and TMCI modes appear as the limiting cases which are distinctly bounded at zero chromaticity only. It is shown that the instability parameters depend only slightly…
Controlling non-linear effects in the transverse dynamics of charged particle beams in circular accelerators opens new possibilities for controlling some of the beam properties. Beam splitting by crossing a stable 1D non-linear resonance is part of the routine operation of the CERN Proton Synchrotron. The beam undergoes trapping and transport inside stable islands created in the horizontal plane to allow multi-turn extraction towards the Super Proton Synchrotron, where the beam is used for fixed-target experiments. This process acts only on the horizontal beam emittance, inducing a reduction o…
New crystal technique - array of bent strips and a fan-type reflector, based on thin straight plates - have been used for research of extraction and collimation a circulating beam in the U-70 accelerator at the energy 50 GeV and 1.3 GeV. It is shown, that new devices can effectively steer a beam in a wide energy range. For protons with energy 50 GeV efficiency of extraction and collimation about 90 % has been achieved which is record for this method. Reduction of particle losses in 2-3 times was observed also in accelerator at application of different crystals in comparison with the usual one-…
Crossing the transition energy is always a delicate process, representing a potential source of strong perturbations of the dynamics of charged particle beams in a hadron circular accelerator. Since the first generation of multi-GeV rings, intense studies have been devoted to understanding the possible harmful mechanisms involved in transition crossing and to devise mitigation measures. Nowadays, several circular particle accelerators are successfully operating across transition and this process is well mastered. In a completely different context, stable resonances of the traverse phase space …
We revise a previous version of this paper proposing a method to transfer emittances from the transverse planes to the longitudinal. It turned out the system showed non-Hamiltonian behavior because the longitudinal component of the transverse electric field at ends of the transverse resonator were not included in the model. Including those fields the 6D emittance is conserved. We review the mechanism behind the emittance conservation. It is still possible to produce an emittance transfer with the RF quadrupole field setting the tunes on synchro-betatron resonance for a short period of time the…
This paper introduces the protection of circular particle accelerators from accidental beam losses. Already the energy stored in the beams for accelerators such as the TEVATRON at Fermilab and Super Proton Synchrotron (SPS) at CERN could cause serious damage in case of uncontrolled beam loss. With the CERN Large Hadron Collider (LHC), the energy stored in particle beams has reached a value two orders of magnitude above previous accelerators and poses new threats with respect to hazards from the energy stored in the particle beams. A single accident damaging vital parts of the accelerator could…
What prevents us from building super-high intensity accelerators? The answer is case-specific, but it often points to one of the following phenomena: machine resonances, various tune shifts (and spreads), and instabilities. These three phenomena are interdependent in all present machines. In this paper we propose a path toward alleviating these phenomena by making accelerators nonlinear. This idea is not new: Orlov (1963) and McMillan (1967) have proposed initial ideas on nonlinear focusing systems for accelerators. However, practical implementations of such ideas proved elusive, until recentl…
Here we calculate the effects of astrophysical gravitational waves (GWs) on the travel times of proton bunch test masses in circular particle accelerators. We show that a high-precision proton bunch time-tagging detector could turn a circular particle accelerator facility into a GW observatory sensitive to millihertz (mHz) GWs. We comment on sources of noise and the technological feasibility of ultrafast single photon detectors by conducting a case study of the Large Hadron Collider (LHC) at CERN.
A diffusion model of the time evolution of loss rates caused by a step in collimator position is presented. It builds upon the model of Seidel (1994) and its assumptions: (1) constant diffusion rate within the range of the step and (2) linear halo tails. These hypotheses allow one to obtain analytical expressions for the solutions of the diffusion equation and for the corresponding loss rates vs. time. The present model addresses some of the limitiations of the previous model and expands it in the following ways: (a) losses before, during, and after the step are predicted; (b) different steady…
Determining a model for the time scaling of the dynamic aperture of a circular accelerator is a topic of strong interest and intense research efforts in accelerator physics. The motivation arises in the possibility of finding a method to reliably extrapolate the results of numerical simulations well beyond what is currently possible in terms of CPU time. In earlier work, a proposal for a model based on Nekhoroshev theorem and Kolmogorov--Arnold--Moser theory was made. This model has been studied in detail and proved successful in describing the evolution of the dynamic aperture in numerical si…
Beam lifetime in storage rings and colliders is affected by, among other effects, lattice nonlinearities. Their control are of great benefit to the dynamic aperture of an accelerator, whose enlargement leads in general to more efficient injection and longer lifetime. This article describes a procedure to evaluate and correct unwanted nonlinearities by using turn-by-turn beam position monitor data, which is an evolution of previous works on the resonance driving terms (RDTs). Effective sextupole magnetic errors and tilts at the ESRF electron storage ring are evaluated and corrected (when possib…
We discuss the goals, the designs, the state of technical readiness, and the critical R&D needs of the accelerators that are currently under discussion as Higgs and electroweak factories. We also address the respective staging options enabling future energy-frontier colliders. The accelerators covered are based on many different techniques and approaches. They include several circular colliders, various linear colliders, colliders based on energy recovery linacs (ERLs), ERL-ring combinations, as well as gamma-gamma colliders. The linear colliders proposed consist of options for the Internation…
A brief historical review is presented of progressing understanding of transverse coherent instabilities of charged particles beams in circular machines when both Coulomb and wake fields are important. The paper relates to a talk given at ICFA Workshop on Mitigation of Coherent Beam Instabilities in Particle Accelerators, 23-27 September 2019 in Zermatt, Switzerland.
The equations of classical spin-orbit motion can be extended to a Hamiltonian system in 9-dimensional phase space by introducing a coupled spin-orbit Poisson bracket and a Hamiltonian function. After this extension and by establishing connections between initial and extended systems it becomes possible to apply the methods of the theory of Hamiltonian systems to the study of polarized particle beam dynamics in circular accelerators and storage rings. Some of those methods have been implemented in the computer code FORGET-ME-NOT.
Fermilab is constructing the Integrable Optics Test Accelerator (IOTA) as the centerpiece of the Accelerator R&D Program towards high-intensity circular machines. One of the factors limiting the beam intensity in present circular accelerators is collective instabilities, which can be suppressed by a spread of betatron frequencies (tunes) through the Landau damping mechanism or by an external damper, if the instability is slow enough. The spread is usually created by octupole magnets, which introduce the tune dependence on the amplitude and, in some cases, by a chromatic spread (tune dependence…
CERN has recently launched the Future Circular Collider (FCC) study to deal with all aspects of an ambitious post-LHC possible programme. The emphasis of the study is on a 100 TeV proton collider to be housed in a 80-100 km new ring in the Geneva region. An electron machine will also be considered as a possible intermediate first step (FCC-ee). The study benefits from earlier work done in the context of TLEP and has already published a parameter table, to serve as the basis for the work to be done. The study aims to publish a conceptual design report at around 2018. The recent discovery of a l…
As the only high-temperature superconducting (HTS) material available as an isotropic, twisted, multifilamentary round wire, Bi-2212 is very promising for expanding the high-field superconducting accelerator magnet toolbox beyond the round-wire, isotropic Nb-Ti and Nb3Sn conductors used by HEP so far. In this paper, we describe the important roles that Bi-2212 might play for future high energy circular colliders including both high energy proton and muon colliders. We describe its present technology status (conductor development, magnet design concepts, prototype magnet status) and then provid…
Particle accelerators have enabled forefront research in high energy physics and other research areas for more than half a century. Accelerators have directly contributed to 26 Nobel Prizes in Physics since 1939 as well as another 20 Nobel Prizes in Chemistry, Medicine and Physics with X-rays. Although high energy physics has been the main driving force for the development of the particle accelerators, accelerator facilities have continually been expanding applications in many areas of research and technology. For instance, active areas of accelerator applications include radiotherapy to treat…
Merlin++ is a C++ charged-particle tracking library developed for the simulation and analysis of complex beam dynamics within high energy particle accelerators. Accurate simulation and analysis of particle dynamics is an essential part of the design of new particle accelerators, and for the optimization of existing ones. Merlin++ is a feature-full library with focus on long-term tracking studies. A user may simulate distributions of protons or electrons in either single particle or sliced macro-particle bunches. The tracking code includes both straight and curvilinear coordinate systems allowi…
The measurement of the betatron tunes in a circular accelerator is of paramount importance due to their impact on beam dynamics. The resolution of the these measurements, when using turn by turn (TbT) data from beam position monitors (BPMs), is greatly limited by the available number of turns in the signal. Due to decoherence from finite chromaticity and/or amplitude detuning, the transverse betatron oscillations appear to be damped in the TbT signal. On the other hand, an adequate number of samples is needed, if precise and accurate tune measurements are desired. In this paper, a method is pr…
A new ion source will be prepared for the CYCLONE30 commercial cyclotron with a much advanced performance compared with the previous one. The newly designed ion source has a very large transparency without deteriorating the beam optics, which is designed to deliver an H- beam at 30 keV. The plasma generator of the ion source is of an axially cusped bucket type, and the whole inner wall, except the cathode filaments and plasma electrode side, functions as an anode. The accelerator assembly consists of three circular aperture electrodes made of copper. The simulation study was focused on finding…
Beam Delivery Simulation (BDSIM) is a program that simulates the passage of particles in a particle accelerator. It uses a suite of standard high energy physics codes (Geant4, ROOT and CLHEP) to create a computational model of a particle accelerator that combines accurate accelerator tracking routines with all of the physics processes of particles in Geant4. This unique combination permits radiation and detector background simulations in accelerators where both accurate tracking of all particles is required over long range or over many revolutions of a circular machine, as well as interaction …
It is proposed to place the arcs of an SLC-type facility inside the tunnel of a Future Circular Collider (FCC). Accelerated by a linear accelerator (linac), electron and positron beams would traverse the bending arcs in opposite directions and collide at centre-of-mass energies considerably exceeding those attainable at circular $e^{+}e^{-}$ colliders. The proposed SLC-type facility would have the same luminosity as a conventional two-linac $e^{+}e^{-}$ collider. Using an optical free-electron laser, the facility could be converted into a $γγ$ collider. A superconducting L-band linac at the pr…
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 both in simulation and experiment. The algorithm was also successfully used to ease the commissioning phase after the installation of new i…
The course gives a summary of longitudinal beam dynamics for both linear and circular accelerators. After discussing different types of acceleration methods and synchronism conditions, it focuses on the particle motion in synchrotrons.
The Future Circular Collider (FCC), currently in the design phase, will address many outstanding questions in particle physics. The technology to succeed in this 100 km circumference collider goes beyond present limits. Ultra-high vacuum conditions in the beam pipe is one essential requirement to provide a smooth operation. Different physics phenomena as photon-, ion- and electron- induced desorption and thermal outgassing of the chamber walls challenge this requirement. This paper presents an analytical model and a computer code PyVASCO that supports the design of a stable vacuum system by pr…
High energy particle colliders have been in the forefront of particle physics for more than three decades. At present the near term US, European and international strategies of the particle physics community are centered on full exploitation of the physics potential of the Large Hadron Collider (LHC) through its high-luminosity upgrade (HL-LHC). A number of next generation collider facilities have been proposed and are currently under consideration for the medium- and far-future of the accelerator-based high energy physics. In this paper we offer a uniform approach to evaluation of various acc…
Nonlinear optics is a promising idea potentially opening the path towards achieving super high beam intensities in circular accelerators. Creation of a tune spread reaching 50% of the betatron tune would provide strong Landau damping and make the beam immune to instabilities. Recent theoretical work has identified a possible way to implement stable nonlinear optics by incorporating nonlinear focusing elements into a specially designed machine lattice. In this report we propose the design of a test accelerator for a proof-of-principle experiment. We discuss possible studies at the machine, requ…
Particle physics experiments in the United States and Asia have greatly contributed to the understanding of elementary particles and their interactions. With the recent discovery of the Higgs boson at CERN, interest in the development of next-generation colliders has been rekindled. A linear electron-positron collider in Japan and a circular collider in China have been proposed for precision studies of the Higgs boson. In addition to the Higgs programme, new accelerator-based long-baseline neutrino mega-facilities are being built in the United States and Japan. Here, we outline the present sta…
Zgoubi is a code which can be used to model accelerators and beam lines, comprised of magnetic and electrostatic elements. It has been extensively developed since the mid-1980s to include circular accelerators and related beam physics. It has been made freely available by its author on a code development site, including a Users' Guide, a data treatment/graphic interfacing tool, and many examples. This startup guide give directions to install the required elements onto a Windows or Unix system to enable running of the Zgoubi code with examples of code written to model the EMMA accelerator based…
