Introduction to Particle Accelerators and their Limitations
Massimo Ferrario, Bernhard J. Holzer
备注：
26 pages, contribution to the CAS - CERN Accelerator School: High Gradient Wakefield Accelerators, 11-22 March 2019, Sesimbra, Portugal. arXiv admin note: substantial text overlap with arXiv:1705.09601
The paper gives a short overview of the principles of particle accelerators, their historical development and the typical performance limitations. After an introduction to the basic concepts, the main emphasis is to sketch the layout of modern storage rings and their limitations in energy and machine performance. Examples of existing machines - among them clearly the LHC at CERN - demonstrate the basic principles and the technical and physical limits that we face today in the design and operation of these particle colliders. Pushing for ever higher beam energies motivates the design of the future collider studies and beyond that, the development of more efficient acceleration techniques.
The paper gives an overview of the principles of particle accelerators and their historical development. After introducing the basic concepts, the main emphasis is on sketching the layout of modern storage rings and discussing their limitations in terms of energy and machine performance. Examples of existing machines, among them the Large Hadron Collider (LHC) at CERN, demonstrate the basic principles of and the technical and physical limits that we face in the design and operation of particle colliders. The push for ever higher beam energies motivates the design of future colliders as well as…
This lecture is a brief introduction to charged particle accelerators. The aim is to provide the reader with basic concepts and tools needed to describe the motion of charged particles under the action of guiding and focussing fields, with an emphasis on those aspects that are relevant to understanding and quantifying how accelerator vacuum systems affect accelerator performance. Even though the focus is on electron accelerators and, in particular, electron storage rings used as synchrotron light sources, most of the concepts described are of general application to a wider class of particle ac…
We describe some of the challenges of particle accelerator control, highlight recent advances in neural network techniques, discuss some promising avenues for incorporating neural networks into particle accelerator control systems, and describe a neural network-based control system that is being developed for resonance control of an RF electron gun at the Fermilab Accelerator Science and Technology (FAST) facility, including initial experimental results from a benchmark controller.
The effective and reliable operation of particle accelerator machines is strongly related to obtaining and keeping the required ultra-high vacuum level. This paper briefly presents some generic requirements to take in consideration for components that need to be installed in a particle accelerator like design constraints, materials choices, chemical cleaning process, outgassing rate, and their possible mitigation. Moreover, it will discuss vacuum acceptance tests put in place in the CERN accelerator complex for both, baked and unbaked system.
Particle accelerators are enabling tools for scientific exploration and discovery in various disciplines. Finding optimized operation points for these complex machines is a challenging task, however, due to the large number of parameters involved and the underlying non-linear dynamics. Here, we introduce two families of data-driven surrogate models, based on deep and invertible neural networks, that can replace the expensive physics computer models. These models are employed in multi-objective optimisations to find Pareto optimal operation points for two fundamentally different types of partic…
Nb3Sn superconducting radiofrequency (SRF) cavities have substantial potential for enabling new performance capabilities for particle accelerators for high energy physics (HEP), as well as for RF cavity-based detectors for dark matter, gravitational waves, and other quantum sensing applications. Outside of HEP, Nb3Sn SRF cavities can also benefit accelerators for nuclear physics, basic energy sciences, and the industry. In this contribution to Snowmass 2021, we overview the potential, status, and outlook of Nb3Sn SRF cavities.
Characterizations of transverse profiles for low-power beams in the accelerators of the proposed linear colliders (ILC and CLIC) using imaging techniques are being evaluated. Assessments of the issues and limitations for imaging relativistic beams with intercepting scintillator or optical transition radiation screens are presented based on low-energy tests at the Fermilab A0 photoinjector and are planned for the Advanced Superconducting Test Accelerator at Fermilab.
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…
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…
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.
Los Alamos is currently developing novel particle accelerator controls and diagnostics algorithms to enable higher quality beams with lower beam losses than is currently possible. The purpose of this workshop was to consider tuning and optimization challenges of a wide range of particle accelerators including linear proton accelerators such as the Los Alamos Neutron Science Center (LANSCE), rings such as the Advanced Photon Source (APS) synchrotron, free electron lasers (FEL) such as the Linac Coherent Light Source (LCLS) and LCLS-II, the European X-ray Free Electron Laser (EuXFEL), the Swiss …
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…
Orbital period in a ring accelerator and time of flight in a linear accelerator depend on the amplitude of betatron oscillations. The variation is negligible in ordinary particle accelerators with relatively small beam emittance. In an accelerator for large emittance beams like muons and unstable nuclei, however, this effect cannot be ignored. We measured orbital period in a linear non-scaling fixed field alternating gradient (FFAG) accelerator, which is a candidate for muon acceleration, and compared with the theoretical prediction. The good agreement between them gives important ground for t…
Current physics models used to interpret experimental measurements of particle beams require either simplifying assumptions to be made in order to ensure analytical tractability, or black box optimization methods to perform model based inference. This reduces the quantity and quality of information gained from experimental measurements, in a system where measurements have a limited availability. However differentiable physics modeling, combined with machine learning techniques, can overcome these analysis limitations, enabling accurate, detailed model creation of physical accelerators. Here we…
The US particle physics community planning exercise (a.k.a. Snowmass) is organized every 7 to 9 years to provide a forum for discussions among the entire particle physics community to develop a scientific vision for the future of particle physics in the U.S. and its international partners. The Snowmass 21 Accelerator Frontier activities include discussions on high-energy hadron and lepton colliders, high-intensity beams for neutrino research and for Physics Beyond Colliders, accelerator technologies, science, education and outreach as well as the progress of core accelerator technologies, incl…
In particle accelerator components, parasitic resonances must be reduced because they heat up the equipment and cause beam instabilities. In this paper, a method for designing and characterizing Higher Order Mode (HOM) couplers for reducing such resonances in a broad bandwidth is proposed. A case study is considered for a specific component, called QuattroTank, showing geometrical discontinuities and thus causing significant electro-magnetic resonances. Results of numerical simulation and experimental emulation prove the capability of the proposed method to reduce the peaks and the $Q-factor o…
The ever increasing demands placed upon machine performance have resulted in the need for more comprehensive particle accelerator modeling. Computer simulations are key to the success of particle accelerators. Many aspects of particle accelerators rely on computer modeling at some point, sometimes requiring complex simulation tools and massively parallel supercomputing. Examples include the modeling of beams at extreme intensities and densities (toward the quantum degeneracy limit), and with ultra-fine control (down to the level of individual particles). In the future, adaptively tuned models …
Machine learning (ML) is a subfield of artificial intelligence. The term applies broadly to a collection of computational algorithms and techniques that train systems from raw data rather than a priori models. ML techniques are now technologically mature enough to be applied to particle accelerators, and we expect that ML will become an increasingly valuable tool to meet new demands for beam energy, brightness, and stability. The intent of this white paper is to provide a high-level introduction to problems in accelerator science and operation where incorporating ML-based approaches may provid…
Particle accelerators technology is one of the generic technologies which is locomotive of the development in almost all fields of science and technology. According to the U.S. Department of Energy: "Accelerators underpin every activity of the Office of Science and, increasingly, of the entire scientific enterprise. From biology to medicine, from materials to metallurgy, from elementary particles to the cosmos, accelerators provide the microscopic information that forms the basis for scientific understanding and applications. The combination of ground and satellite based observatories and part…
Accurate spin tracking is a valuable tool for understanding spin dynamics in particle accelerators and can help improve the performance of an accelerator. In this paper, we present a detailed discussion of the integrators in the spin tracking code gpuSpinTrack. We have implemented orbital integrators based on drift-kick, bend-kick, and matrix-kick splits. On top of the orbital integrators, we have implemented various integrators for the spin motion. These integrators use quaternions and Romberg quadratures to accelerate both the computation and the convergence of spin rotations. We evaluate th…
An electron lens is planned for the Fermilab Integrable Optics Test Accelerator as a nonlinear element for integrable dynamics, as an electron cooler, and as an electron trap to study space-charge compensation in rings. We present the main design principles and constraints for nonlinear integrable optics. A magnetic configuration of the solenoids and of the toroidal section is laid out. Single-particle tracking is used to optimize the electron path. Electron beam dynamics at high intensity is calculated with a particle-in-cell code to estimate current limits, profile distortions, and the effec…
In physics research particle accelerators are highly valued, and extraordinarily expensive, technical instruments. The high cost of particle accelerators results from the immense lengths required to accelerate particles to high energies, using radio frequency cavities. A current promising field of research, laser-driven particle acceleration has the potential to reduce the size, cost, and energy consumption of particle accelerators by orders of magnitude. To understand and control particle acceleration in plasmas using ultra-small spatial configurations, researchers have been developing comput…
This introductory lecture outlines the impressive progress of radio frequency technology, from the first table-top equipment to the present gigantic installations. The outcome of 83 years of evolution is subsequently submitted to an anatomical analysis, which allows identifying the main components of a modern RF system and their interrelations.
Particle accelerator projects share many characteristics with industrial projects. However, experience has shown that best practice of industrial project management is not always well suited to particle accelerator projects. Major differences include the number and complexity of technologies involved, the importance of collaborative work, development phases that can last more than a decade, and the importance of telerobotics and remote handling to address future preventive and corrective maintenance requirements due to induced radioactivity, to cite just a few. The openSE framework is a system…
Particle accelerators are invaluable discovery engines in the chemical, biological and physical sciences. Characterization of the accelerated beam response to accelerator input parameters is of-ten the first step when conducting accelerator-based experiments. Currently used techniques for characterization, such as grid-like parameter sampling scans, become impractical when extended to higher dimensional input spaces, when complicated measurement constraints are present, or prior information is known about the beam response is scarce. In this work, we describe an adaptation of the popular Bayes…
This note aims to provide a complete and comprehensible derivation of the contributions to amplitude detuning in first order from multipoles up to dodecapolar order. In addition, the principle of feed-down is explored and example terms are given. The influence of an AC-Dipole is also included in the amplitude detuning. The derivation starts from very basic principles and maths useful for the derivation, such as Taylor and Binomial expansion is given at the beginning of the note.
Experimental Demonstration of a Two-Dimensional Nonlinear Integrable System in a Particle Accelerator
Fermi National Accelerator Laboratory（费米国家加速器实验室）；Consortium for Advanced Science and Technology (CASE), University of Chicago（芝加哥大学先进科学技术联盟）；Michigan State University（密歇根州立大学）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Northern Illinois University（北伊利诺伊大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
At present, a variety of image-based diagnostics are used in particle accelerator systems. Often times, these are viewed by a human operator who then makes appropriate adjustments to the machine. Given recent advances in using convolutional neural networks (CNNs) for image processing, it should be possible to use image diagnostics directly in control routines (NN-based or otherwise). This is especially appealing for non-intercepting diagnostics that could run continuously during beam operation. Here, we show results of a first step toward implementing such a controller: our trained CNN can pre…
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…
The McMillan system is a novel method to increase the tune spread of a beam without decreasing its dynamic aperture due to the systems integrability. While the ideal system is based on an infinitely thin kick, the physical design requires a thick electron lens, including a solenoid. Particle transport through the lens is difficult to simulate due to the nature of the force on the circulating beam. This paper demonstrates accurate simulation of a thick McMillan lens in a solenoid using symplectic integrators derived from Yoshidas method.
Fundamental questions on the nature of matter and energy have found answers thanks to the use of particle accelerators. Societal applications, such as cancer treatment or cancer imaging, illustrate the impact of accelerators in our current life. Today, accelerators use metallic cavities that sustain electricfields with values limited to about 100 MV/m. Because of their ability to support extreme accelerating gradients, the plasma medium has recently been proposed for future cavity-like accelerating structures. This contribution highlights the tremendous evolution of plasma accelerators driven …
The complexity and cost of building and running high-power electrical systems make the use of simulations unavoidable. The simulations available today provide great understanding about how systems really operate. This paper helps the reader to gain an insight into simulation in the field of power converters for particle accelerators. Starting with the definition and basic principles of simulation, two simulation types, as well as their leading tools, are presented: analog and numerical simulations. Some practical applications of each simulation type are also considered. The final conclusion th…
We derive a power series representation of an arbitrary electromagnetic field near some axis through the coaxial field components on the axis. The obtained equations are compared with Fourier-Bessel series approach and verified by several examples. It is shown that for each azimuthal mode we need only two real functions on the axis in order to describe the field in a source free region near to it. The representation of dipole mode in a superconducting radio-frequency gun is analyzed.
Beam-driven collinear wakefield accelerators (CWAs) that operate by using slow-wave structures or plasmas hold great promise toward reducing the size of contemporary accelerators. Sustainable acceleration of charged particles to high energies in the CWA relies on using field-generating relativistic electron bunches with a highly asymmetric peak current profile and a large energy chirp. A new approach to obtaining such bunches has been proposed and illustrated with the accelerator design supported by particle tracking simulations. It has been shown that the required particle distribution in the…
Using a cyclotron based model problem, we demonstrate for the first time the applicability and usefulness of a uncertainty quantification (UQ) approach in order to construct surrogate models for quantities such as emittance, energy spread but also the halo parameter, and construct a global sensitivity analysis together with error propagation and $L_{2}$ error analysis. The model problem is selected in a way that it represents a template for general high intensity particle accelerator modelling tasks. The presented physics problem has to be seen as hypothetical, with the aim to demonstrate the …
Recently it was proposed to apply a bent single crystal with decreasing curvature instead of uniform bending for improvement of extraction and collimation of a circulating beam in particle accelerators. In the given paper created crystal devices with a variable curvature, realizing this idea are described. Results of measurement of curvature along a crystal plate are informed. It is shown, that with the help of the developed devices it is possible to carry out also high energy beam focusing. The mathematical description of this process is proposed.
Particle accelerators use a great variety of power converters for energizing their sub-systems; while the total number of power converters usually depends on the size of the accelerator or combination of accelerators (including the experimental setup), the characteristics of power converters depend on their loads and on the particle physics requirements: this paper aims to provide an overview of the magnet power converters in use in several facilities worldwide.
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 …
We report on systematic and high-precision measurements of dephasing, an effect that fundamentally limits the performance of laser wakefield accelerators. Utilizing shock-front injection, a technique providing stable, tunable and high-quality electron bunches, acceleration and deceleration of few-MeV quasi-monoenergetic beams were measured with sub-5-fs and 8-fs laser pulses. Typical density dependent electron energy evolution with 65-300 micrometers dephasing length and 6-20 MeV peak energy was observed and is well described with a simple model.
The use of transverse electric (TE) waves has proved to be a powerful, noninvasive method for estimating the densities of electron clouds formed in particle accelerators. Results from the plasma simulation program VORPAL have been a useful guide for experimental studies related to this method, which have been performed at various accelerator facilities. This paper provides results of the simulation and modeling work done in conjunction with experimental efforts carried out at CesrTA. The discussion starts from the phase shift induced by electron clouds in the transmission of the wave, followed…
The goal of this manuscript is to give an introduction into the design of the magnet lattice and as a consequence into the transverse dynamics of the particles in a synchrotron or storage ring. Starting from the basic principles of how to design the geometry of the ring we will briefly review the transverse motion of the particles and apply this knowledge to study the layout and optimization of the principal elements, namely the lattice cells. The detailed arrangement of the accelerator magnets within the cells is explained and will be used to calculate well defined and predictable beam parame…
During the CERN Accelerator School 'Superconductivity for accelerators', the students were divided into 18 groups, and 6 different exercises (case studies), involving the design and analysis of superconducting magnets and RF cavities, were assigned. The problems covered a broad spectrum of topics, from properties of superconducting materials to operation conditions and general dimensions of components. The work carried out by the students turned out to be an extremely useful opportunity to review the material explained during the lectures, to become familiar with the orders of magnitude of the…
The Snowmass 2021 Accelerator Frontier topical group \# 6 on Advanced Accelerator Concepts, covers new R\&D concepts for particle acceleration, generation, and focusing. Based on community input, this report describes how leveraging these concepts to efficiently harness the interaction of charged particles with extremely high electromagnetic fields at very high frequencies can provide the keys to reaching ultra high acceleration gradients (GeV/m and beyond). These methods have potential to reduce the dimensions, C0$_2$ footprint, and costs of future high energy physics machines, with added pot…
Ideas of use the particle channeling in bent crystals for steer the beams have been checked up and advanced in many experiments. However, until now, this method of beam formation has limitations in application, since the channeling process involves beam particles with low angular divergence, limited by the angle of Lindhard. Here we test at the U-70 accelerator two crystal devices, the focusing crystal and multistrip crystal, which expand the boundaries of application of bent crystals at accelerators.
Virtual Diagnostic (VD) is a computational tool based on deep learning that can be used to predict a diagnostic output. VDs are especially useful in systems where measuring the output is invasive, limited, costly or runs the risk of altering the output. Given a prediction, it is necessary to relay how reliable that prediction is, i.e. quantify the uncertainty of the prediction. In this paper, we use ensemble methods and quantile regression neural networks to explore different ways of creating and analyzing prediction's uncertainty on experimental data from the Linac Coherent Light Source at SL…
Bayesian optimization has been shown to be a powerful tool for solving black box problems during online accelerator optimization. The major advantage of Bayesian based optimization techniques is the ability to include prior information about the problem to speed up optimization, even if that information is not perfectly correlated with experimental measurements. In parallel, neural network surrogate system models of accelerator facilities are increasingly being made available, but at present they are not widely used in online optimization. In this work, we demonstrate the use of an approximate…
We briefly give some of the characteristics of the beam-driven, plasma-based particle accelerator known as the plasma wakefield accelerator (PWFA). We also mention some of the major results that have been obtained since the birth of the concept. We focus on high-energy particle beams where possible.
The notions of acceleration gradient and deflection gradient are generalized to phasor quantities (complex-valued functions) in the context of dielectric laser acceleration (DLA). It is shown that the electromagnetic forces imparted on a near-resonant particle traversing a unit cell of a grating-type DLA can be conveniently described by generalized acceleration and deflection gradients. A~simple formulation of the Panofsky-Wenzel theorem in terms of the generalized gradients is given. It is shown that all particle transfer properties of a DLA unit cell can be derived from a single, complex-val…
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…
