Opening

• Frank Tecker (CERN)

Electromagnetic Theory

• Christine Vollinger (CERN)

The purpose of this course is to provide an introduction to Electromagnetic Theory. The foundations of electrodynamics starting from the nature of electrical force up to the level of Maxwell equations solutions are presented. It starts with the introduction of the concept of a field, which plays a very important role in the understanding of electricity and magnetism. In addition, moving electric charge is discussed as a topic of special importance in accelerator physics.

Kinematics of Particle Beams - Special Relativity

• Frank Tecker (CERN)

This is an introductory lecture on special relativity which doesn’t require much mathematical background. The theory of special relativity, originally proposed by Albert Einstein in his famous 1905 paper, has had profound consequences on our view of physics, space, and time. The goal of this lecture is to introduce the basic concepts of special relativity without overloading it with formulas. The lecture addresses Galilean and Lorentz transformations, emphasizing the conceptual incompatibility of classical kinematics and electrodynamics. The lecture also briefly introduces some famous phenomena behind special relativity including length contraction, time dilation, relativistic kinematics, practical application of the theory and more.

History of particle accelerators

• Maurizio Vretenar

This lecture traces the history of particle accelerators from the pioneers in the 1930s to the modern world of international mega-projects. Key developments are given in scientific and historical context, and qualitative descriptions are given of accelerator breakthroughs that have allowed orders of magnitude improvements in the course of a few decades.

Local Introduction

• Christos Leonidopoulos (The University of Edinburgh (GB))

Transverse Linear Beam Dynamics I

• Wolfgang Hillert

The subject of this introductory course is transverse dynamics of charged par-ticle beams in linear approximation. Starting with a discussion of the most important types of magnets and defining their multipole strengths, the linearised equations of motion of charged particles in static magnetic fields are derived using an orthogonal reference frame following the design orbit. Analytical solutions are determined for linear elements of a typical beam transfer line(drift, dipole and quadrupole magnets), and stepwise combined by introducing the matrix formalism in which each element’s contribution is represented by a single transfer matrix. Applying this formalism allows calculating single particle’s trajectories in linear approximation. After introducing the beam emittance as the area occupied by a particle beam in phase space, a linear treatment of transverse beam dynamics based on appropriately defined opticalfunctions is introduced. Formalism is applied to the concepts of both weak and strong focus, in particular, in discussing the properties of the widely used FODO cell. Specific characteristics of transverse beam dynamics in periodic systems like circular accelerators are studied in detail, emphasising the effects of linear field errors on-orbit stability and introducing the phenomena of optical resonances. Finally, the dynamics of off-momentum particles is presented, introducing dispersion functions and explaining effects like chromaticity.

Accelerator Applications

• Maurizio Vretenar

Of the 50,000+ particle accelerators in the world, the vast majority are not used for particle physics, but instead for real-world applications. From radiotherapy for cancer treatment to ion implantation for silicon devices, through to the hardening of tarmac roads with electron beams: the uses of particle beams are constantly growing in number. This lecture aims to give a broad overview of the many uses of particle accelerators, covering technologies ranging in size from around ten-centimetre long industrial electron linacs through to synchrotron light sources built as national scale facilities. The lecture also includes challenges and future perspectives that are unique to the use of accelerators for wider societal applications.

1S1M

Normal conducting Magnets

• Gijs De Rijk

Warm magnets are magnets that function in normal ambient temperature conditions. These types mostly use a soft steel yoke for field amplification and either copper or aluminium coils or permanent magnets to generate the field. Magnets powered with such normal-conducting coils are often called classical, iron-dominated or resistive magnets. These magnets have been the workhorse for most linear and circular accelerators and beam transfer lines for decades.

Transverse Linear Beam Dynamics II

• Wolfgang Hillert

The subject of this introductory course is transverse dynamics of charged par-ticle beams in linear approximation. Starting with a discussion of the most important types of magnets and defining their multipole strengths, the linearised equations of motion of charged particles in static magnetic fields are derived using an orthogonal reference frame following the design orbit. Analytical solutions are determined for linear elements of a typical beam transfer line(drift, dipole and quadrupole magnets), and stepwise combined by introducing the matrix formalism in which each element’s contribution is represented by a single transfer matrix. Applying this formalism allows calculating single particle’s trajectories in linear approximation. After introducing the beam emittance as the area occupied by a particle beam in phase space, a linear treatment of transverse beam dynamics based on appropriately defined opticalfunctions is introduced. Formalism is applied to the concepts of both weak and strong focus, in particular, in discussing the properties of the widely used FODO cell. Specific characteristics of transverse beam dynamics in periodic systems like circular accelerators are studied in detail, emphasising the effects of linear field errors on-orbit stability and introducing the phenomena of optical resonances. Finally, the dynamics of off-momentum particles is presented, introducing dispersion functions and explaining effects like chromaticity.

RF systems I

• Christine Vollinger (CERN)

Radio-frequency (RF) systems deliver the power to change the energy of a charged particle beam, and they are integral parts of linear and circular accelerators. A longitudinal electrical field in the direction of the beam is generated in a resonant structure, the RF cavity. As it directly interacts with the bunches of charged particles, the cavity can be considered as a coupler to transport energy from an RF power power amplifier to the beam. The power amplifier itself is driven by a low-level RF system assuring that frequency and phase are suitable for acceleration, and feedback loops improve the longitudinal beam stability. The spectrum of RF systems in particle accelerators in terms of frequency range and RF voltage is wide. Special emphasis is given to the constraints and requirements defined by the beam, which guides the appropriate choices for the RF systems.

Superconducting Magnets

• Gijs De Rijk

Superconductivity allows to construct and operate magnets at field values beyond 2 Tesla, the practical limitation of normal-conducting magnets exploiting ferro-magnetism. The field of superconducting magnets is dominated by the field generated in the coil. The stored energy and the electromagnetic forces generated by the coil are the main challenges to be overcome in the design of these magnets.

Beam Diagnostics I

• Peter Forck

Accurate determination of beam parameters is fundamental to the operation, optimization, and advancement of any accelerator facility. This lecture discusses the operating principles of commonly used beam diagnostics for both electron and proton beams. The first part focuses on beam instrumentation such as Current Transformers (CTs) and Faraday Cups (FCs) for measuring beam current, as well as Beam Position Monitors (BPMs) for monitoring bunched beams. BPMs are used for single-bunch position detection and precise closed orbit determination. Furthermore, position data from BPMs provide access to key synchrotron lattice parameters, including tune and chromaticity. These monitors operate by detecting the electromagnetic fields of the beam and are predominantly non-invasive, making them well-suited for continuous monitoring during machine operation.

Hands-ON Lattice calculations I

Hands-ON Lattice calculations II

Transverse Linear Beam Dynamics III

• Wolfgang Hillert

The subject of this introductory course is transverse dynamics of charged par-ticle beams in linear approximation. Starting with a discussion of the most im-portant types of magnets and defining their multipole strengths, the linearizedequations of motion of charged particles in static magnetic fields are derivedusing an orthogonal reference frame following the design orbit. Analyticalsolutions are determined for linear elements of a typical beam transfer line(drift, dipole and quadrupole magnets), and stepwise combined by introducingthe matrix formalism in which each element’s contribution is represented bya single transfer matrix. Application of this formalism allows to calculate sin-gle particle’s trajectories in linear approximation. After introducing the beamemittance as the area occupied by a particle beam in phase space, a lineartreatment of transverse beam dynamics based on appropriately defined opticalfunctions is introduced. The formalism is applied to the concepts of both weakand strong focusing, in particular discussing the properties of the widely-usedFODO cell. Specific characteristics of transverse beam dynamics in periodicsystems like circular accelerators are studied in detail, emphazising the effectsof linear field errors on orbit stability and introducing the phenomena of opti-cal resonances. Finally, the dynamics of off-momentum particles is presented,introducing dispersion functions and explaining effects like chromaticity.

RF systems II

• Christine Vollinger (CERN)

Radio-frequency (RF) systems deliver the power to change the energy of a charged particle beam, and they are integral parts of linear and circular accelerators. A longitudinal electrical field in the direction of the beam is generated in a resonant structure, the RF cavity. As it directly interacts with the bunches of charged particles, the cavity can be considered as a coupler to transport energy from an RF power power amplifier to the beam. The power amplifier itself is driven by a low-level RF system assuring that frequency and phase are suitable for acceleration, and feedback loops improve the longitudinal beam stability. The spectrum of RF systems in particle accelerators in terms of frequency range and RF voltage is wide. Special emphasis is given to the constraints and requirements defined by the beam, which guides the appropriate choices for the RF systems.

Transverse Linear Beam Dynamics IV

• Wolfgang Hillert

"The subject of this introductory course is transverse dynamics of charged par-ticle beams in linear approximation. Starting with a discussion of the most important types of magnets and defining their multipole strengths, the linearised equations of motion of charged particles in static magnetic fields are derived using an orthogonal reference frame following the design orbit. Analytical solutions are determined for linear elements of a typical beam transfer line(drift, dipole and quadrupole magnets), and stepwise combined by introducing the matrix formalism in which each element’s contribution is represented by a single transfer matrix. Applying this formalism allows calculating single particle’s trajectories in linear approximation. After introducing the beam emittance as the area occupied by a particle beam in phase space, a linear treatment of transverse beam dynamics based on appropriately defined optical functions is introduced. Formalism is applied to the concepts of both weak and strong focus, in particular, in discussing the properties of the widely used FODO cell. Specific characteristics of transverse beam dynamics in periodic systems like circular accelerators are studied in detail, emphasising the effects of linear field errors on-orbit stability and introducing the phenomena of optical resonances. Finally, the dynamics of off-momentum particles is presented, introducing dispersion functions and explaining effects like chromaticity.

Beam Diagnostics II

• Peter Forck

In the second lecture, the working principle of frequently used beam instruments for electron and proton beams concerning the transverse and longitudinal profile measurement is discussed. A broad range of instruments is available for transverse profile measurement, typically based on the interaction of beam particles with matter and the subsequent detection of secondary particles or photons. These include Secondary Emission Monitors (SEM grids), wire scanners, scintillation screens, Optical Transition Radiation (OTR) screens, and Ionization Profile Monitors (IPMs). Transverse profile data can be used to determine beam emittance in transfer lines through various reconstruction methods. Longitudinal bunch profiles are measured using several techniques—either by broadband detection of the bunch’s electric field, electro-optical sampling, or via synchrotron radiation emission. The application of Beam Loss Monitors (BLMs) is also briefly addressed, emphasizing their role in machine protection and diagnostics.

Linear Imperfections I

• Davide Gamba (CERN)

After briefly discussing sources of imperfections, we characterize them in terms of dipole, quadrupolar, and skew quadrupolar errors and move on to discuss how these imperfections are modeled in beam dynamics codes. We continue by reviewing the concepts of dispersion and chromaticity and explain how they are measured before turning to imperfections that are caused by multipoles, in particular, by feed-down. We conclude by addressing errors that are introduced by imperfect diagnostic equipment such as misaligned position monitors and mention means of how to identify this problem.

Hands-ON Lattice calculations III

Hands-ON Lattice calculations IV

Transverse Linear Beam Dynamics V

• Wolfgang Hillert

The subject of this introductory course is transverse dynamics of charged par-ticle beams in linear approximation. Starting with a discussion of the most important types of magnets and defining their multipole strengths, the linearised equations of motion of charged particles in static magnetic fields are derived using an orthogonal reference frame following the design orbit. Analytical solutions are determined for linear elements of a typical beam transfer line(drift, dipole and quadrupole magnets), and stepwise combined by introducing the matrix formalism in which each element’s contribution is represented by a single transfer matrix. Applying this formalism allows calculating single particle’s trajectories in linear approximation. After introducing the beam emittance as the area occupied by a particle beam in phase space, a linear treatment of transverse beam dynamics based on appropriately defined optical functions is introduced. Formalism is applied to the concepts of both weak and strong focus, in particular, in discussing the properties of the widely used FODO cell. Specific characteristics of transverse beam dynamics in periodic systems like circular accelerators are studied in detail, emphasising the effects of linear field errors on-orbit stability and introducing the phenomena of optical resonances. Finally, the dynamics of off-momentum particles is presented, introducing dispersion functions and explaining effects like chromaticity.

Vacuum

• Mike Gerd Seidel

This lecture introduces major physics and technology aspects of accelerator vacuum systems. Following an introduction, in the second section generic vacuum quantities such as pressure, gas density, the gas equation, pumping speed, conductance are introduced. Since accelerators typically have lengthy vacuum tubes, one-dimensional calculation is in many cases sufficient to compute a pressure profile for an accelerator, and methods for doing so are developed in the next section. In the fourth section accelerator specific aspects of vacuum are considered. This includes lifetime limiting effects for the particle beam, such as bremsstrahlung, elastic and inelastic scattering. Requirements for vacuum properties are derived. In the fifth section types of components and suitable materials for accelerator vacuum systems are described. Such components are for example flange systems, vacuum chambers for accelerators and the different types of pumps.

Transverse Linear Beam Dynamics VI

• Wolfgang Hillert

The subject of this introductory course is transverse dynamics of charged par-ticle beams in linear approximation. Starting with a discussion of the most important types of magnets and defining their multipole strengths, the linearised equations of motion of charged particles in static magnetic fields are derived using an orthogonal reference frame following the design orbit. Analytical solutions are determined for linear elements of a typical beam transfer line(drift, dipole and quadrupole magnets), and stepwise combined by introducing the matrix formalism in which each element’s contribution is represented by a single transfer matrix. Applying this formalism allows calculating single particle’s trajectories in linear approximation. After introducing the beam emittance as the area occupied by a particle beam in phase space, a linear treatment of transverse beam dynamics based on appropriately defined optical functions is introduced. Formalism is applied to the concepts of both weak and strong focus, in particular, in discussing the properties of the widely used FODO cell. Specific characteristics of transverse beam dynamics in periodic systems like circular accelerators are studied in detail, emphasising the effects of linear field errors on-orbit stability and introducing the phenomena of optical resonances. Finally, the dynamics of off-momentum particles is presented, introducing dispersion functions and explaining effects like chromaticity.

Linear Imperfections II

• Davide Gamba (CERN)

After briefly discussing sources of imperfections, we characterize them in terms of dipole, quadrupolar, and skew quadrupolar errors and move on to discuss how these imperfections are modeled in beam dynamics codes. We continue by reviewing the concepts of dispersion and chromaticity and explain how they are measured before turning to imperfections that are caused by multipoles, in particular, by feed-down. We conclude by addressing errors that are introduced by imperfect diagnostic equipment such as misaligned position monitors and mention means of how to identify this problem.

Linear Imperfections III

• Davide Gamba (CERN)

We introduce the BPM-corrector response coefficient R12 as the key quantity to characterise the effect of imperfections on the beam dynamics before addressing how the effect of multiple imperfections are combined. We then introduce local beam bumps as a means to adjust the beam position locally and move on to discuss orbit correction and the orbit response matrix. We place special attention to different methods, including singular value decomposition, to invert the response matrix. After covering quadrupolar errors and their detrimental effects, such as beta beating and filamentation, we learn how to measure beam sizes with quadrupole scans and with multiple wire scanners. We close this session with a discussion of how to adjust beam size parameters with so-called matching quadrupoles.

Linear Accelerators I

• David Alesini

Linear Accelerators (Linacs) are a systems that allow to accelerate charged particles through a linear trajectory by electromagnetic fields. This kind of accelerators find several applications in fundamental research and industry. The main devices used to accelerate the particle beam are described in the first part of the lecture with their main parameters. This includes both Standing (SW) and Traveling Wave (TW) radiofrequency cavities, for different type of accelerated particles (protons, ions and electrons) such as Drift Tube Linacs (DTL), multi cell cavities, Side Coupled Cell (SCC) and disk loaded structures. In the second part of the lecture, the fundamental principles of the longitudinal and transverse beam dynamics of accelerated particles will be highlighted. Finally, we briefly illustrate the radiofrequency quadrupole (RFQ) devices.

Sustainability for Accelerators

• Mike Gerd Seidel

The main focus of the lecture is given to the power conversion process in accelerators from grid to beam and its efficiency. Considered types of facilities include proton drivers, light sources, particle colliders, and example parameters are discussed. By maximizing the energy efficiency of technical systems and entire concepts the overall power consumption of research infrastructures can be minimized, thereby improving sustainability and reducing carbon footprint. Other aspects of sustainability discussed in the lecture include: the use of critical materials, the carbon footprint of civil construction and heat recovery.

Linear Accelerators II

• David Alesini

Linear Accelerators (Linacs) are a systems that allow to accelerate charged particles through a linear trajectory by electromagnetic fields. This kind of accelerators find several applications in fundamental research and industry. The main devices used to accelerate the particle beam are described in the first part of the lecture with their main parameters. This includes both Standing (SW) and Traveling Wave (TW) radiofrequency cavities, for different type of accelerated particles (protons, ions and electrons) such as Drift Tube Linacs (DTL), multi cell cavities, Side Coupled Cell (SCC) and disk loaded structures. In the second part of the lecture, the fundamental principles of the longitudinal and transverse beam dynamics of accelerated particles will be highlighted. Finally, we briefly illustrate the radiofrequency quadrupole (RFQ) devices.

Longitudinal BD in Circular Machines I

• Frank Tecker (CERN)

The lectures present an introduction to longitudinal beam dynamics for circular accelerators. It presents different circular accelerator types (betatron, cyclotron, synchrocyclotron, synchrotron), and focuses more on the longitudinal beam dynamics in synchrotrons. The operation principle of synchrotrons is described, synchrotron oscillations in energy and phase are discussed together with their representation in phase space. The lecture discusses the equations of motion, the stability conditions for the longitudinal oscillations, and introduces the Hamiltonian of longitudinal synchrotron motion. It also explains the bunch transfer from one accelerator to the next and shows the importance of a proper matching of the longitudinal parameters. Finally, the RF manipulations in the PS for the generation of the bunch structure of the LHC beam are explained.

Hands-ON Lattice calculations V

Hands-ON Lattice calculations VI

Cyclotrons

• Mike Gerd Seidel

Due to its simplicity the classical cyclotron has been used very early for applications in science, medicine and industry. Higher energies and intensities were achieved through the concepts of the sector focused isochronous cyclotron and the synchro-cyclotron. Besides those the fixed field alternating gradient accelerator (FFA) represents the most general concept among these types of fixed field accelerators, and the latter one is actively studied and developed for future applications.

Longitudinal BD in Circular Machines II

• Frank Tecker (CERN)

"The lectures present an introduction to longitudinal beam dynamics for circular accelerators. It presents different circular accelerator types (betatron, cyclotron, synchrocyclotron, synchrotron), and focuses more on the longitudinal beam dynamics in synchrotrons. The operation principle of synchrotrons is described, synchrotron oscillations in energy and phase are discussed together with their representation in phase space. The lecture discusses the equations of motion, the stability conditions for the longitudinal oscillations, and introduces the Hamiltonian of longitudinal synchrotron motion. It also explains the bunch transfer from one accelerator to the next and shows the importance of a proper matching of the longitudinal parameters. Finally, the RF manipulations in the PS for the generation of the bunch structure of the LHC beam are explained.

Electron Beam Dynamics I

• Lenny Rivkin (Paul Scherrer Institute (CH))

Beam dynamics of charged particles in the presence of synchrotron radiation is the subject of these lectures. The basic physics of synchrotron radiation emission and its influence on the beam dynamics in the storage rings shape the equilibrium properties of stored beams. The balance between the radiation damping and quantum fluctuations due to the emission of light determines the design of electron storage rings based colliders and synchrotron light sources. These effects also play significant role in the design of future high energy muon and hadron colliders.

Injection and Extraction

• Matthew Alexander Fraser (CERN)

This lecture gives an overview of the beam injection and extraction principles for accelerators. After a brief general introduction, it explains different methods of injecting the beam for hadron and lepton machines. It describes single- and multi-turn hadron injection, charge-exchange H- injection, then betatron and synchrotron injection for leptons. For extraction, it presents single- and multi-turn extraction, as well as resonant extraction methods. Finally, the requirements for linking several accelerators by a transfer line are presented.

Electron Beam Dynamics II

• Lenny Rivkin (Paul Scherrer Institute (CH))

Beam dynamics of charged particles in the presence of synchrotron radiation is the subject of these lectures. The basic physics of synchrotron radiation emission and its influence on the beam dynamics in the storage rings shape the equilibrium properties of stored beams. The balance between the radiation damping and quantum fluctuations due to the emission of light determines the design of electron storage rings based colliders and synchrotron light sources. These effects also play significant role in the design of future high energy muon and hadron colliders.

Sources

• Daniel Charles Faircloth

This presentation outlines the many ways that the initial beam can be made for particle accelerators. Brief introductions to plasma physics and beam formation are given. Thermionic and photo emission electron guns, with both DC and Radio Frequency (RF) acceleration are outlined. Positive ion sources for producing H+ ions and multiply charged heavy ions are covered. Hot cathode filament sources and cold cathode sources are explored. RF discharge sources (inductively coupled, microwave and ECR) are discussed, as are laser, vacuum arc, and electron beam sources. The physical principles of negative ion production are outlined and different types of negative ion source technologies are described. Polarised particle sources are mentioned briefly.

Collective Effects I

• Kevin Shing Bruce Li (CERN)

Collective effects in particle accelerators are one of the key constituents for determining the ultimate particle accelerator performance.Their role is becoming increasingly important as particle accelerators are being pushed ever closer towards the intensity and beam brightness frontiers. They are slightly peculiar in their nature as their impact and significance depend not only on external fields but also on the beam properties themselves.This results in a highly coupled and convoluted system. In these lectures we will give a brief overview over collective effects in particle accelerators in general. We will cover the topics in a highly conceptual and illustrative manner. The goal will be for the students to get an intuitive impression on the nature and the aftermath of collective effects.The lectures will cover different types of collective effects along with their manifestation in accelerators and briefly outline the limitations they impose along with a few means for potential mitigation techniques.

Introduction to Non-Linear longitudinal Beam Dynamics

• Heiko Damerau (CERN)

After discussing how to account for the periodicity in rings, we first generalise the response coefficient R12, and then the orbit response matrix to such systems. We move on to use the response matrix to correct the orbit and generalise the concept by introducing dispersion-free steering before turning to gradient errors and stop bands. Measuring and correcting the tune addresses one parameter of great importance for operating rings, whereas analysing the orbit response matrix with codes like LOCO measures many more, including the beta functions. We then digress on skew quadrupolar errors and betatron coupling and their detrimental effect. Before closing we describe how to correct the chromaticity and mention a number of non-standard imperfections, so-called bloopers.

Collective Effects II

• Kevin Shing Bruce Li (CERN)

Collective effects in particle accelerators are one of the key constituents for determining the ultimate particle accelerator performance.Their role is becoming increasingly important as particle accelerators are being pushed ever closer towards the intensity and beam brightness frontiers. They are slightly peculiar in their nature as their impact and significance depend not only on external fields but also on the beam properties themselves.This results in a highly coupled and convoluted system. In these lectures we will give a brief overview over collective effects in particle accelerators in general. We will cover the topics in a highly conceptual and illustrative manner. The goal will be for the students to get an intuitive impression on the nature and the aftermath of collective effects.The lectures will cover different types of collective effects along with their manifestation in accelerators and briefly outline the limitations they impose along with a few means for potential mitigation techniques.

Hands-ON calculations (longitudinal) - Intro

Hands-ON calculations (longitudinal) - I

Hands-ON calculations (longitudinal) - II

Collective Effects III

• Kevin Shing Bruce Li (CERN)

Collective effects in particle accelerators are one of the key constituents for determining the ultimate particle accelerator performance.Their role is becoming increasingly important as particle accelerators are being pushed ever closer towards the intensity and beam brightness frontiers. They are slightly peculiar in their nature as their impact and significance depend not only on external fields but also on the beam properties themselves.This results in a highly coupled and convoluted system. In these lectures we will give a brief overview over collective effects in particle accelerators in general. We will cover the topics in a highly conceptual and illustrative manner. The goal will be for the students to get an intuitive impression on the nature and the aftermath of collective effects.The lectures will cover different types of collective effects along with their manifestation in accelerators and briefly outline the limitations they impose along with a few means for potential mitigation techniques.

Secondary beams and targets

• Daniel Charles Faircloth

This presentation outlines the methods of creating secondary beams by driving a primary beam into a target. The tungsten targets used to produce neutron beams at the ISIS pulsed spallation neutron source are described along with the graphite target used to produce muon beams. Higher power neutron targets are mentioned: liquid mercury for SNS and rotating targets for ESS. Future plans for even higher power powder targets are outlined. The use of magnetic horns to capture secondary beams from targets are described and their use at FAIR to produce antiproton beams. The extensive radiation shielding and remote handling systems required in secondary beam facilities are discussed. ‘Isotope Separation On-Line (ISOL)’ and ‘In Flight Fragmentation’ techniques for producing beams of radioactive nuclei are described and their key components outlined. Positron production at KEK is discussed, and a future proposal for a Higgs Factory mentioned.

Collective Effects IV

• Kevin Shing Bruce Li (CERN)

Collective effects in particle accelerators are one of the key constituents for determining the ultimate particle accelerator performance.Their role is becoming increasingly important as particle accelerators are being pushed ever closer towards the intensity and beam brightness frontiers. They are slightly peculiar in their nature as their impact and significance depend not only on external fields but also on the beam properties themselves.This results in a highly coupled and convoluted system. In these lectures we will give a brief overview over collective effects in particle accelerators in general. We will cover the topics in a highly conceptual and illustrative manner. The goal will be for the students to get an intuitive impression on the nature and the aftermath of collective effects.The lectures will cover different types of collective effects along with their manifestation in accelerators and briefly outline the limitations they impose along with a few means for potential mitigation techniques.

Computational tools I

• Andrea Latina (CERN)

Numerical Methods and Computational Tools" aims to outline good practices in scientific computing and guide the novice through the multitude of tools available. This lectures aim to clarify important aspects of numerical computing to help avoid making bad but unfortunately common mistakes. We describe the most critical aspects associated with numerical computing with a finite precision floating-point representation of real numbers. Given the indispensable role of computers in the daily life of a scientist, numerical stability is essential knowledge for every modern scientist. In this first lecture, we suggest also reference readings and explain through examples the importance of well-designed and well-chosen numerical methods and algorithms. The second lecture provides pointers to established resources and describes the main tools available for scientific computing. We explain which tool or solution should be used for a specific purpose, dispelling common misconceptions. We also outline the most common tools for designing and optimising particle accelerators, whether they are rings or linacs. Also, we will unveil powerful shell commands that can speed up simulations, facilitate data processing, and increase your scientific throughput. We will exclusively refer to free and open-source software running on Linux or other Unix-like operating systems

Hands-ON calculations (longitudinal) - III

Hands-ON calculations (longitudinal) - IV

Hands-ON calculations (longitudinal) - V

Seminar - The Big Picture: from Particles to the Universe

• Neil Turok

Time and Frequency domain signals I

• Hermann Schmickler

Depending on the application people use time-domain or frequency domain signals in order to measure or describe processes. First we will look at the definition of these terms, produce some mathematical background and then apply the tools to measurements made in the accelerator domain. We will first look at signals produced by a single bunch passing once through a detector (transfer line, linac), then periodic single bunch passages (circular accelerator) and at the end multi-bunch passages in a circular accelerator. The bunches themselves are considered rigid.

Advanced accelerator concepts I

• Massimo Ferrario

Recent years have seen spectacular progress in the development of innovative acceleration methods that are not based on traditional RF accelerating structures. These novel developments are at the interface of laser, plasma and accelerator physics and may potentially lead to much more compact and cost effective accelerator facilities. While primarily focusing on the ability to accelerate charged particles with much larger gradients than traditional RF structures, these new techniques have yet to demonstrate comparable performances to RF structures in terms of both beam parameters and reproducibility. To guide the developments beyond the necessary basic R&D and concept validations, a common understanding and definition of required performance and beam parameters for an operational user facility is now needed. These innovative user facilities can include "table-top" light sources, medical accelerators, industrial accelerators or even high-energy colliders. This paper will review the most promising developments in new acceleration methods and it will present the status of on-going projects.

Time and Frequency domain signals II

• Hermann Schmickler

Depending on the application people use time-domain or frequency domain signals in order to measure or describe processes. First we will look at the definition of these terms, produce some mathematical background and then apply the tools to measurements made in the accelerator domain. We will first look at signals produced by a single bunch passing once through a detector (transfer line, linac), then periodic single bunch passages (circular accelerator) and at the end multi-bunch passages in a circular accelerator. The bunches themselves are considered rigid.

Advanced accelerator concepts II

• Massimo Ferrario

Recent years have seen spectacular progress in the development of innovative acceleration methods that are not based on traditional RF accelerating structures. These novel developments are at the interface of laser, plasma and accelerator physics and may potentially lead to much more compact and cost effective accelerator facilities. While primarily focusing on the ability to accelerate charged particles with much larger gradients than traditional RF structures, these new techniques have yet to demonstrate comparable performances to RF structures in terms of both beam parameters and reproducibility. To guide the developments beyond the necessary basic R&D and concept validations, a common understanding and definition of required performance and beam parameters for an operational user facility is now needed. These innovative user facilities can include "table-top" light sources, medical accelerators, industrial accelerators or even high-energy colliders. This paper will review the most promising developments in new acceleration methods and it will present the status of on-going projects.

Computational tools II

• Andrea Latina (CERN)

Numerical Methods and Computational Tools" aims to outline good practices in scientific computing and guide the novice through the multitude of tools available. This lectures aim to clarify important aspects of numerical computing to help avoid making bad but unfortunately common mistakes. We describe the most critical aspects associated with numerical computing with a finite precision floating-point representation of real numbers. Given the indispensable role of computers in the daily life of a scientist, numerical stability is essential knowledge for every modern scientist. In this first lecture, we suggest also reference readings and explain through examples the importance of well-designed and well-chosen numerical methods and algorithms. The second lecture provides pointers to established resources and describes the main tools available for scientific computing. We explain which tool or solution should be used for a specific purpose, dispelling common misconceptions. We also outline the most common tools for designing and optimising particle accelerators, whether they are rings or linacs. Also, we will unveil powerful shell commands that can speed up simulations, facilitate data processing, and increase your scientific throughput. We will exclusively refer to free and open-source software running on Linux or other Unix-like operating systems.

A first taste of Non-Linear Beam Dynamics I

• Hannes Bartosik (CERN)

Nonlinear dynamics can impact the performance of a particle accelerator in a number of different ways, depending on the type of the accelerator and the parameter regime in which it operates. Effects can range from minor changes in beam properties or behaviour, to serious limitations on beam stability and machine performance. In these notes, we provide a brief introduction to nonlinear dynamics in accelerators. After a review of some relevant results from linear dynamics, we outline some of the main ideas of nonlinear dynamics, framing the discussion in the context of two examples of different types of accelerator: a single-pass system (a bunch compressor) and a periodic system (a storage ring). We show how an understanding of the origins and nature of the nonlinear behaviour, together with the use of appropriate analysis tools, can prove useful in predicting the effects of nonlinear dynamics in different systems, and allow the design of appropriate corrections or mitigations.

Colliders and luminosity

• Hermann Schmickler

Modern particle physics relies on high energy particle accelerators to provide collisions of various types of elementary particles in order to deduce fundamental laws of physics or properties of individual particles. The only way to generate particle collisions at extremely high energies is to collide particles of counter-rotating beams...called "particle-colliders". This write-up gives a short briefing on the physics motivation of various particle colliders ( colliders, colliders, ...), a summary of the historical evolution and a mathematical treatment to describe collider performance.

A first taste of Non-Linear Beam Dynamics II

• Hannes Bartosik (CERN)

Nonlinear dynamics can impact the performance of a particle accelerator in a number of different ways, depending on the type of the accelerator and the parameter regime in which it operates. Effects can range from minor changes in beam properties or behaviour, to serious limitations on beam stability and machine performance. In these notes, we provide a brief introduction to nonlinear dynamics in accelerators. After a review of some relevant results from linear dynamics, we outline some of the main ideas of nonlinear dynamics, framing the discussion in the context of two examples of different types of accelerator: a single-pass system (a bunch compressor) and a periodic system (a storage ring). We show how an understanding of the origins and nature of the nonlinear behaviour, together with the use of appropriate analysis tools, can prove useful in predicting the effects of nonlinear dynamics in different systems, and allow the design of appropriate corrections or mitigations.

Particle motion in Hamiltonial Formalism I

• Yannis Papaphilippou (CERN)

The purpose of this lecture is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation and integration of equations of motion, in order to describe the particle trajectory evolution with respect to time. Starting with the relativistic Hamiltonian of particles in E/M fields and a series of canonical (or symplectic) transformations and approximations, the accelerator ring Hamiltonian is derived. Thereby, introductory concepts of beam dynamics such as invariants and transport matrices are revisited and extended towards generic concepts such as action-angle variables and symplectic maps. Thereby, the ground is prepared for the advanced methods and tools used for studying non-linear motion in particle accelerators.

Synchrotron light circular machines & FELs I

• Eduard Prat Costa

Synchrotron light sources and X-ray free-electron laser (FEL) facilities are unique tools providing extremely brilliant X-rays that allow the observation of matter with atomic spatial resolution. On the one hand, synchrotron light sources consist of electron circular accelerators and produce synchrotron radiation in bending magnets and undulators. On the other hand, X-ray FEL facilities are based on electron linear accelerators and generate more coherent and shorter pulses suitable for time-resolved experiments. In these lectures we will qualitatively describe synchrotron and X-ray FEL facilities. We will start explaining some fundamental concepts related to synchrotron and FEL radiation. We will then describe the two kinds of machines, including the history and current facilities, the typical layout, and some basic concepts about the electron beam dynamics and properties.

Synchrotron light circular machines & FELs II

• Eduard Prat Costa

Synchrotron light sources and X-ray free-electron laser (FEL) facilities are unique tools providing extremely brilliant X-rays that allow the observation of matter with atomic spatial resolution. On the one hand, synchrotron light sources consist of electron circular accelerators and produce synchrotron radiation in bending magnets and undulators. On the other hand, X-ray FEL facilities are based on electron linear accelerators and generate more coherent and shorter pulses suitable for time-resolved experiments. In these lectures we will qualitatively describe synchrotron and X-ray FEL facilities. We will start explaining some fundamental concepts related to synchrotron and FEL radiation. We will then describe the two kinds of machines, including the history and current facilities, the typical layout, and some basic concepts about the electron beam dynamics and properties.

Particle motion in Hamiltonial Formalism II

• Yannis Papaphilippou (CERN)

The purpose of this lecture is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation and integration of equations of motion, in order to describe the particle trajectory evolution with respect to time. Starting with the relativistic Hamiltonian of particles in E/M fields and a series of canonical (or symplectic) transformations and approximations, the accelerator ring Hamiltonian is derived. Thereby, introductory concepts of beam dynamics such as invariants and transport matrices are revisited and extended towards generic concepts such as action-angle variables and symplectic maps. Thereby, the ground is prepared for the advanced methods and tools used for studying non-linear motion in particle accelerators.

Designing a synchrotron - a real life example

• Yannis Papaphilippou (CERN)

This lecture's goal is to review several aspects of beam dynamics applied to the design and operation of an existing synchrotron. Our choice is the CERN Super Proton Synchrotron (SPS) whose enormous versatility has been demonstrated since its design and operation. It has served as high energy synchrotron serving fixed target experiments (West Area, North Area, CNGS, HIRADMAT), collider of protons and anti-protons (allowing the W and Z bosons discovery in 1983), accelerator of electrons and positrons for injection into the Large Electron-Positron (LEP) Collider, accelerator of protons and ions for the Large Hadron Collider (LHC), or even for extracting protons towards a plasma wakefield acceleration experiment (AWAKE). In this respect, the choice of the SPS basic parameters are reviewed such as energy, bending field and circumference, its optics design for arcs and insertions, the manipulation of transition energy, collective effects, namely instabilities, space-charge and e-cloud but also electron/positron beam dynamics (equilibrium beam properties, energy loss per turn, damping times).

Putting it all together

• Hermann Schmickler

At the end of the course a so called "minimum take-away" will be compiled from all previous courses. This will help students to identify the essential messages, which make the foundation of all accelerator physics and technologies, from all other information, which can be considered as "general accelerator culture". The journey will start with a summary of the most used mathematical concepts and end with the most important accelerator technologies.

Closing

• Frank Tecker (CERN)