Opening / Local presentation

• Kalina Dimitrova (University of Sofia - St. Kliment Ohridski (BG))
• Frank Tecker (CERN)

Introduction and demands for high intensity

• Yannis Papaphilippou (CERN)

Frontiers for linear machines

• Mamad Eshraqi (ESS - European Spallation Source ERIC (SE))

Linear accelerators constitute the backbone of high-intensity beam facilities and continue to expand their reach in science, medicine, and energy. This lecture presents the main technological and scientific frontiers of modern linacs, addressing the challenges of achieving multi-megawatt beam power with high efficiency and reliability. The key components of high-power proton and ion linacs are reviewed, including ion sources, normal- and superconducting accelerating structures, RF power generation, cryogenics, and beam dynamics control. Examples are drawn from operational and emerging facilities such as SNS, ESS, SPIRAL2, FRIB, and accelerator-driven systems for energy applications (MYRRHA, CIADS, DONES). The transition to superconducting continuous-wave operation, strategies for beam loss mitigation, redundancy, and remote maintainability are discussed as enablers of long-term availability.

Frontiers for circular machines

• Chris Rogers (ISIS)

Many applications of hadron accelerators require high intensities which often employment acceleration or storage in rings. Circular machines are particularly sensitive to effects that build up over many turns. This lecture reviews and summarises issues in high intensity and introduces technology approaches that may mitigate some of the effects.

Wakefields and Impedances I

• Andrea Mostacci (Sapienza University of Rome (IT))

Wakefields and beam coupling impedances play a central role in determining the collective dynamics and stability of charged particle beams in accelerators. This lecture introduces the fundamental physical concepts underlying wakefield generation and their formal description in both the time and frequency domains.   After a general introduction to the physics of wakefields, the perturbative framework commonly adopted in accelerator physics is presented, together with its main assumptions and limitations. Particular emphasis is placed on the rigid beam approximation and the kick approximation, which allow a simplified yet powerful description of beam–environment interactions. Wake functions and wake potentials are defined and discussed, leading naturally to the introduction of longitudinal and transverse coupling impedances and their principal properties and formulae.   The case of single particle Green function as well as the bunch case are treated, giving the definition of the typically used quantities to describe such effects. Coupling impedance is introduced as Fourier Transform of the wake function, relevant to describe such interactions in ring accelerators.   The deep connection between wakefields and electromagnetic fields is highlighted through the Panofsky–Wenzel theorem, and the harmonic nature of wake functions and impedances is emphasized. The lecture establishes the formal definitions and tools required for advanced applications addressed in subsequent lectures.   Special attention is given to the frequency ranges relevant for hadron machines, where low-frequency impedance contributions are often dominant. The general concepts are illustrated with two of the most important and ubiquitous impedance sources in accelerators: the resistive wall and cavity higher-order modes, including trapped modes.   The goal of the lecture is to provide a solid conceptual and mathematical foundation for understanding beam–structure interaction and its impact on accelerator performance.

Wakefields and Impedances II

• Andrea Mostacci (Sapienza University of Rome (IT))

Building upon the theoretical foundations introduced in the previous lecture, this second lecture on Wakefields and Impedances focuses on applications, practical examples, and their impact on modern accelerator design and operation. The role of impedance studies in contemporary machines is discussed, highlighting how beam coupling impedance has become a central ingredient in performance optimization, intensity upgrades, and reliability of working accelerators.   Representative examples of impedance contributions are presented, illustrating how seemingly small and distributed sources can collectively determine machine limitations. The complementary roles of analytical, numerical, and experimental approaches are examined. Analytical models remain essential for understanding scaling laws and for estimating the cumulative effect of numerous small discontinuities. Numerical simulations enable accurate treatment of complex geometries and realistic structures, while experimental techniques provide validation and benchmarking of impedance models.   Wakefield effects in linear accelerators are discussed separately, emphasizing differences with respect to circular machines and the implications for beam quality and stability.   Beyond their potentially detrimental impact, wakefields can also be exploited constructively. The lecture briefly explores scenarios where wakefields are beneficial, including wakefield-based devices, and advanced acceleration concepts beyond plasma-based schemes.   The concept of a comprehensive machine impedance model is introduced as a practical tool for design and operation. Examples are drawn from the LHC impedance model, operational experience and mitigation strategies in existing machines, and perspectives for future colliders and light sources. The lecture concludes by connecting impedance control, higher-order mode damping strategies, and advanced accelerator concepts within a unified framework of beam–structure interaction.

One slide - one minute

Bench Measurements and Simulations of Beam Coupling Impedance

• Andrea Mostacci (Sapienza University of Rome (IT))

The optimisation of device coupling impedance is a key aspect in the design of accelerator components, directly impacting beam stability, high intensity limitations as well as the overall machine performance. This lecture presents a comprehensive approach to impedance characterisation and optimisation by means of numerical simulations and bench measurement techniques.   On the experimental side, the coaxial wire method is discussed as a versatile tool for impedance measurements of various device under test configurations, including resistive beam pipes, collimators, beam pipe cross-section transitions, and magnetic kickers. The coaxial wire method allows to excite in the device under test a field similar to the one generated by an ultra-relativistic point charge. It is a well-known technique and we discuss the basics as well as some recent relevant advances. In addition, resonant and non-resonant bead-pull techniques are presented for the characterisation of accelerating and deflecting RF structures.   From the numerical perspective, the direct simulation of bunch-induced wake potentials is introduced as a powerful method to derive wake functions and coupling impedance. The connection between the electromagnetic properties of a device and its modal structure (i.e. the field patterns supported by the geometry) is emphasised, highlighting their role in determining the impedance spectrum.   Particular attention is devoted to the estimation of measurement artefacts through dedicated simulations of the bench setup, enabling a consistent interpretation of experimental data. Finally, the potential of emerging multi-physics simulation tools is discussed, especially in view of increasingly complex devices where electromagnetic, thermal, and mechanical effects are strongly coupled.   The lecture aims to provide a coherent framework linking measurements, simulations, and physical interpretation for the effective optimisation of accelerator components.

Lattice design for high intensity rings

• Yannis Papaphilippou (CERN)

Space Charge Effects in Linacs

• Emanuele Laface (ESS)

High-intensity hadron linacs stand at the forefront of accelerator science, delivering the beam brilliance required by spallation sources, neutrino factories, and future colliders. Yet the same space-charge forces that enable high current and brightness can degrade beam quality, drive instabilities, and impose stringent intensity limits. This lecture offers a concise roadmap for understanding—and ultimately mitigating—these constraints. After a brief physical motivation, we develop the theory from first principles. Starting with Maxwell’s equations in the beam rest frame, we derive the self-consistent Poisson–Vlasov system and recover the classical four-dimensional Kapchinskij–Vladimirskij (KV) solution. Step by step, participants trace how the KV distribution leads to the envelope equations and to practical metrics such as tune depression. We then move beyond this ideal model to realistic beam distributions, examining both analytical treatments and numerical approaches, notably particle-in-cell (PIC) simulations. Numerical integration techniques will be explored further in a companion lecture—“Numerical Methods in High-Intensity Linacs”—which delves into solving the complex collective dynamics, such as space-charge forces, encountered in modern accelerators.

Sources and Low Energy Beam Transfer

• Daniel Charles Faircloth (ISIS)

Particle accelerators are fundamentally limited by the performance of the ion source and Low Energy Beam Transport (LEBT) system: if the initial beam is inadequate then, then the efficacy of the rest of the accelerator is irrelevant. The many ways to generate ions and shape them into beams are discussed, focusing on the limitations of each part of the process: from plasma generation to beam extraction, species separation, acceleration and beam transportation. Capacitively Coupled Plasma (CCP), Electromagnetic cavity plasma, Inductively Coupled Plasma (ICP), and the ion source technologies that employ them are discussed along with lifetime and intensity limitations. The Volume and Caesiated Surface methods are described for intense negative ion production. The practicalities of extraction and beam transportation are outlined for electrostatic and solenoid magnetic field LEBT systems. The importance of space charge compensation is emphasised for transporting high-current, low-energy hadron beams.

Neutron Sources

• Mamad Eshraqi (ESS - European Spallation Source ERIC (SE))

This lecture reviews the evolution of neutron sources from early fission reactors to present-day accelerator-based spallation facilities. The physical principles of neutron production, moderation, and detection are introduced, together with the technological developments that have led to the current generation of high-brightness sources. The characteristics and performance of major facilities—ILL, SINQ, SNS, J-PARC, CSNS, and the European Spallation Source (ESS)—are compared, illustrating progress in target design, moderation concepts, and accelerator capability. Particular emphasis is placed on the ESS, a 5 MW, 2 GeV superconducting proton linac coupled to a rotating tungsten target, designed to deliver the highest long-pulse neutron brightness worldwide. Applications ranging from condensed matter and life sciences to energy research, cultural heritage, and fundamental physics are discussed.

Neutrino Factories and Muon Colliders

• Chris Rogers (ISIS)

Accelerated muon beams have been proposed for collisions at the highest energy or for production of well-characterised neutrino beams. These applications require production and acceleration of high intensity muon sources. In this lecture I discuss the limitations of muon accelerators at high intensity.

High-Intensity linac beam-dynamics

• Alessandra Lombardi (CERN)

In this lecture we describe the components of a high intensity linac starting from the source to the high energy end. Then for each component we will see the mechanism that limit the intensity and the possible mitigations.

Numerical methods in high-intensity linacs

• Emanuele Laface (ESS)

Numerical methods were historically developed to tackle equations that resist analytical solutions—first in celestial mechanics, where the complexity of planetary orbits defied closed-form answers, and today in modern physics applications such as particle accelerators. In high-intensity linacs, many collective effects, foremost among them space charge, give rise to nonlinear dynamics that are analytically intractable and must be addressed through numerical integration. This lecture provides an overview of the key numerical techniques used to model beam dynamics in particle accelerators. We will review classical methods such as Runge–Kutta and Störmer–Verlet, examining their strengths and limitations in the context of multi-particle tracking and self-consistent field evolution. The focus will then shift to geometric integration methods, which are specifically designed to preserve fundamental physical invariants of Hamiltonian systems, such as phase-space volume and symplectic structure. Among these, we will highlight Lie operator splitting techniques and the Yoshida symplectic integrator, discussing their derivation, implementation, and practical advantages in accelerator simulations.

Linac Instabilities + mitigations

• Alessandra Lombardi (CERN)

In this lecture we describe the components of a high intensity linac starting from the source to the high energy end. Then for each component we will see the mechanism that limit the intensity and the possible mitigations.

Space Charge in Circular Machines

• Foteini Asvesta (CERN)

Space charge is one of the main limiting factors for low-energy and high-brightness machines. The course approaches space charge from the incoherent perspective to showcase how effects such as the space charge tune spread and the space charge driven resonances can appear in a circular machine. Furthermore, the concept of periodic resonance crossing and its impact on the beam characteristics is discussed. In addition, some of the existing techniques for mitigations are presented. Finally, different ways of simulating the space charge effect are introduced.

Free study time

Transverse HI ring beam-instabilities + mitigations I

• Xavier Buffat (CERN)

Several applications of circular hadron accelerators require intense beams, yet the interaction of the charged particles with their surroundings leads to a variety of self-destructing mechanisms, so-called beam instabilities, severly limitating to the performance of the machines. In this lecture, we focus on issues arising in the transverse. We will review the most common instability mechanisms, the existing models as well as current strategies to stabilize them through Landau damping with active feedback systems.

Cyclotrons

• Mike Gerd Seidel (PSI)

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. Several properties, such as CW operation, make the cyclotron concept suitable for the acceleration of hadron beams with high average intensity. Relativistic effects limit the energies in reach to approximately 1GeV.

Transverse HI ring beam-instabilities + mitigations II

• Xavier Buffat (CERN)

Several applications of circular hadron accelerators require intense beams, yet the interaction of the charged particles with their surroundings leads to a variety of self-destructing mechanisms, so-called beam instabilities, severly limitating to the performance of the machines. In this lecture, we focus on issues arising in the transverse. We will review the most common instability mechanisms, the existing models as well as current strategies to stabilize them through Landau damping with active feedback systems.

Diagnostics in High Intensity Beams I

• Peter Forck (GSI)

Performant beam diagnostics are essential for the successful operation of high-current accelerator facilities, to achieve its design parameters. The usage of standard and advanced beam instrumentation is reviewed. In the first part of the lecture, the methods beam current, transverse profile, and emittance are presented. Invasive diagnostics, such as screens, wire scanners, and grids, may be destroyed by the high beam power; hence, the use of non-invasive types, such as Ionisation Profile Monitors and beam-induced fluorescence, is beneficial. Given the significant non-linear effects present in high-current beams, special emphasis is placed on emittance measurement using tomographic reconstruction methods.

Electron Cloud

• Lotta Mether (CERN)

Diagnostics in High Intensity Beams II

• Peter Forck (GSI)

The second part of the lecture focuses on the principles, technical implementation, and application of Beam Position Monitors (BPMs). The expected signal shape is derived and illustrated for a representative use case, providing guidance for proper interpretation and application. BPMs enable the evaluation of the transverse position of beam bunches with time resolutions ranging from individual bunch-by-bunch measurements to millisecond-scale averages. In synchrotron applications, the closed orbit -measured on the millisecond timescale- is determined and utilized as input for feedback systems to mitigate external disturbances and power supply fluctuations. By interpreting the bunch position as representative of a "macro-particle," key beam parameters such as tune, beta function, dispersion, and chromaticity can be extracted. For high-current operation, spectral modifications due to tune shifts and tune spread are briefly addressed. The lecture concludes with a concise overview of bunch length measurement techniques and the role of Beam Loss Monitors (BLMs) in machine protection and diagnostics.

Intrabeam Scattering

• Andrzej Wolski (University of Liverpool)

Intrabeam scattering refers to the effects of the Coulomb interaction acting between pairs of charged particles within a bunch in an accelerator. One of the main consequences of intrabeam scattering is a change in the emittances of a bunch: in some circumstances (in particular, in hadron storage rings operating above transition), the transverse and longitudinal emittances may grow over time without limit. This may restrict the performance of machines for which maintaining low beam emittance is an important requirement. In this lecture, we will look at some of the models used to analyse the effects of intrabeam scattering and consider in particular the Piwinski formulae for the emittance growth rates. Predicted changes in emittance will be compared with measurements in a number of machines operating in different parameter regimes.

Beam-Beam Effects in Hadron Colliders

• Xavier Buffat (CERN)

The electromagnetic interaction of the two beams on each other, so-called beam-beam force, is one of the main limitations in view of reaching the highest luminosity. In this lecture, we cover the main models to describe the beam-beam effect that drive the design of modern colliders as well as various strategies to push the performance beyond existing machines.

FFAs

• Mike Gerd Seidel (PSI)

"The fixed field alternating gradient accelerator (FFA) represents the most general concept among the types of non-cycling accelerators including cyclotrons. A constant bending field presents an important advantage for the acceleration of high intensity beams. FFA’s utilize strong focusing to reduce the radial orbit variation as compared to cyclotrons with a weak focusing strength. The lecture covers scaling and non-scaling FFA’s and illustrates the conceptual advantages using several concrete design examples.  "

Longitudinal HI ring beam-instabilities + mitigations I

• Ivan Karpov (CERN)

The interaction of charged particles with the beam coupling impedance can lead to undamped or exponentially increasing oscillations in the longitudinal plane. To ensure the stability and reproducibility of beam parameters, many hadron synchrotrons must rely on Landau damping or active damping provided by feedback systems. Understanding the intensity threshold and beam evolution after perturbation is essential for pushing the performance of existing and future facilities. In these lectures, we first discuss the fundamentals of synchrotron motion and the role of the beam coupling impedance. Then, van Kampen modes and the formalisms for analysing beam stability are introduced. We use them to determine the threshold at which Landau damping is lost and examine two mechanisms of longitudinal single-bunch instabilities: azimuthal and radial mode coupling. Finally, the latest developments regarding multi-bunch instabilities are presented, and possible mitigation strategies are briefly discussed.

Sustainability for High-Intensity Machines

• Mike Gerd Seidel (PSI)

The main focus of the lecture is given to the power conversion process in high intensity accelerators from grid to beam and its efficiency. 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.

Longitudinal HI ring beam-instabilities + mitigations II

• Ivan Karpov (CERN)

The interaction of charged particles with the beam coupling impedance can lead to undamped or exponentially increasing oscillations in the longitudinal plane. To ensure the stability and reproducibility of beam parameters, many hadron synchrotrons must rely on Landau damping or active damping provided by feedback systems. Understanding the intensity threshold and beam evolution after perturbation is essential for pushing the performance of existing and future facilities. In these lectures, we first discuss the fundamentals of synchrotron motion and the role of the beam coupling impedance. Then, van Kampen modes and the formalisms for analysing beam stability are introduced. We use them to determine the threshold at which Landau damping is lost and examine two mechanisms of longitudinal single-bunch instabilities: azimuthal and radial mode coupling. Finally, the latest developments regarding multi-bunch instabilities are presented, and possible mitigation strategies are briefly discussed.

CST installation check

Numerical methods in high-intensity rings

• Alexandre Lasheen (CERN)

Particle Matter interaction

• Giuseppe Lerner (CERN)

This lecture introduces key concepts in particle-matter interactions, including cross sections, mean free path, and their relation to interaction probabilities. Photon and charged particle interactions are covered, followed by nuclear interactions of hadrons. The main features of electromagnetic and hadronic showers initiated by high-energy projectiles are then presented. The lecture concludes with an introduction to Monte Carlo codes for modelling radiation-matter interactions, and a first look at LHC-type radiation showers.

Cryogenics

• Benjamin Bradu (CERN)

The main objective of this CERN Accelerator School course on cryogenics is to give a better understanding about the importance of having an accurate modelling of the interactions between the cryogenics and the high intensity hadron beams at the design stage of superconducting accelerators to avoid operation limitation once the machine is operated. After a summary about the basic cryogenic concepts, the main cryogenic challenges for the superconducting hadron accelerators are introduced and discussed. A focus is made on the beam-induced heat loads produced on the beam screens with their impact on the cryogenic system. It concerns synchrotron radiation, impedance effects and electron clouds phenomena. Then, this course is intended to introduce the possible limitations that can occur between the high intensity hadron beams and the cryogenics, and how these limitations can be anticipated and mitigated. As examples, several use cases are presented at the end using the CERN accelerators that are under operation (LHC), under construction (HL-LHC) and under study (FCC-hh).

Beam loss Mechanisms + Machine Protection

• Annika Nordt (European Spallation Source, Lund, Sweden)

This session provides an introduction on what can possibly go wrong when operating a particle accelerator and how to prevent this from happening. Depending on the type of machine and type of particles used, the damage potential can be insignificant or significant, leading to different mitigative measures required to reduce the likelihood of accidents to occur. We will present a list of criteria that can be used to determine a comprehensive strategy for protecting the machine from damage. Further, we will explain how to develop a machine protection strategy and how to implement relevant principles accordingly by providing hands-on examples, covering the full life cycle from early concept, to detailed design, to construction, early commissioning, as well as operation and maintenance of a machine.

Beam Loss consequences

• Giuseppe Lerner (CERN)

This lecture examines beam losses in high-energy particle accelerators and their implications for machine infrastructure, reliability, and safe operation. Following an introduction to the mechanisms and primary sources of beam loss, we explore their consequences in detail, focusing on three key areas: equipment and magnet damage, Radiation to Electronics (R2E), and Radiation Protection (RP). The discussion is grounded in operational experience from CERN’s accelerator complex, with particular emphasis on the Large Hadron Collider (LHC) as a case study. We conclude with an outlook on beam loss challenges at future collider projects, covering the electron-positron stage of the Future Circular Collider (FCC-ee) and the muon collider

Beam Loading

• Heiko Damerau (CERN)

Radio-frequency (RF) systems in particle accelerators are usually designed to transfer energy to the beam or to define its longitudinal structure. However, charged particles passing through an RF cavity induce a voltage which acts back on themselves and on subsequent particles. The additional contribution of the beam to the cavity voltage moreover changes the effective properties of the RF system and is generally referred to as beam loading. The fundamental theorem of beam loading is introduced to derive the effect of a single bunch passage through an RF cavity. The choice of the cavity parameters, notably shunt impedance divided by quality factor, plays an important role to reduce the beam induced voltage. Extending the single bunch case to the periodic passage of bunches allows to calculate the steady state cavity detuning due to beam loading for a continuous bunch pattern. Special emphasis is given to the partially filled ring, with gaps in the filling pattern, which is the most common case of transient beam loading in electron and hadron synchrotrons.

Case study Introduction

• Heiko Damerau (CERN)
• Leandro Intelisano
• Alexandre Lasheen (CERN)
• Michela Neroni
• Jake Flowerdew
• Christine Vollinger (CERN)

RFQ + Cavities (NC + SC)

• Ciprian Plostinar (ESS)

This lecture introduces the fundamental principles and practical aspects of radiofrequency (RF) cavities in particle accelerators, with emphasis on their role in overcoming intensity limitations in hadron beams. Starting from the historical development of early accelerators, the presentation traces the evolution of RF acceleration, outlines the theoretical foundations, and describes the essential technologies. Special attention is given to the Radiofrequency Quadrupole (RFQ), a key structure for low-energy hadron acceleration, with design principles illustrated through the ESS RFQ and the ISIS FETS RFQ as physics and engineering case studies. Practical cavity designs are reviewed for both normal-conducting structures and superconducting cavities. Real-world examples are discussed from facilities including ESS, CERN, and ISIS

Beam Based Impedance Measurements

• Alexandre Lasheen (CERN)

RF design for high- intensity

• Ciprian Plostinar (ESS)

This lecture addresses the design of radiofrequency (RF) cavities for high-intensity hadron accelerators. Beginning with an overview of the global demand for high-power proton beams and their applications, the talk outlines the full design process for RF cavities, from requirements definition to optimisation. Key design considerations are discussed in the context of beam loading, higher-order modes, thermal management, coupling and tuning, multipacting, radiation effects, and long-term reliability. Figures of merit such as accelerating gradient, transit time factor, quality factor, shunt impedance, and the Kilpatrick limit are presented as essential parameters guiding cavity optimisation. The lecture then illustrates the optimisation process for both normal-conducting drift tube linac (DTL) cavities and superconducting elliptical cavities, highlighting trade-offs between efficiency, stability, and manufacturability. Practical demonstrations with simulation tools such as SuperFish and CST are included, as well as a real-world live demonstration from the European Spallation Source (ESS).

Case studies

• Alexandre Lasheen (CERN)
• Christine Vollinger (CERN)
• Heiko Damerau (CERN)
• Michela Neroni
• Leandro Intelisano
• Jake Flowerdew

Case studies

• Leandro Intelisano
• Jake Flowerdew
• Alexandre Lasheen (CERN)
• Christine Vollinger (CERN)
• Heiko Damerau (CERN)
• Michela Neroni

Free study time

Collimation

• Nuria Fuster Martinez (IFIC)

Collimation systems are essential in particle accelerators to safely and efficiently manage unavoidable beam losses during operation. These systems rely on collimators which are specially designed movable jaws or absorbers positioned close to the beam envelope to intercept and localize beam losses. Their role is particularly critical in high-intensity hadron machines, where uncontrolled losses can lead to equipment damage or operational downtime. While the specific requirements vary across accelerator types, circular accelerators, especially present and future high-energy colliders, cannot function safely without a well-optimized collimation system. This lecture offers an overview of the fundamental principles, design challenges and operational strategies for beam collimation, with emphasis on high-intensity hadron accelerators. The Large Hadron Collider (LHC), the most advanced example to date, will serve as the main reference for illustrating state-of-the-art collimation approaches and technologies.

Vacuum Issues

• Sergio Calatroni (CERN)

Beam dynamics and stability define the requirements on the vacuum static and dynamic pressure inside an accelerator. High intensity beams may however strongly impact the dynamic pressure, through phenomena such as electron cloud, photon and ion induced desorption. The lecture will present these phenomena and mitigation measures that are typically used in particle accelerators. In a second part of the lecture, we will also introduce the direct effect of high-intensity beams on vacuum components, via resistive wall heating or induced resonances, including their effect on the dynamic pressure. This second part will be object of the case study on the next day.

Injection, Extraction I

• Yann Dutheil (CERN)

High-intensity hadron beams underpin the CERN physics programme, enabling discovery at frontiers like the Large Hadron Collider (LHC) as well as through the diverse programme on the injector complex. However, transferring and preserving these beams impose strict demands on injection and extraction systems to maintain brightness and ensure reliable machine operation. Drawing upon extensive operational experience and recent developments within the CERN accelerator complex, this lecture provides a comprehensive overview of beam transfer techniques tailored for high-energy synchrotrons. The presentation begins by establishing the fundamental principles of beam transfer, with a focus on high-intensity hadron beam challenges. Building on these concepts, the lecture explores advanced beam manipulation schemes employed at CERN. These sophisticated methods allow for precise control over phase space density and extraction dynamics, utilising novel capture and resonance mechanisms to maximise efficiency and minimise beam losses. Finally, the lecture addresses the specific intensity limitations encountered in modern machines. Key topics include machine protection challenges at the LHC, mitigation of beam losses through crystal shadowing, and the management of hardware constraints such as beam-induced RF heating and impedance in kicker systems.

Case study Introduction

• Sergio Calatroni (CERN)
• Benoit Salvant (CERN)
• Patrick Krkotic
• Ingrid Mases Sole (Goethe University Frankfurt (DE))
• Elena De La Fuente Garcia (Universidad Politecnica de Madrid (ES))
• David Amorim (EPFL)

Beam Intercepting devices

• Antonio Perillo Marcone (CERN)

Injection, Extraction II

• Yann Dutheil (CERN)

Ions

• Markus Steck (GSI)

Ions provided by accelerators are used in fields like atomic and nuclear physics, material science, medical applications and high energy collisions. The lecture will focus on specific aspects of ion acceleration which are limiting the availability of high intensity ion beams. One aspect is the interaction of ions with matter in the course of the acceleration process. Methods like beam cooling, beam accumulation and deceleration are applied in order to provide ions according to the request by experiments. Due to the high charge of the ions they experience stronger Coulomb interaction resulting in high intrabeam scattering rates and strong space charge effects.

Case studies

• David Amorim (EPFL)
• Ingrid Mases Sole (Goethe University Frankfurt (DE))
• Elena De La Fuente Garcia (Universidad Politecnica de Madrid (ES))
• Patrick Krkotic
• Chiara Antuono
• Sergio Calatroni (CERN)
• Benoit Salvant (CERN)

Case studies

• Benoit Salvant (CERN)
• Chiara Antuono
• David Amorim (EPFL)
• Patrick Krkotic
• Elena De La Fuente Garcia (Universidad Politecnica de Madrid (ES))
• Ingrid Mases Sole (Goethe University Frankfurt (DE))
• Sergio Calatroni (CERN)

HI radioactive ion beams

• Thierry Stora (CERN)

Radioactive Ion Beams (RIB) have been produced for the past 70 years across a wide range of facilities, first based on the isotope mass separation online (ISOL) technique, and later by In-Flight (IF) fragmentation technique. While different new facilities spread across all continents, CERN has hosted some early facilities, and the longest one still in operation, ISOLDE, since 1964. It also hosts CERN-MEDICIS, a batch mode isotope mass separation facility, aiming at high radionuclide activities, and hence high RIB intensities. High Intensity can adopt a large range of definition in our field, which will depend to a large extend of the type of radionuclides and the accelerator used and accelerator chain to produce the desired beams. Intensities as low as a few ion/min (eg zeptoA) to few 1e9 ion/s (eg nanoA) produced online, or a few 1e12ion/s (eg microA) theoretically expected for online, or experimental long-lived, isotope production can all be considered “High Intensity”. This wide range of orders of magnitudes originate from the intrinsic limitations related to the isotope production in the target, to efficiencies related to their ionization and acceleration, to the sometimes-short-half-life of the considered radionuclides, and to the difficulty to handle and maintain facilities with significant radiological risks. The lecture will give a general introduction of these different elements and provide a range of selected examples thus illustrating the present state of the art of the field of “High Intensity” HI-RIB production.

Operation + Maintenance issues

• Antonio Perillo Marcone (CERN)

Cooling of high- intensity beams

• Markus Steck (GSI)

Beam cooling has been developed to produce beams of superior beam quality and to support the preparation of high intensity hadron beams. A general introduction into the methods of electron cooling and stochastic cooling will provide the basis to explain the properties of cooled beams. Beam cooling supports the accumulation of high intensity secondary or heavy ion beams. The intensity is limited by reduction of the beam phase space volume which results in stronger intrabeam scattering, instabilities and space charge dominated beams. The cooling technology is presently extended towards higher beam energies aiming at luminosity increase in colliders.

Hadron Colliders

• Markus Zerlauth (CERN)

The talk will provide an overview of the hadron colliders built to date and the design and operational challenges that each of these machines has faced. Many of these are inherent to the ongoing effort to optimise the instantaneous and integrated luminosity of the machines, which inevitably leads to many technological challenges that must be met and overcome. We will summarise how these challenges have been successfully met in the past and present machines and outline the role they could play in ambitious future accelerator projects such as the HL-LHC upgrade and the FCC project.

HI for Accelerator Driven Systems

• Ulrich Dorda (SCK CEN)

After presenting the motivation for an Accelerator Driven System (ADS), the requirements on the accelerator are derived. Using the MYRRHA project as example, the beam optics/dynamics design and operational concept of such an accelerator is discussed. Finally, the main technology choices and challenges are presented.

Closing

Departure day