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))

Frontiers for circular machines

• Chris Rogers (ISIS)

Wakefields and Impedances I

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

Wakefields and Impedances II

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

One slide - one minute

Bench Measurements and Simulations of Beam Coupling Impedance

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

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)

Neutron Sources

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

Neutrino Factories and Muon Colliders

• Chris Rogers (ISIS)

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)

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)

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)

Longitudinal HI ring beam-instabilities + mitigations I

• Ivan Karpov (CERN)

Sustainability for High-Intensity Machines

• Mike Gerd Seidel (PSI)

Longitudinal HI ring beam-instabilities + mitigations II

• Ivan Karpov (CERN)

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)

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)

Beam Based Impedance Measurements

• Alexandre Lasheen (CERN)

RF design for high- intensity

• Ciprian Plostinar (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)

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)

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