Intensity Limitations in Hadron Beams, 15 - 27 June 2025, Borovets, Bulgaria

15 Jun 2025, 08:30 → 27 Jun 2025, 19:30 Europe/Zurich

Christine Vollinger (CERN), Frank Tecker (CERN)

Pushing the Limits: Intensity Limitations in Hadron Beams

In collaboration with the Faculty of Physics, Sofia University, the CERN Accelerator School is organising a topical course on Intensity Limitations in Hadron Beams. 

An unprecedented intensity demand for hadron beams has become the norm today for a variety of particle accelerators from different fields. 

This CERN Accelerator School course explores the challenges of generating and maintaining high-intensity hadron beams, crucial for a variety of applications in fundamental research.

Achieving peak performance in these machines requires a deep understanding of the factors that can limit beam intensity. During a two weeks course, we will delve into the limitations which these beams encounter in both linear accelerators (linacs) and circular accelerators.

This course provides a comprehensive overview of these limitations, including:

• Beam interactions with the surroundings: We'll examine how the beam interacts with its environment, starting from vacuum chambers and other accelerator components up to beam intercepting devices.
• Wakefields and impedances: Learn about the electromagnetic fields generated by the beam itself and derive their impact on beam stability.
• High-intensity instabilities: Explore the various instabilities that can arise in high-intensity beams, and understand how to mitigate them.
• Space charge effects: Understand the impact of the beam's own electric charge on its dynamics.
• Collective effects: Discover how the combined behaviour of particles in the beam can lead to complex phenomena.

The course also examines specific intensity limitations encountered in diverse applications, such as:

• Neutron sources
• Radioactive ion beams
• Neutrino factories and muon colliders
• Hadron colliders
• Accelerator Driven Systems for energy production

Through a combination of lectures and case studies, you'll gain the knowledge and learn about the required tools to analyse, understand, and overcome intensity limitations in hadron beams.

Who can apply?

The course is aimed at 

• postgraduate students in the accelerator domain (ie. minimum of Bachelor’s degree or equivalent)
• employees in accelerator laboratories, university departments and companies manufacturing accelerator equipment
• engineers and scientists with a few years’ experience in accelerator physics, engineering, or related fields.

 

We welcome applications from all countries and nationalities. Applicants are responsible for ensuring that their registration fee and travel cost is covered by their home institute or employer, or, failing this, themselves. 

Early applicants will be given priority in the selection process. With a limited number of participants, we strongly advise you to apply early to secure your place. Waiting until the deadline may reduce your chances of being selected. Keep in mind that there is a limited number of single rooms available. Once the course is complete, we will close the registration. 

As usual, we will accept GRANT applications for participants from countries developing the accelerator field, which will otherwise have no possibility of taking part. Applications need to fulfil the same requirements as mentioned above. Further details can be found under ‘Apply for a Student Grant’.

Important dates

• Friday 8 November 2024 - registration opens
• Tuesday 1 April 2025 - Grant Registration deadline
• Wednesday 30 April 2025 – final deadline for applications (unless course is fully booked)
• Friday 2 May 2025- registration fee payment deadline
• Sunday 15 June 2025 (afternoon/evening) - participants arrivals
• Friday 27 June 2025 (morning) - departure

BUL Poster Vs2.pdf

Timetable_Int_Lim_2025_ver2.5.pdf

Sunday 15 June

08:30 → 20:00 Arrival day and registration

20:00 → 22:00 Dinner

Monday 16 June

08:30 → 09:30 Opening / Local presentation

Speaker: Frank Tecker (CERN)

09:40 → 10:40 Introduction and demands for high intensity

Speaker: Yannis Papaphilippou (CERN)

10:40 → 11:10 Coffee break

11:10 → 12:15 Frontiers for linear machines

Speaker: Mamad Eshraqi (ESS - European Spallation Source ERIC (SE))

12:15 → 13:45 Lunch

13:45 → 14:45 Frontiers for circular machines

Speaker: Chris Rogers

14:55 → 15:55 Wakefields and Impedances I

Speaker: Prof. Andrea Mostacci (Sapienza University of Rome (IT))

16:00 → 16:30 Coffee break

16:30 → 17:30 Wakefields and Impedances II

Speaker: Prof. Andrea Mostacci (Sapienza University of Rome (IT))

17:30 → 18:45 One slide - one minute

18:45 → 20:00 Welcome reception

20:00 → 22:00 Dinner

Tuesday 17 June

08:30 → 09:30 Bench Measurements and Simulations of Beam Coupling Impedance

Speaker: Prof. Andrea Mostacci (Sapienza University of Rome (IT))

09:40 → 10:40 Lattice design for high intensity rings

Speaker: Yannis Papaphilippou (CERN)

10:40 → 11:10 Coffee break

11:10 → 12:15 Space Charge Effects in Linacs

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.

Speaker: Emanuele Laface (CERN)

12:15 → 13:45 Lunch

13:45 → 14:45 Sources and Low Energy Beam Transfer

Speaker: Daniel Charles Faircloth

14:55 → 15:55 Neutron Sources

Speaker: Mamad Eshraqi (ESS - European Spallation Source ERIC (SE))

16:00 → 16:30 Coffee break

16:30 → 17:30 Neutrino Factories and Muon Colliders

Speaker: Chris Rogers

17:30 → 20:00 Poster session

20:00 → 22:00 Dinner

Wednesday 18 June

08:30 → 09:30 High-Intensity linac beam-dynamics

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.

Speaker: Alessandra Lombardi (CERN)

09:40 → 10:40 Numerical methods in high-intensity linacs

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.

Speaker: Emanuele Laface (CERN)

10:40 → 11:10 Coffee break

11:10 → 12:15 Linac Instabilities + mitigations

Speaker: Alessandra Lombardi (CERN)

12:15 → 13:20 Space Charge in Circular Machines

Speaker: Foteini Asvesta (CERN)

13:20 → 14:45 Lunch

14:45 → 17:30 Free study time

20:00 → 22:00 Dinner

Thursday 19 June

08:30 → 09:30 Transverse HI ring beam-instabilities + mitigations I

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.

Speaker: Xavier Buffat (CERN)

09:40 → 10:40 Cyclotrons

Speaker: Mike Gerd Seidel

10:40 → 11:10 Coffee break

11:10 → 12:15 Transverse HI ring beam-instabilities + mitigations II

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.

Speaker: Xavier Buffat (CERN)

12:15 → 13:45 Lunch

13:45 → 14:45 Diagnostics in High Intensity Beams I

Speaker: Peter Forck

14:55 → 15:55 Electron Cloud

Speaker: Lotta Mether (CERN)

16:00 → 16:30 Coffee break

16:30 → 17:30 Diagnostics in High Intensity Beams II

Speaker: Peter Forck

20:00 → 22:00 Dinner

Friday 20 June

08:30 → 09:30 Intrabeam Scattering

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.

Speaker: Prof. Andrzej Wolski (University of Liverpool)

Intrabeam Scattering - Animations Off.pdf

Intrabeam Scattering - Animations On.pdf

Intrabeam Scattering - Notes.pdf

09:40 → 10:40 Beam-Beam Effects in Hadron Colliders

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.

Speaker: Xavier Buffat (CERN)

10:40 → 11:10 Coffee break

11:10 → 12:15 FFAs

Speaker: Mike Gerd Seidel

12:15 → 13:45 Lunch

13:45 → 14:45 Longitudinal HI ring beam-instabilities + mitigations I

Speaker: Ivan Karpov (CERN)

14:55 → 15:55 Sustainability for High-Intensity Machines

Speaker: Mike Gerd Seidel

16:00 → 16:30 Coffee break

16:30 → 17:30 Longitudinal HI ring beam-instabilities + mitigations II

Speaker: Ivan Karpov (CERN)

17:30 → 18:15 CST installation check

20:00 → 22:00 Dinner

Saturday 21 June

09:00 → 19:00 Excursion

20:00 → 22:00 Dinner

Sunday 22 June

08:30 → 09:30 Numerical methods in high-intensity rings

Speaker: Alexandre Lasheen (CERN)

09:40 → 10:40 Particle Matter interaction

Speaker: Dr Giuseppe Lerner (CERN)

10:40 → 11:10 Coffee break

11:10 → 12:15 Cryogenics

Speaker: Benjamin Bradu (CERN)

12:15 → 13:45 Lunch

13:45 → 14:45 Beam loss Mechanisms + Machine Protection

Speaker: Annika Nordt (European Spallation Source, Lund, Sweden)

14:55 → 15:55 Beam Loss consequences

Speaker: Dr Giuseppe Lerner (CERN)

16:00 → 16:30 Coffee break

16:30 → 17:30 Beam Loading

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.

Speaker: Heiko Damerau (CERN)

17:30 → 18:00 Case study Introduction

20:00 → 22:00 Dinner

Monday 23 June

08:30 → 09:30 RFQ + Cavities (NC + SC)

Speaker: Ciprian Plostinar

09:40 → 10:40 Beam Based Impedance Measurements

Speaker: Alexandre Lasheen (CERN)

10:40 → 11:10 Coffee break

11:10 → 12:15 RF design for high- intensity

Speaker: Ciprian Plostinar

12:15 → 13:45 Lunch

13:45 → 15:30 Case studies

15:30 → 16:00 Coffee break

16:00 → 18:30 Case studies

20:00 → 22:00 Dinner

21:00 → 23:00 Cinema event

Tuesday 24 June

08:30 → 12:15 Free study time

12:15 → 13:45 Lunch

13:45 → 14:45 Collimation

Speaker: Nuria Fuster Martinez

14:55 → 16:00 Vacuum Issues

Speaker: Sergio Calatroni (CERN)

16:00 → 16:30 Coffee break

16:30 → 17:30 Injection, Extraction I

Speaker: Yann Dutheil (CERN)

17:30 → 18:00 Case study Introduction

20:00 → 22:00 Dinner

Wednesday 25 June

08:30 → 09:30 Beam Intercepting devices

Speaker: Antonio Perillo Marcone (CERN)

09:40 → 10:40 Injection, Extraction II

Speaker: Yann Dutheil (CERN)

10:40 → 11:10 Coffee break

11:10 → 12:15 Ions

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.

Speaker: Markus Steck

12:15 → 13:45 Lunch

13:45 → 15:30 Case studies

15:30 → 16:00 Coffee break

16:00 → 18:30 Case studies

20:00 → 22:00 Dinner

Thursday 26 June

08:30 → 09:30 HI radioactive ion beams

Speaker: Thierry Stora (CERN)

09:40 → 10:40 Operation + Maintenance issues

Speaker: Antonio Perillo Marcone (CERN)

10:40 → 11:10 Coffee break

11:10 → 12:15 Cooling of high- intensity beams

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.

Speaker: Markus Steck

12:15 → 13:45 Lunch

13:45 → 14:45 Hadron Colliders

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.

Speaker: Markus Zerlauth (CERN)

14:55 → 16:00 HI for Accelerator Driven Systems

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.

Speaker: Mr Ulrich Dorda (SCK CEN)

16:00 → 16:30 Coffee break

16:30 → 17:30 Closing

20:00 → 22:00 Banquet

Friday 27 June

08:30 → 18:00 Departure day