Name: CAS course on "Introduction to Accelerator Physics", 25 September - 08 October 2023, Santa Susanna, Spain
Start: 2023-09-25T08:30:00+02:00
End: 2023-10-08T22:00:00+02:00
Location: No location set

Sunday 24 September 2023
Monday 25 September 2023

08:30 Arrival day and registration
Arrival day and registration
08:30 - 20:30
Tuesday 26 September 2023
08:30 Opening - Frank Tecker (CERN)
Opening
- Frank Tecker (CERN)
08:30 - 09:30
09:45 Electromagnetic Theory I - Irina Shreyber
Electromagnetic Theory I
- Irina Shreyber
09:45 - 10:45
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.
10:45 Coffee break
Coffee break
10:45 - 11:15
11:15 History of particle acceleration - Suzie Sheehy (University of Oxford and University of Melbourne)
History of particle acceleration
- Suzie Sheehy (University of Oxford and University of Melbourne)
11:15 - 12:15
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.
12:15 Lunch
Lunch
12:15 - 13:45
13:45 Electromagnetic Theory II - Irina Shreyber
Electromagnetic Theory II
- Irina Shreyber
13:45 - 14:45
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.
15:00 Transverse Linear Beam Dynamics I - Wolfgang Hillert Wolfgang Hillert
Transverse Linear Beam Dynamics I
- Wolfgang Hillert
- Wolfgang Hillert
15:00 - 16:00
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.
16:00 Coffee break
Coffee break
16:00 - 16:30
16:30 Accelerator Applications - Suzie Sheehy (University of Oxford and University of Melbourne)
Accelerator Applications
- Suzie Sheehy (University of Oxford and University of Melbourne)
16:30 - 17:30
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.
17:45 1 slide 1 minute
1 slide 1 minute
17:45 - 18:45

18:45 Welcome reception
Welcome reception
18:45 - 20:00
Wednesday 27 September 2023
08:30 Kinematics of Particle Beams - Relativity - Irina Shreyber
Kinematics of Particle Beams - Relativity
- Irina Shreyber
08:30 - 09:30
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.
09:45 Warm Magnets - Gijs De Rijk
Warm Magnets
- Gijs De Rijk
09:45 - 10:45
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.
10:45 Coffee break
Coffee break
10:45 - 11:15
11:15 Transverse Linear Beam Dynamics II - Wolfgang Hillert
Transverse Linear Beam Dynamics II
- Wolfgang Hillert
11:15 - 12:15
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.
12:15 Lunch
Lunch
12:15 - 13:45
13:45 Linear Accelerators I - David Alesini
Linear Accelerators I
- David Alesini
13:45 - 14:45
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.
15:00 Transverse Linear Beam Dynamics III - Wolfgang Hillert
Transverse Linear Beam Dynamics III
- Wolfgang Hillert
15:00 - 16:00
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.
16:00 Coffee break
Coffee break
16:00 - 16:30
16:30 Linear Accelerators II - David Alesini
Linear Accelerators II
- David Alesini
16:30 - 17:30
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.
17:45 Superconducting Magnets - Gijs De Rijk
Superconducting Magnets
- Gijs De Rijk
17:45 - 18:45
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.
Thursday 28 September 2023
08:30 Transverse Linear Beam Dynamics IV - Wolfgang Hillert
Transverse Linear Beam Dynamics IV
- Wolfgang Hillert
08:30 - 09:30
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.
09:45 Computational tools I - Andrea Latina (CERN)
Computational tools I
- Andrea Latina (CERN)
09:45 - 10:45
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.
10:45 Coffee break
Coffee break
10:45 - 11:15
11:15 Transverse Linear Beam Dynamics V - Wolfgang Hillert
Transverse Linear Beam Dynamics V
- Wolfgang Hillert
11:15 - 12:15
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.
12:15 Lunch
Lunch
12:15 - 13:45
13:45 Longitudinal BD in Circular Machines I - Frank Tecker (CERN)
Longitudinal BD in Circular Machines I
- Frank Tecker (CERN)
13:45 - 14:45
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.
15:00 Time and Frequency domain signals I - Hermann Schmickler
Time and Frequency domain signals I
- Hermann Schmickler
15:00 - 16:00
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.
16:00 Coffee break
Coffee break
16:00 - 16:30
16:30 Hands-ON Lattice calulations I - Tirsi Prebibaj (CERN) Davide Gamba (CERN) Giulia Russo (CERN)
Hands-ON Lattice calulations I
- Tirsi Prebibaj (CERN)
- Davide Gamba (CERN)
- Giulia Russo (CERN)
16:30 - 17:30
17:45 Hands-ON Lattice calulations II - Davide Gamba (CERN) Giulia Russo (CERN) Tirsi Prebibaj (CERN)
Hands-ON Lattice calulations II
- Davide Gamba (CERN)
- Giulia Russo (CERN)
- Tirsi Prebibaj (CERN)
17:45 - 18:45
Friday 29 September 2023

08:30 Free
Free
08:30 - 12:15

12:15 Lunch
Lunch
12:15 - 13:45
13:45 Longitudinal BD in Circular Machines II - Frank Tecker (CERN)
Longitudinal BD in Circular Machines II
- Frank Tecker (CERN)
13:45 - 14:45
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.
15:00 Linear Imperfections I - Volker Ziemann
Linear Imperfections I
- Volker Ziemann
15:00 - 16:00
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.
16:00 Coffee break
Coffee break
16:00 - 16:30
16:30 Time and Frequency domain signals II - Hermann Schmickler
Time and Frequency domain signals II
- Hermann Schmickler
16:30 - 17:30
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.
17:45 Linear Imperfections II - Volker Ziemann
Linear Imperfections II
- Volker Ziemann
17:45 - 18:45
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.
18:45 Discussion session
Discussion session
18:45 - 20:00
Saturday 30 September 2023
08:30 Beam Instrumentation - Peter Forck
Beam Instrumentation
- Peter Forck
08:30 - 09:30
Determining beam parameters is essential for the operation and development of any accelerator facility. The working principle of frequently used beam instruments for electron and proton beams is discussed. The first part of the lecture comprises beam instrumentation for beam current determination and the usage of beam position monitors (BPM) for bunched beams. BPMs are applied for position detection of a single bunch and accurate closed orbit determination. Moreover, the position reading delivers synchrotron lattice parameters such as tune and chromaticity. Those monitors are based on detecting the beam's electromagnetic field and are dominantly non-invasive.
09:45 Computational tools II - Andrea Latina (CERN)
Computational tools II
- Andrea Latina (CERN)
09:45 - 10:45
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.
10:45 Coffee break
Coffee break
10:45 - 11:15
11:15 Beam Diagnostics - Peter Forck
Beam Diagnostics
- Peter Forck
11:15 - 12:15
The working principle of frequently used beam instruments for electron and proton beams concerning the transverse and longitudinal profile measurement is discussed. A large variety of monitors for transverse profile measurement exists, based on the energy loss of the beam particles in matter followed by the detection of secondary particles or photons (SEM-Grids, wire scanners, scintillation screens, optical transition radiation screens, ionization profile monitors). Based on profile measurements, the beam emittance at transfer lines can be deduced by several methods. The bunch shape is determined with several methods, either based on the broadband measurement of the bunch electric field, by electro-optical techniques or related to the emission of synchrotron photons.
12:15 Lunch
Lunch
12:15 - 13:45
13:45 Colliders and luminosity - Hermann Schmickler
Colliders and luminosity
- Hermann Schmickler
13:45 - 14:45
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 ($e^+e^-$ colliders, $pp$ colliders, ...), a summary of the historical evolution and a mathematical treatment to describe collider performance.
15:00 Linear Imperfections - corrections - Volker Ziemann
Linear Imperfections - corrections
- Volker Ziemann
15:00 - 16:00
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.
16:00 Coffee break
Coffee break
16:00 - 16:30
16:30 Hands-ON Lattice calulations III - Davide Gamba (CERN) Tirsi Prebibaj (CERN) Giulia Russo (CERN)
Hands-ON Lattice calulations III
- Davide Gamba (CERN)
- Tirsi Prebibaj (CERN)
- Giulia Russo (CERN)
16:30 - 17:30
17:45 Hands-ON Lattice calulations IV - Davide Gamba (CERN) Giulia Russo (CERN) Tirsi Prebibaj (CERN)
Hands-ON Lattice calulations IV
- Davide Gamba (CERN)
- Giulia Russo (CERN)
- Tirsi Prebibaj (CERN)
17:45 - 18:45

Sunday 8 October 2023

08:30 Departure Day
Departure Day
08:30 - 14:30

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