CAS course on "RF for Accelerators", 18 June - 01 July 2023, Berlin Germany

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In the presentation theoretical foundations of electromagnetic fields are reviewed. First, general terms and concepts of field theory are discussed (scalar fields, vector fields, normal and tangential fields, dot product, cross product etc.) and then Maxwell’s equations in the integral form and material equations are recapitulated. It is shown how Maxwell’s equations in the integral form...

"The measurement of radio-frequency (RF) signals and the characterization of RF components, systems and subsystems used in particle accelerators is based on particular measurement instruments, like the RF vector network analyzer (VNA) and the spectrum analyzer (SA), but also on general-purpose instruments, like the oscilloscope and others. Before going into some details of SAs and VNAs, the...

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In the presentation, theoretical foundations of electromagnetic fields are reviewed. First, general terms and concepts of field theory are discussed (scalar fields, vector fields, normal and tangential fields, dot product, cross product etc.) and then Maxwell’s equations in the integral form and material equations are recapitulated. It is shown how Maxwell’s equations in the integral form...

"S.Rudys, V.Kalendra, S.Svirskas, S.Balciunas, R.Grigalaitis, S.Lapinskas, J.Banys
Faculty of Physics, Vilnius University, Vilnius, Lithuania
web site: http://www.lms.ff.vu.lt
The dielectric response of materials provides information about the orientational adjustment of dipoles and the translational adjustment of mobile charges present in a dielectric medium in response to an applied...

RF cavities are not only used to accelerate particle beams but they also kick beams or manipulate particles in the longitudinal phase space. They are used in linear and circular machines, some must have adjustable frequencies and some even accommodate multiple harmonics. Their operational use stretches from sub-per-mil duty cycles to continuous operation, they provide accelerating gradients...

In the presentation foundations of electromagnetic simulations are recapitulated. Initially, the need for numerical methods used in electromagnetic simulations is motivated. Then, spatial discretization is discussed in a general way. This will be followed by a detailed introduction to the finite-integration technique, which allows to transfer of Maxwell’s equations into their discrete...

The measurement of radio-frequency (RF) signals and the characterization of RF components, systems and subsystems used in particle accelerators is based on particular measurement instruments, like the RF vector network analyzer (VNA) and the spectrum analyzer (SA), but also on general-purpose instruments, like the oscilloscope and others. Before going into some details of SAs and VNAs, the...

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In the presentation foundations of electromagnetic simulations are recapitulated. Initially, the need for numerical methods used in electromagnetic simulations is motivated. Then, spatial discretization is discussed in a general way. This will be followed by a detailed introduction to the finite-integration technique, which allows to transfer Maxwell’s equations into their discrete...

This Presentation will give a short intro in the numerical simulation of electromagnetic fields.
The pro and cons of various numerical solvers are discussed. Main focus of the presentation is the live demo of the modelling and optimisation of a WR90 Waveguide to Coax coupler. Advanced solver settings such as sensitivity analysis e.g. are demonstrate. The presentation is aimed to prepare the...

We reviewed the main types of RF power amplifiers used for particle accelerators.
It covers vacuum beam tubes, specifically gridded tubes, including tetrodes, inductive output tubes, klystrons, and transistor amplifiers, with power outputs greater than 10 kW CW or 100 kW pulsed at frequencies from 50 MHz to 1 GHz.
Functioning principle and construction aspects of these various items were...

RF cavities are not only used to accelerate particle beams but they also kick beams or manipulate particles in the longitudinal phase space. They are used in linear and circular machines, some must have adjustable frequencies and some even accommodate multiple harmonics. Their operational use stretches from sub-per-mil duty cycles to continuous operation, they provide accelerating gradients...

We reviewed the main types of RF power amplifiers used for particle accelerators.
It covers vacuum beam tubes, specifically gridded tubes, including tetrodes, inductive output tubes, klystrons, and transistor amplifiers, with power outputs greater than 10 kW CW or 100 kW pulsed at frequencies from 50 MHz to 1 GHz.
Functioning principle and construction aspects of these various items were...

This talk gives a first introduction of longitudinal beam dynamics for both linear and circular accelerators.
It covers the basic methods of acceleration in a linac. For radio-frequency (RF) acceleration, it introduces the concepts of synchronicity and the oscillation around the synchronous particle, including the criterium for stability of the oscillations.
For circular accelerators, the...

The focus for this educational text is selected examples of high-frequency electronic circuits and their components employed for the accurate phasing and synchronisation of accelerator cavities. Examples have been chosen to describe the basics of RF electronics. The starting point is transmission lines, connectors, discontinuities and the handling of reflection. The application of simple...

We reviewed the techniques of transport of high-power radiofrequency power from a RF power source to the cavities of an accelerator.
Waveguide and coaxial lines are explained showing power limits.
Main power couplers are also explained, on the construction side of it.

The focus of this educational text is selected examples of high-frequency electronic circuits and their components employed for the accurate phasing and synchronisation of accelerator cavities. Examples have been chosen to describe the basics of RF electronics. The starting point is transmission lines, connectors, discontinuities and the handling of reflection. The application of simple...

The contribution is on issues being especially related to normal conducting cavities operating at non-relativistic beam energies. Various types of cavities are introduced w.r.t. their operation mode, application, pros, and cons. Special emphasis is put on their production and the challenges along the way from finalised RF design up to the operating cavity. This covers the choice of material,...

The lectures treat longitudinal beam tracking in synchrotrons. After introducing the basics of creating an accelerator model and discretisation, the lecture discusses the choice of the time frame and coordinates for longitudinal tracking. Concerning tracking without intensity effects, it touches on symplectic, periodic boundary conditions, and RF gymnastics. Concerning collective effects, the...

We discuss recent progress in Terahertz and optical radiation generation and its use in acceleration and beam manipulation. The advantage of using short wavelength radiation is overcoming breakdown phenomena, enabling high gradient accelerators with lower bunch charge. Early results on guns, beam manipulation devices and accelerator structures are discussed.

The lectures treat longitudinal beam tracking in synchrotrons. After introducing the basics of creating an accelerator model and discretisation, the lecture discusses the choice of the time frame and coordinates for longitudinal tracking. Concerning tracking without intensity effects, it touches on symplectic, periodic boundary conditions, and RF gymnastics. Concerning collective effects, the...

The lectures covers design, engineering, fabrication, testing and operation of superconducting systems for particle accelerator.
The main focus of this lecture is to cover the technological aspects of SRF Superconductivity.
Part I starts with explaining the benefits offered by RF superconductivity, and the conditions required for the operation in this regime, introducing the temperature...

The lectures cover the design, engineering, fabrication, testing and operation of superconducting systems for particle accelerators.
The main focus of this lecture is to cover the technological aspects of SRF Superconductivity.
Part I starts with explaining the benefits offered by RF superconductivity, and the conditions required for the operation in this regime, introducing the temperature...

"RF cavities loaded with magnetic alloy (MA) or ferrite ring cores are used in synchrotrons and storage rings if the maximum RF frequency is in the order of a few MHz. A simple model for the description of cavities of this type is derived. The most important parameters are defined, and some properties of the material and of the cavity are summarised.
Different cavity configurations,...

The lectures cover the design, engineering, fabrication, testing and operation of superconducting systems for particle accelerators.
The main focus of this lecture is to cover the technological aspects of SRF Superconductivity.
Part I starts with explaining the benefits offered by RF superconductivity, and the conditions required for the operation in this regime, introducing the temperature...

Modern particle accelerators use electromagnetic energy at RF frequencies to accelerate particles. This course outlines the fundamental concepts needed to understand the monitoring and control of electromagnetic fields. Often this area of study is called “Low-Level RF”. The course is aimed at non-electrical engineers with little experience in RF. The course is designed to illustrate frequency...

The lecture reviews general concepts of beam-induced electromagnetic fields in accelerator devices. The concept of momentum kick is introduced and thus wake function and wake potential. 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...

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...

The lecture reviews general concepts of diagnostics for beam intensity diagnostics, beam transverse position and bunch length as well as beam arrival. Such concepts are discussed with some examples. Concerning the beam intensity, current transformers and passive cavity are presented by showing the working principle and the main properties. Strip-lines and cavity beam position monitors have...

The lecture reviews general concepts of diagnostics for beam intensity diagnostics, beam transverse position and bunch length as well as beam arrival. Such concepts are discussed with some examples. Concerning the beam intensity, current transformers and passive cavity are presented by showing the working principle and the main properties. Strip-lines and cavity beam position monitors have...

Modern particle accelerators use electromagnetic energy at RF frequencies to accelerate particles. This course outlines the fundamental concepts needed to understand the monitoring and control of electromagnetic fields. Often this area of study is called “Low-Level RF”. The course is aimed at non-electrical engineers with little experience in RF. The course is designed to illustrate frequency...

In the first part of the lecture, the main characteristics of synchrotron motion, namely, synchronous particle and phase, bucket area and emittance are introduced. The equations of longitudinal particle motion in a single RF system of a proton synchrotron are re-derived and the phase equation is analysed for small and large amplitude particles. The particle motion below and above transition...

Modern particle accelerators use electromagnetic energy at RF frequencies to accelerate particles. This course outlines the fundamental concepts needed to understand the monitoring and control of electromagnetic fields. Often this area of study is called “Low-Level RF”. The course is aimed at non-electrical engineers with little experience in RF. The course is designed to illustrate frequency...

In order to maximise the power delivered to the cavity we must minimise reflections. Reflections are minimised when the source and load impedances are equal, however this is difficult when the cavity impedance is orders of magnitude higher than the source. A power coupler acts like a transformer changing the cavity impedance “seen” by the source allowing matching. This lecture looks at what...

In this lecture, dealing with intensity effects, the equations of motion with induced beam voltage are analysed.
This allows, first, to describe single-bunch potential well distortion and loss of Landau damping. Then the linearised Vlasov equation is used to derive step-by-step the Lebedev equation. This matrix equation is applied to find the thresholds, growth rates and spectra of...

Beyond increasing the energy of charged particles, RF frequency systems in accelerators allow to control longitudinal beam properties like distance between the bunches, their length, position in time, as well as the orbit length in a synchrotron. This is essential to adapt the beam parameters to the requirements of experiments or downstream accelerators. Already with a single-harmonic RF...

The lectures “High-Beta Cavities I and II” cover the main concepts that underly acceleration of relativistic beams, with a focus on traveling wave acceleration. These include the concepts of phase velocity and synchronism with the beam, group velocity, periodically loaded accelerating structures, the Brillouin diagram and the fundamental theorem of beam loading derived from an energy balance...

Beyond increasing the energy of charged particles, RF frequency systems in accelerators allow to control longitudinal beam properties like distance between the bunches, their length, position in time, as well as the orbit length in a synchrotron. This is essential to adapt the beam parameters to the requirements of experiments or downstream accelerators. Already with a single-harmonic RF...

Many applications require RF cavities that deflect the beam transversely, where the field needs to vary faster than can be achieved using magnets. This lecture studies dipole modes used for these applications and uses Panofsky-Wenzel theorem to look at transverse voltages, beam loading and mode requirements. The lecture also looks at modern TE and TEM deflecting mode cavities as well as...

The lectures “High-Beta Cavities I and II” cover the main concepts that underly acceleration of relativistic beams, with a focus on traveling wave acceleration. These include the concepts of phase velocity and synchronism with the beam, group velocity, periodically loaded accelerating structures, the Brillouin diagram and the fundamental theorem of beam loading derived from an energy balance...

Higher Order Modes (HOM) in accelerating structures are resonant electromagnetic fields excited and left behind by charged particle bunches. They can dramatically degrade the beam quality in accelerators, such as the multi-bunch energy spread and transverse emittance and therefore, one has to study and make them harmless carefully. In this lecture, various methods of HOM mitigation are...

The lecture “Multipactor and Breakdown” gives an introduction into the two main arcing phenomena encountered in high-power RF systems. The basic resonant character of multipactor and the role of secondary electron yield is shown. For vacuum breakdown, the lecture introduces how this is often observed in high-power systems followed by an overview of the main physical processes the lead up to...