RF Basics I and II

Maxwell's equations are introduced in their general form, together with a basic set of mathematical operations needed to work with them. After simplifying and adapting the equations for application to radio frequency problems, we derive the most important formulae and characteristic quantities for cavities and waveguides. Several practical examples are given to demonstrate the use of the derived equations and to explain the importance of the most common figures of merit.Comment: presented at the CERN Accelerator School CAS 2011: High Power Hadron Machines, Bilbao, 24 May - 2 June 201

Multipacting Simulations of Tuner-adjustable waveguide coupler (TaCo) with CST

Tuner-adjustable waveguide couplers (TaCo) are used to feed microwave power to different RF structures of LINAC4. This paper studies the multipacting phenomenon for TaCo using PIC solver of CST PS. Simulations are performed for complete field sweeps and results are analysed

RF-Separated Beam Project for the M2 Beam Line at CERN

Within the framework of the Physics Beyond Colliders initiative at CERN, discussions are underway on the feasibility of producing radio-frequency (RF) separated beams for Phase-2 of the AMBER experiment at the M2 beam line in the North experimental area of the CERN SPS. The technique of RF separation is applied to enrich the content of a certain particle type within a beam consisting of different species at the same momentum. It relies on the fact that each particle type has a different velocity, decreasing with rest mass. The successor of the COMPASS experiment, AMBER, requires for its Phase-2 measurements high-intensity, high-purity kaon (and antiproton) beams, which cannot be delivered with the currently existing conventional M2 beam line. The present contribution introduces the principle of RF separation and explains its dependence on different parameters of beam optics and hardware. The first examination of potential showstoppers for the RF-separated beam implementation is presented, based on the particle production rates, beam line transmission for specific optics settings, limitations for overall beam intensity and purity posed by beam line acceptance and radiation protection. Different beam optics settings have been examined, providing either focused or parallel beams inside the RF cavities. The separation and transmission capability of the different optics settings for realistic characteristics of RF cavities are discussed and the preliminary results of the potential purity and intensity of the RF-separated beam are presented. They illustrate the high importance of an RF-separated kaon beam for many of the AMBER Phase-2 data taking programs, such as spectroscopy, prompt-photon production, Primakoff reactions and kaon charge-radius measurement

Superconducting RF at CERN: Operation, Projects, and R

The CERN SRF infrastructure was originally set up for Nb on Cu-coated cavities for large electron positron collider (LEP) and later for large hadron collider (LHC). Today, Superconducting RF has become a vital technology not only for LHC but also for high intensity and energy upgrade of isotope separator on line device (HIE-ISOLDE) and the high luminosity (HL)-LHC project. More superconducting cavities will be needed for a potential high energy (HE)-LHC or for any of the future circular collider options, which are currently under study. To meet these demands, CERN has improved its SRF infrastructure over the recent years and has started several R&D; lines including improved thin film coating techniques, high-power couplers, cold-test diagnostics, etc. This paper will give an overview of CERN's SRF activities today, and the challenges of future projects

Cavity types

In the field of particle accelerators the most common use of RF cavities is to increase the particle velocity of traversing particles. This feature makes them one of the core ingredients of every accelerator, and in the case of linear accelerators they are even the dominant machine component. Since there are many different types of accelerator, RF cavities have been optimized for different purposes and with different abilities, e.g., cavities with fixed or variable RF frequency, cavities for short or long pulses/CW operation, superconducting and normal-conducting cavities. This lecture starts with a brief historical introduction and an explanation on how to get from Maxwell's equations to a simple cavity. Then, cavities will be classified by the type of mode that is employed for acceleration, and an explanation is given as to why certain modes are used in particular cavity types. The lecture will close with a comparison of normal versus superconducting cavities and a few words on the actual power consumption of superconducting cavities

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

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 from a few kilo Volts up to 100 million volts per metre using frequencies from a few Million Hertz up to 10s of Gigahertz. Depending on the specific use case their design and the used materials may be very different but they can all be classified using a well-established set of RF cavity characteristics. This lecture will derive these basic quantities from Maxwell’s equations and give examples of various cavity types. Furthermore, the description of an RF cavity via lumped circuit parameters will be introduced

Strahlhalo in hochintensiven Hadronenlinacs

Das Ziel dieser Arbeit ist, die relevantesten Mechanismen der Haloentwicklung für Teilchenstrahlen in Hochintensitätslinearbeschleunigern zu behandeln. In der Einleitung werden die vielfältigen Anwendungen dieser Linearbeschleuniger (kurz: Linac) vorgestellt. Es wird weiterhin erklärt warum im Falle der CERN Studie zur Konstruktion eines supraleitenden Protonenlinacs (SPL) ein Linac gewählt wurde um einen hochintensiven Protonenstrahl zu liefern, anstatt eines anderen Beschleunigertyps. Anschließend werden die grundlegenden Gleichungen abgeleitet, welche zum Verständnis der Haloentwicklung benötigt werden. Diese Gleichungen werden dann benutzt um den Einfluss von anfänglicher und statistisch verteilter Strahlfehlanpassung auf hochintensive Teilchenstrahlen zu untersuchen. Grundlegende Konzepte wie: das Teilchen-Kern Modell (particle-core model), Enveloppenmoden, parametrische Resonanzen, der "freie Energie" Ansatz und die Idee der Kern-Kern Resonanzen werden eingeführt und erweitert um Teilchenstrahlen in realistischen Fokussierungskanälen zu studieren. Eine Grundidee dieser Arbeit ist, das Strahlverhalten nicht nur in vereinfachten theoretischen Fokussierungsstrukturen zu beschreiben, sondern die Strahldynamik in realistischen Beschleunigern zu untersuchen. Alle Effekte welche mit vereinfachten analytischen Modellen abgeleiten werden, werden so mit beobachtbaren Effekten in Linearbeschleunigern in Zusammenhang gebracht. Dieser Ansatz bringt es mit sich, dass leistungsfähige Simulationsprogramme benutzt werden um die Trajektorien der äußersten Randteilchen einer Verteilung zu verfolgen, welche aus bis zu 100 Millionen Makropartikeln besteht. Gegen Ende der Arbeit wird eine Reihe von Regeln aufgestellt und es wird aufgezeigt, welchen Einfluss diese Regeln auf das Design eines typischen Linacs für hochintensive Teilchenstrahlen (den CERN SPL) hat. Die Beispiele in dieser Arbeit beziehen sich auf zwei Entwicklungsstadien dieses Linearbeschleunigers: den ersten konzeptionellen Designreport (SPL I) und den zweiten revidierten Report (SPL II).This document aims to cover the most relevant mechanisms for the development of beam halo in high-intensity hadron linacs. The introduction will outline the various applications of high-intensity linacs and it will explain why, in the case of the CERN Superconducting Proton Linac (SPL) study a linac was chosen to provide a high-power beam, rather than a different kind of accelerator. The basic equations, needed for the understanding of halo development will be derived and employed to study the effects of initial and distributed mismatch on high-current beams. The basic concepts of the particle-core model, envelope modes, parametric resonances, the free-energy approach, and the idea of core-core resonances will be introduced and extended to study beams in realistic linac lattices. The approach taken is to study the behavior of beams not only in simplified theoretical focusing structures but to highlight the beam dynamics in realistic accelerators. All effects which are described and derived with simplified analytic models, are tested in realistic lattices and are thus related to observable effects in linear accelerators. This approach involves the use of high-performance particle tracking codes, which are needed to simulate the behavior of the outermost particles in distributions of up to 100 million macro particles. In the end a set of design rules will be established and their impact on the design of a typical high-intensity machine, the CERN SPL, will be shown. The examples given in this document refer to two different design evolutions of the SPL study: the first conceptual design report (SPL I) and the second conceptual design report (SPL II)

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

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 from a few kilo Volts up to 100 million volts per metre using frequencies from a few Million Hertz up to 10s of Gigahertz. Depending on the specific use case their design and the used materials may be very different but they can all be classified using a well-established set of RF cavity characteristics. This lecture will derive these basic quantities from Maxwell’s equations and give examples of various cavity types. Furthermore, the description of an RF cavity via lumped circuit parameters will be introduced