Query: Introduction to rf linear accelerators

title: Introduction to rf linear accelerators
abstract: The basic features of RF linear accelerators are described. The concept of the 'loaded cavity' essential for the synchronism waveparticle, is introduced, and formulae describing the action of elec tromagnetic fields on the beam are given. The treatment of intense beams is mentioned, and various existing linear accelerators are presented as examples.

title: INTRODUCTION TO RF LINEAR ACCELERATORS
abstract: After a short introduction to applications of RF linacs and their advantages and drawbacks as opposed to circular accelerators, the model of RF resonant cavities and their excitation by RF sources or beam is introduced. Then beam dynamics notions, essential to linacs, such as transit time factor, synchronism, r.m.s. properties, matching and mismatching in linear or nonlinear forces, are presented.

title: Introduction to RF linear accelerators
abstract: After a short introduction to applications of RF linacs and their advantages and drawbacks as opposed to circular accelerators, the model of RF resonant cavities and their excitation by RF sources or beam is introduced. Then beam dynamics notions, essential to linacs, such as transit time factor, synchronism, r.m.s. properties, matching and mismatching in linear or nonlinear forces, are presented.

title: Introduction to RF linear accelerators (linacs)
abstract: The history of linear accelerators is now more than 50 years old and after a difficult start presented many remarkable successes. Theory and technology encounter difficult problems briefly presented here with the solutions so far developed on orbit stability, focusing, RF structure and beam dynamics computations. Questions still remain however about high intensity limits which, when answered, might still open a more brilliant future for these types of machine. 1 BRIEF HISTORY OF LINACS The first accelerators built for nuclear physics were of electrostatic type; such machines were efficient but limited in voltage due to electrical breakdown. In 1924 a proposal was made by Ising to add several accelerations without having anywhere the total voltage. The method was based on the use of drift tubes and time varying fields, as sketched  Drift tube accelerator of Ising Along the axis of metallic tubes, charged particles can drift without being subject to any electric field except at their ends, in the gaps between two consecutive drift tubes, according to their respective voltage V. If an accelerating voltage is applied initially to all the tubes and is switched off on each of them between the time of entrance and exit of a charged particle, the particle will receive in each gap a succession of accelerations. In practice, voltage pulses are more appropriate, as used in present day induction linacs; needless to say, however, that at the time of the proposal shape and timing of high voltage pulses were not good enough to produce a useful operation. In 1928, Wideroe proposed to replace voltage pulses by an RF voltage (with a constant frequency, the drift tube lengths have to increase with the b of the particles) The method was tested on a single drift tube (input output) and with 25 kV RF peak voltage, it was possible to observe an acceleration of 50 keV for singly charged Na and K ions. In 1931 Sloan and Lawrence built a real linac of 30 drift tubes giving to Hg ions an energy of 1.25 MeV; lengthening it later in 1934 to 36 drift tubes and increasing their voltage they reached 2.8 MeV. the intensity was of course very low and the beam quality not specified: R.F. voltage differed from Ising pulses, having no real flat top, phase stability (see Section 2) was not yet discovered and focusing was not ensured, except maybe by ES lens effect (see Section 5) No further development occurred until the war, due to the lack of proper high power RF technology (limited then to 10 MHz) and to the discovery of the cyclotron. The length of the Sloan and Lawrence machine approached 2 m with a bmax of only a few thousandths; with the 1) More details on the subject can be found in a Los Alamos report LA 11601 MS, Proton Linear Accelerators, or in a CERN Yellow Report (in French) CERN 87 09 same RF wavelength of 30 m acceleration of protons would have led to a prohibitive length. In cyclotrons, on the contrary, the spiralling of the trajectories together with some focusing effect allowed the succession of many accelerations over a limited extent, leading to the possibility of producing 10 MeV protons. The development of radars offered, after the war, pulsed high voltage equipment in the metric and centimetric wave ranges; science and technology of electromagnetism and beam dynamics of already high level were then available. The parallel development of circular accelerators (synchrocyclotrons and synchrotrons) was also helpful with the discovery of phase stability. Ginzton, Hansen, Chodorow, Slater, Walkinshaw used 3 GHz to accelerate electrons. Alvarez and Panofsky used 200 MHz for protons. 2 LONGITUDINAL MOTION. PHASE STABILITY.  The RF voltage V applied is larger and there are two phases per RF period for which the voltage has the right value Vs  When the field is rising the phase is stable since a particle arriving too early will be less accelerated and slip slightly in phase until the next gap; vice versa for a late particle. The other phase is unstable. The stable phase is called the synchronous phase phs and one has Vs Vcosph s with ph 0 corresponding to the crest (proton case) Fig. 2 Phase instability In a first approach one can replace the discrete gap configuration by an equivalent continuous interaction (in Section 5 will appear a justification) One may say that the field distribution along the axis in the successive gaps presents an analogy with a standing wave pattern, sum of a forward and a backward wave. One would then consider the interaction of the forward synchronous wave with the particles. Introducing relativity symbols and letting phs bs g s refer to the synchronous particle, one has g 1 W m0c 2 and putting dg g g s one can write, following the path of a particle, along the axis m0c 2 w d dg ds qET w cosph cosphs dph ds o c 1 b 1 bs o c dg bs g s 3 whence m0c 3 d ds bs g s 3 o dph ds qET cos ph cos phs Forgetting about the change in gs one then obtains dg 2 2qETbs g s 3 om0c sin ph phcos phs C where ET is the amplitude of the synchronous wave. Such a motion derives from the Hamiltonian H o c dg 2 2bs g s 3 qET m0c 2 sin ph phcos phs Neglecting the change in gs is only valid for heavy particles (protons and ions) for which it is slow enough. It corresponds to an acceleration fighting against a constant breaking force (or to a forced pendulum model as often presented for circular machines) One gets from it the usual stability bucket of Figs. 3 and 4; Fig. 5 shows the phase space plot relative to an operation with phs 0 (fixed point as used by Sloan and Lawrence) Taking into account the change in gs opens up the bucket and gives the so called golf club,  (notice that the coordinates used are not conjugate) Fig. 3 Classical stability bucket Fig. 4 Non accelerating bucket Fig. 5 Fixed point operation

title: High Gradient issues in S band RF Acceleration Structure for Hadrontherapy accelerators and Radio Frequency Quadrupoles
abstract: The achievement of high gradient in the linac structures is a key issue in design facility for high energy physics and other applications. This thesis is focused on the study of the high gradient limitations in the normal conducting radio frequency accelerating structures. One of the effects that could appear during high power operation of the accelerating structures is the RF vacuum arcs or breakdowns. This occurs due to the high electromagnetic fields in the structure. Such events have an impact on the structure performance and the quality of the accelerated beam. Breakdowns lead to surface damage that can detune the resonant frequency of the structure and change the phase advance between cells which is important for synchronizing the structure with the beam. Therefore, this phenomenon requires a detailed study on the dedicated developed systems.A general introduction of the RF theory and the basic concepts related to linear accelerators is given in this thesis. Some examples of the accelerating structure designs are given, the analysis of which will be carried out in subsequent chapters. The main limiting quantities and the issues related to RF breakdown phenomena are also discussed in detail. The advantages that high gradient technology offers for medical application and a summary of the current activities in the development of high gradient hadron therapy linacs are also described. The study of BD phenomenon is focused in two kinds of RF structures: a 3 GHz high gradient structure and 4 vane RFQs designed for applications in hadron therapy linacs. The results of the breakdown experiments are presented together with the instruments and facilities used.The high power tests on a 3 GHz prototype of accelerating structure for hadron therapy have been successfully performed at the CERN Sbox, and the maximum operation limit of a linac in terms of maximum achievable fields and breakdown probability have been determined. The conditioning and another measurements have been performed. The data analysis techniques used for the breakdowns localization in this structure are presented in detail in comparison with post processing results. A statistical investigation of the breakdown occurrences is also made to understand the underlying processes of these events. The data collected have been compared with CLIC X band RF prototypes results in order to estimate the structure performance. The description of the high power set up and the updates are described.A first systematic study of breakdown events in RFQs is presented. Two RFQs designed for different frequencies and applications are considered. The design features and the relative merits of these structures are discussed. The long term behaviour of the RFQs is also presented. The main changes observed during breakdown events are discussed and a technique of identification of breakdown location is proposed based on these observations. The experimental work presented in this thesis is carried out in order to compare the physics of breakdowns occurring in the high gradient accelerating structures and RFQs. These studies have been applied to determine the breakdown limitations and to predict the structure performances. The final goal of the overall breakdown research is to understand the phenomenon, to maximize the structure performance and to confirm the ability of using high gradient technologies for various applications.

title: RF linear accelerators
abstract: 1.  Topics for Linacs 6. Longitudinal Particle Dynamics 7. Transverse Particle Dynamics 8. Radiofrequency Quadrupole Linac 9. Multiparticle Dynamics with Space Charge 10. Beam Loading 11. Wakefields 12. Special Linacs and Special Techniques 13.

title: Introduction to Non linear Longitudinal Beam Dynamics
abstract: The interaction of a charged particle beam with radio frequency (RF) systems in most linear or circular accelerators is an non linear process. The large longitudinal electric fields for acceleration and longitudinal beam manipulations can only be generated thanks to the resonant build up of the field in a high quality oscillator, the RF cavity, driven by a sinusoidal and hence inherently non linear excitation. The course gives an introduction to linear and non linear longitudinal beam dynamics, deriving the equations of motion, as well as the RF potential and the Hamiltonian of the longitudinal beam dynamics. Profiting from the non linear dynamics, longitudinal beam manipulations to control bunch length, distance with multiple RF systems are shown as examples. Additionally, the distribution of the synchrotron frequencies of the particles in a bunch can be modelled thanks to the non linearity of the applied RF voltage. Doubleor even multi harmonic RF systems are a powerful technique to improve the longitudinal stability of high intensity beams.

title: Introduction to Superconducting RF Structures and the Effect of High Pressure Rinsing
abstract: This presentation begins by describing RF superconductivity and SRF accelerating structures. Then the use of superconducting RF structures in a number of accelerators around the world is reviewed; for example, the International Linear Collider (ILC) will use ~16,000 SRF cavities with ~2,000 cryomodules to get 500 GeV e+/e colliding energy. Field emission control was (and still is) a very important practical issue for SRF cavity development. It has been found that high pressure ultrapure water rinsing as a final cleaning step after chemical surface treatment resulted in consistent performance of single and multicell superconducting cavities.

title: A Brief Introduction to RF Power Sources
abstract: In previous discussion of linear acceleration, we have treated the microwave power which is used in the accelerator as a sort of magical substance which is provided upon demand in any quantity and with any time structure required. This is obviously an oversimplification. Indeed, the generation and transportation of RF power is a major industry in its own right, with customers far beyond the pedestrian world of accelerators. In this set of notes, we will briefly describe the role of klystrons, modulators, and pulse compression in the production of RF power.

title: Coupler Kick and Cavity Tilt Effects on Emittance Preservation in Linear Accelerators
abstract: The effects of the coupler kicks and the cavity tilts on the beam dynamics in long linear accelerator are studied. The dispersive and wakefield caused beam emittance dilution are analytically evaluated using two particle model of the beam. The numerical simulations for the European XFEL project are presented.  The emittance preservation in linear accelerator for Xray free electron lasers or future ee linear collider is one of the basic requirements to achieve design goals of the facilities. In an ideal linear accelerator, the required design emittance of electron beam is achieved by adiabatic damping of beam initial emittance. However, in a real accelerator the imperfections of the machine components are leading to emittance degradation along the linac [1, 2] In this paper, we consider the emittance dilution of the beam caused by the accelerating sections random tilts and the RF coupler wake fields. The numerical study is performed for the 1.3 GHz superconducting main linear accelerator of European XFEL project  The cavity random tilts leads to the beam coherent oscillations and the wake field and chromatic emittance dilution of the beam. The interactions of the beam with couplers are exciting the monopole transverse wake fields resulting on the bunch orbit kicks. Using two particle model of the beam, the emittance dilutions are evaluated analytically. The numerical results for the main linac of European XFEL project are presented. EQUATION OF MOTION, PARTICLE TRACKING AND ANALYTICAL MODEL In our consideration of transverse beam dynamics in high energy linear accelerator we neglect the space charge effects and assume a rigid longitudinal distribution of the beam. Under these assumptions the equation of motion for transverse coordinate s z x of the particle with longitudinal position z in the accelerator, position s in the bunch and small relative energy deviation s z can be written as F G 1 Kx 1 x x (1) where derivative is over position z in the linac, and are the nominal beam energy and acceleration gradient respectively (in terms of relativistic Lorenz factor K is the normalized quadrupole fields. The function G represents the on axis deflecting monopole field generated by the randomly tilted cavities and the RF coupler wakefields. The function F represents the transverse dipole wakefields excited by interaction of offaxis beam with the cavities and couplers. In terms of beam and accelerator parameter the functions G and F can be written as s z W E eQ z s G 0 r k (2)