Simulation, measurement and mitigation of the beam induced … · 2016. 11. 17. · Several...

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Master Thesis

Simulation, measurement and mitigation ofthe beam induced power loss in the SPS

injection kickers

Mario Beck

Supervisor: Prof. Dr.-Ing. John JelonnekDr. Giovanni Rumolo

Period: 01.04.2015 – 23.09.2015

Geneva, 23.09.2015

Post adress: Institut für Hochfrequenztechnik und Elektronik Tel.: +49 (0) 721 608 4 2522Kaiserstraße 12 Secr.: +49 (0) 721 608 4 2523D-76131 Karlsruhe Fax: +49 (0) 721 608 4 5027

E-Mail: [email protected]: Engesserstraße 5, Geb. 30.10 Web: www.ihe.kit.edu

KIT – University of the State of Baden-Wuerttemberg and National Laboratory of the Helmholtz Association www.kit.edu

Declaration

I hereby declare that I wrote my Master Thesis on my own and that I have followed the regulationsrelating to good scientific practice of the Karlsruhe Institute of Technology (KIT) in its latest form.I did not use any unacknowledged sources or means and I marked all references I used literally orby content.

Geneva, 23.09.2015

Mario Beck

Abstract

The kickers, used to impart fast deflection to the beam in an accelerator, may suffer from high heat-ing due to beam induced power loss created by their large impedance. In order to reduce the powerloss in the SPS injection kickers (MKP-S and MKP-L), their impedance is investigated using theCST Wakefield Solver.Therefore in this work, the existing model of the MKP-S kicker is compared to measurements andthen refined. The influence of transition pieces, installed inside the measured tank, is investigatedemploying simulations. The impact of the decoupling network, between the HV-conductor and theGND-conductor, is investigated using lumped element networks in the simulation. The effect onthe impedance of measuring two kickers in series is investigated executing simulations. The im-provements made to the MKP-S model are translated to the MKP-L model.The power loss reduction achievable through offsetting the beam out of the centre of the kickersaperture in the direction of the ground conductor is investigated by simulations for both kickers.The results are validated through measurements on the MKP-S: An MKP-L was not available formeasurements. Calculations show that the maximal power loss reduction achievable by that mea-sure for the MKP-L is 30%.Several serigraphy designs are introduced, simulated and their feasibility is discussed. The mostpromising concept, including also the transition pieces and thus shielding the cavities betweenthemselves and the kicker, is realised as a prototype and measured. The measurements prove theimpedance reduction through the serigraphy design. Calculations show that this serigraphy couldreduce the power loss in the MKP-S by 45% in the MKP-L by 70%.

Contents

1. Introduction 11.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2. Technology - Particle accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1. Purpose of accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.2. Linear accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.3. Circular accelerators - Synchrotron . . . . . . . . . . . . . . . . . . . . . 51.2.4. The CERN accelerator chain . . . . . . . . . . . . . . . . . . . . . . . . . 5

2. Essentials 92.1. Wakefields and beam coupling impedance . . . . . . . . . . . . . . . . . . . . . . 92.2. Beam structure in the SPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3. Power loss calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4. Kicker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4.1. Purpose and requirements . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4.2. Structure and function principle . . . . . . . . . . . . . . . . . . . . . . . 142.4.3. Heating issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3. Electromagnetic simulations of the MKPs 213.1. Kicker model for the simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.1. Initial model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.1.2. Influence of the transition pieces . . . . . . . . . . . . . . . . . . . . . . . 243.1.3. Influence of the decoupling network . . . . . . . . . . . . . . . . . . . . . 253.1.4. Transfer on MKP-L model . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1.5. Influence of two kickers in series . . . . . . . . . . . . . . . . . . . . . . . 26

3.2. Effect on impedance of the beam offset . . . . . . . . . . . . . . . . . . . . . . . 263.3. Effect on impedance of the serigraphy . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3.1. MKE serigraphy applied to the MKP-S . . . . . . . . . . . . . . . . . . . 283.3.2. Longitudinal serigraphy coupler . . . . . . . . . . . . . . . . . . . . . . . 293.3.3. Longitudinal serigraphy coupler between transition pieces . . . . . . . . . 343.3.4. Longitudinal serigraphy coupler with wires . . . . . . . . . . . . . . . . . 383.3.5. Transversal serigraphy coupler . . . . . . . . . . . . . . . . . . . . . . . . 38

4. Bench measurements of the MKP-S impedance 414.1. Measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.2. Initial impedance measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

i

ii Contents

4.3. Beam offset impedance measurements . . . . . . . . . . . . . . . . . . . . . . . . 444.4. Serigraphy impedance measurements . . . . . . . . . . . . . . . . . . . . . . . . . 47

5. Power loss reduction in the MKPs 515.1. Effect of the beam offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.2. Effect of the serigraphy options . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6. Conclusion 55

A. Ferrite dimensions 57

B. Ferrite Ferroxcube 8C11 data sheet 61

C. Ferrite material properties for the simulation 65

1. Introduction

This chapter first gives the motivation for this thesis and afterwards gives a short introduction intothe accelerator technology relevant to this project.

1.1. Motivation

In circular particle accelerators, injection and extraction of the particle beam is usually performedusing the so called kicker magnets. The kicker can thus be described as a device that deflects theparticle beam into or out of a circular accelerator. A kicker is not involved in the accelerationprocess. It is generally only pulsed once per accelerating cycle. However, since the device is situ-ated along the beam path, the beam passes through it every turn. In order to produce the magneticfield that steers the beam, the kicker contains ferrites. Particles travelling in the accelerator induceelectro magnetic fields in it. This fields lead to a magnetization of the ferrite, which heats up thematerial. Passing continually through the kicker during the acceleration phase, the beam leads to asteady increase of the kicker temperature. Thus, it can also be described as beam power loss.A problem is now that the ferrite starts to outgas above a certain temperature. Outgassing describesthe release of molecules out of the material. One direct result of this effect is the degradation ofthe vacuum in the accelerator. That has a possible impact on the beam quality due to the increasedcollision rate with the molecules of the rest gas. Another risk of the heating is, that once the temper-ature of the ferrite reaches the Curie temperature, the kicker fails and there would be no possibilityto properly steer the beam. To avoid that scenario, there is a protection interlock system that dumpsthe beam once a certain temperature level is reached in the kicker. Because the field induced by thebeam becomes stronger with the amount of particles in the beam, the degree of the heating highlydepends on the beam intensity. So kicker heating issues may limit plans to operate the acceleratorwith higher intensities. Hence a solution for that problem is needed. An actual measurement of thekickers increasing temperature of the kicker and the degrading vacuum is displayed in figure 1.1.Some kickers have already been equipped with active external water cooling to bring down thetemperature [ABC+04]. However due to space limitations that is not possible for all kicker types.Another measure, which has already been implemented to reduce the heating, is ferrite shielding.The idea of this approach is to prevent the beam induced field from penetrating the ferrite. But dueto different kicker layouts the existing shielding can not be easily transferred from one kicker toanother.In this thesis, techniques to overcome the beam induced heating in the kickers are investigated. Inparticular the shielding approach will be further pursued.Therefore a short introduction into the accelerator technology is given in the continuation of this

1

2 1. Introduction

Time [h]0 2 4 6 8 10 12 14

Pres

sure

[nb

ar]

0.2

0.3

0.4

0.5

0.6

0.7

Tem

pera

ture

[°C

]

50

52

54

56

58

60

Figure 1.1.: Vacuum degradation (blue curve) and rise of temperature (red curve) of four MKP-Ltype injection kicker in a vacuum tank (MKP.11955) over an operation duration of 14hours in 2015. Note that the slow change in vacuum is related to the ferrite temperaturewhereas the fast change in vacuum is not. Data source: CERN TIMBER.

chapter. The following chapter explains the theory of wakefields and impedances as well as thepower loss calculation. Also the essentials of a kicker are discussed. Chapter 3 then describes thekicker model for the simulations and its improvements. After that, the executed simulations aredocumented. The next chapter verifies the simulations by measurements. In chapter 5 the powerloss reduction for the proposed changes is calculated. Finally chapter 6 concludes the achievementsof the thesis and summarises the results. Also, an outlook to further tasks is given.

1.2. Technology - Particle accelerators

This project was carried out at CERN. The CERN (Conseil Européen pour la Recherche Nucléaire)is the European organization for particle physics research. Its purpose is to perform fundamentalphysical research, with the aim to better understand the structure of the universe. Thus its maintask is to provide and operate the world’s biggest particle accelerators. Hence, and since the thesisin addition discusses a component of an accelerator, a short introduction into particle acceleratorsis given.

1.2. Technology - Particle accelerators 3

1.2.1. Purpose of accelerators

Accelerators are devices that increase the energy of particles, with the chief aim to create the con-ditions to study very small structures. They are used in medicine and industry, but their mainpurpose is to search the fundamental particles. For acceleration the particles are grouped togetherin so called bunches of particles. All the bunches circulating in an accelerator form the particlebeam. The search for fundamental particles is carried out by letting the accelerated beams collide.Collisions can either be with a fixed target, where the particle beam hits a block of known mate-rial, or between counter propagating beams. As a product of the collisions, fundamental particlesare created and examined through detectors. Hence, detectors can be described as microscopesfor the smallest structures. The higher the collision energy, the smaller the observable de Brogliewavelength λ of the fundamental particles get. This can seen on equation 1.1 [Wie15].

λ =h

p=h · cE

(1.1)

Here h is the Planck constant, p the momentum, c is the speed of light and E the energy of theparticle. As the energy is also described by E = m · c2 it is evident, that the higher the energy, theheavier and energy-richer the discoverable particles can get [Hin08].There are multiple types of particle accelerators each one with its own advantages and drawbacks.At CERN only linear accelerators and synchrotrons are used. The discussion of these acceleratorsis kept short, as there is plenty of literature covering this topics in depth. Other accelerator types,together with a deeper discussion of the presented machines, can be found for example in [Wie15].Please note that the term machine is used as a synonym for particle accelerators here, as that iscustomary in the accelerator physics.

1.2.2. Linear accelerators

The basic idea of particle accelerators is simple: Electro-magnetic fields are used to guide chargedparticles on wanted trajectories and increase their energy. The first machines used an electrostaticfield for the acceleration [Wie15]. The high voltage, which would be needed to accelerate particlesto very high energies using this technique, is hardly produceable. That is why nowadays highfrequency alternating voltage fields are used. The approach hereby is to use the same voltagemultiple times to accelerate the particles. This technique used in a linear arrangement makes alinear accelerator. It has to be pointed out that the terms LINear ACcelerator and LINAC are onlyused for a linear arrangement of a machine in combination with Radio-Frequency-acceleration(RF-acceleration). They are not used for linear machines using electrostatic acceleration to speedup the particles [Hin08].Here, we will focus on the design as described by Widerøe [Wid28] and on cavity resonators. Thelast one mentioned is a modern linear accelerator concept, that is using standing waves at higherfrequencies to accelerate the particles. All listed are used to accelerate protons and ions and areutilised by CERN.

4 1. Introduction

The Widerøe design

The Widerøe structure consists of electrodes in form of tubes, the so called drift tubes. Like all partsof an accelerator around the particles, they are placed in vacuum to avoid unwanted collisions withgas elements. The particles to accelerate now fly in bunches through these drift tubes. As the tubesform a Faraday cage, particles travelling through them, are not influenced by any field and passthrough at constant speed. Between the tubes however, the particle bunches see an electric fieldand are accelerated by it. To make sure that the particle bunches always gain energy the varyingfield of the tubes has to be synchronized with the traverse of the particle. This is done by an RF-generator that brings them periodically to a positive or negative electrical potential. To ensure anaccelerating voltage direction between the tubes, the time of flight from one gap to another has to beexactly half an RF frequency period [Wid28]. This is achieved by adjusting the drift tubes length.As the particles become faster the further they are accelerated, but the RF period stays the same,the drift tubes have to get longer, the further they are away from the source. This is also shown infigure 1.2.

source

RF

++ - -

beam axis

++++++++

protons

source

RF

-- + +

beam axis

++++++++

protons

Figure 1.2.: Principle of the Widerøe LINAC. The time between the two figures is half a period.The red arrows show the direction of the acceleration between the tubes.Source: wikipedia.org/wiki/Linearbeschleuniger.

Cavity resonators

Another way to increase the energy of particles is to use a cavity resonator. Mostly a cylindricalcavity, rotationally symmetric around the beam axis is used, which is terminated with conductingwalls. Due to electrically conducting walls, it houses a standing wave. The most important modefor acceleration in the cavity is the TM010 mode [Hin08]: This mode contains the acceleratingelectrical field in longitudinal direction. Hereby the resonance frequency is approximately definedby the inner radius not by the length [Hin08]. That results in a relatively compact design. Anotheradvantage is that the cavity can be adjusted to different particle velocities by controlling the phase


in the resonator. Thus multiple cavities can be connected in series via drift tubes to achieve higherenergies.

1.2.3. Circular accelerators - Synchrotron

It is obvious that linear accelerators have to be very long to achieve high particle energies. Theidea behind circular accelerators is to use the accelerator line multiple times instead of once as inthe linear case [Hin08]. Thus, higher energies can be achieved while occupying less space. Since,the beam has to be moved from one accelerator into another following a curved trajectory, effortshave to be made to bend the beam. Here only the synchrotron is discussed, as it is the only one ofrelevance for this thesis.The synchrotron uses deflecting magnets in a circular arrangement in order to bend the beam.It has to be operated with a pre-accelerator [Hin08]. To accelerate the particles mostly cavitiesare used. Every turn the beam gets more energized. To keep the particle on its orbit the fieldof the deflecting magnets has to be adjusted after every rotation. This enlargement of the field istherefore proportional to the momentum of the particles and thus has to be synchronous to its energy(synchro-tron) [Wie15]. As the magnetic field achievable, even with superconducting magnets, islimited, the circumference has to becomes larger, in order to reach higher energies.A disadvantage is that, because the beam is constantly bent, the particles lose energy [Hin08]. Thisloss of energy has to be compensated by the acceleration.A synchrotron can be operate as a storage ring, when the beam is not accelerated but kept at aconstant energy level.CERN’s Super Proton Synchrotron (SPS) which will be frequently referred to in this thesis, is asynchrotron with 7 km circumference.

1.2.4. The CERN accelerator chain

As all accelerators have a limited dynamic range of particle energy, several accelerators can becascaded in order to to accelerate the particles to very high energies. The CERN accelerator chainallows accelerating protons to a maximal energy of 6.5 TeV. A sketch of it is displayed in figure 1.3.At the moment, CERN runs two linear accelerators, four synchrotrons and one collider. Dependingon particle type and experiment, one LINAC is combined with up to three synchrotrons. Directlyafter the sources, the LINACs come first in the accelerator chain. LINAC2 is connected to theproton source while the ion source feeds LINAC3. The synchrotrons then, after further addingenergy to the particles, deliver them either to the next item in the chain or to experiments. Theseexperiments use for example beam impacts with fixed targets. As they are not directly related tothis thesis, experiments are not further discussed here.The Proton Synchrotron (PS) and the SPS are able to accelerate a single beam of either protons orions. On the contrary the Proton Synchrotron Booster (PSB) only accelerates protons delivered byLINAC2 whereas the Low Energy Ion Ring (LEIR) only accelerates ions provided by LINAC3.The Large Hydron Collider (LHC) takes a special stand as it functions as well as an accelerator

6 1. Introduction

with two counter-rotating rings or as a collider at four intersecting points of these rings. Whenthe proton or ion particle beam is delivered to the LHC, the other machines need to be used aspre-accelerators. The SPS is the last item in the chain and delivers consecutively two beams to theLHC, one fore each ring. In the LHC, they are first brought to higher energies and then to collisionat the four intersections where the experiments ALICE, ATLAS, CMS and LHCb are installed. Asboth beams can be accelerated up to 6.5 TeV, the maximum center-of-mass energy is 13 GeV.


Figure 1.3.: The CERN accelerator chain. Source: jetgoodson.com/thesisGallery.html

8 1. Introduction

2. Essentials

This chapter first gives an introduction into wakefields and impedances. After that, the beam struc-ture in the SPS is explained. In section 2.3, this information is used to derive the calculation ofpower loss in an accelerator. At the end, the description of the kicker device can be found.

2.1. Wakefields and beam coupling impedance

This section follows [ZRR13] and [Wie15] in the derivation of the wakefields.Assume a charged particle bunch is travelling through a beam pipe at high energy. Further, the beampipe is first assumed to be a uniform and perfectly conducting tube in vacuum. Flying through thetube, the charged particles interact with it. The electrical field, extending from the bunch to thewalls of the beam pipe, is shown in figure 2.1 on the left side. The bunch induces a longitudinalelectrical field [Cha93]. As the beam moves on the field follows it, which is easily possible in aperfectly conducting tube.Now the beam pipe is assumed to be resistive. In this case, the electric field induced by the bunch istrailing the bunch [Wie15]. This delay, but also any change of tube diameter or material disturbingthe following field, leads to the creation of wakefields. This is sketched in figure 2.1 on the rightside. These wakefiels now interact electromagnetically with the charged particles themselves. Thisleads to instabilities of the particle beam in accelerators [Cha93]. The field induced into the lossypipe, leads to an energy loss of the beam and heats up the pipe. As the field also influences chargesin the beam pipe, it can also be described as an image current following the beam [Uma89].To describe the wakefield mathematically, a test particle q should be influenced by the wakefieldcreated by a particle q0. Both particles may be situated on the beam axis and flying with the speed oflight c. q should follow q0 by the distance z. A wake function describes the effect that the wakefieldcreated by q0 has on q. The longitudinal wake function W||(z) is now achieved by integrating thelongitudinal (in beam direction) force F|| acting on the test particle over the length L of the structurethe particles are flying trough (s(0, L)) [ZRR13].

W||(z) =1

q0q

∫ L

0

F||(s, z) ds (2.1)

The force can also be described as q multiplied by E||, the longitudinal electrical field induced byq0 [ZRR13]. Plugging that into formula 2.1 leads to formula 2.2.

W||(z) =1

q0

∫ L

0

E||(s, z) ds (2.2)

9

10 2. Essentials

++++++++

particle bunch

beam axis

beam pipe wall wakefield

Figure 2.1.: Creation of wakefields due to the interaction of a charges with their environment, incombination with a change of the beam pipe diameter. Source: [Wie15]

Here only the wakefield longitudinal direction is considered, as it is the only one relevant for thefollowing calculations. Formulas for the transversal plan can for example be found in [CMTZ13].Compared to the wakefields, which describe the interaction of the particles with their environmentin the time domain, the impedance describes this interaction in the frequency domain [Wie15].Thus, the longitudinal impedance Z||(ω) can be found by transforming the longitudinal wake func-tion W||(z) into the frequency domain [ZRR13]:

Z||(ω) =

∫ ∞−∞

W||(z)e−jωz

cdz

c(2.3)

Because of its relation to the wakefields, this impedance is also referred to as beam couplingimpedance. Using formula 2.3, changes in the diameter, or material surrounding the beam,can be described as a frequency dependent impedance. Thus, all sections in an acceleratorcan be described as impedances. The unit of the impedance is Ohm and its value is stronglydependent of the material, the size of the section and the frequency investigated [Cha93]. Intensecoupling and resulting out of that high energy losses, can be observed if the beam and thesection of the accelerator have spectral components in the same frequency area [Wie15]. Thisphenomenon is counted to the collective effects which described the mutual influencing of particles.

2.2. Beam structure in the SPS

The beam’s shape in time and frequency domain is prespecified by the experiments and thus can notbe changed. First, the beam is described in the time domain. Two proton beam types are acceleratedin the SPS. A beam that has bunches of particles spaced by 25 ns and one that contains spaces of50 ns. The 50 ns version is simply achieved by leaving out every second bunch of the 25 ns beam.So, the space in the machine can also be described as divided into 25 ns slots. 72 bunches in a rowform a so called train. This corresponds to one PS fill that is injected into the SPS. When the SPSis filled, it houses 4 trains spaced by 225 ns (9 slots) as displayed in 2.2. In total that leads to a

2.2. Beam structure in the SPS 11

bunc

hin

tens

ity

time1800 ns 225 ns

4 x 72 bunches,25 ns spacing

train

Figure 2.2.: The 25 ns SPS-beam composition in the time domain.

time domain beam length of 72 · 4 · 25ns + 3 · 225ns = 7.875µs. Travelling with the speed of light,a particle needs approximately 23µs to travel around the 7 km long accelerator. Thus, the wholebeam occupies around 1/3 of the machine.The particles in one bunch are assumed to be Gaussian distributed, with a standard deviation of0.666 ns (∼ 0.2 m) [ZRR13] in the longitudinal direction. This is called the average bunch lengthσ. In figure 2.3 the Fourier transform of the 25 ns beam into the frequency domain is shown. The

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency [GHz]

Nor

mal

ized

mag

nitu

de

Beam spectrumBunch spectrum

Figure 2.3.: Spectra of the 25 ns beam and a bunch in the SPS. Source: [ZRR13]

peaks with 40 MHz spacing refer to the 25 ns bunch spacing in the time domain. The figure alsoshows that, as expected, the whole beam spectrum is enveloped by the Gaussian distribution thatrepresents the spectrum of the Gaussian bunch.

12 2. Essentials

2.3. Power loss calculation

The derivation of the power loss in this thesis follows [ZRR13].In order to calculate the power loss, first the energy loss for a bunch passing once through an accel-erator structure is derived. The total energy lossEL of a bunch of particles with the distribution λ(z)

can be found, by integrating its longitudinal wake function over all particles [ZRR13]. Therefore,it is assumed that the bunch interacts with itself. To take that into account the bunch is divided upinto slices. A source slice eNbunchλ(z′)dz′ of the bunch shall affect a witness slice eNbunchλ(z)dz

behind it [ZRR13]. Thereby, e is the charge of a particle and Nbunch the number of particles inthe bunch, as λ(z) is assumed to be normalized to unity. Now, the wake functions of all precedingsource slices are integrated for every witness slice. That results in the energy influencing everywitness slice and thus being lost from the source slices [ZRR13]. To achieve the total energy loss,that energy is then integrated over the full bunch extension as shown in formula 2.4.

EL = e2N2bunch

∫ ∞−∞

λ(z)dz

∫ ∞−∞

λ(z′)W||(z − z′)dz′. (2.4)

In a circular accelerator the bunch goes trough the same element multiple times. In this scenario,to calculate the total lost energy, the revolutions have to be taken into account, too. Supposing thebunch rotates k times in an accelerator with the circumference C, adding up all the turns leads to:

EL =e2N2

bunch

2π

∫ ∞−∞

λ(z)dz

∫ ∞−∞

λ(z′)∞∑

k=−∞

W||(kC + z − z′)dz′. (2.5)

The energy loss can also be represented in the frequency domain using impedances (see section2.1). This is done by applying the Fourier transformation. Using formula 2.5 that results to:

EL =e2N2

bunchω0

2π

∞∑p=−∞

(|λ(pω0)|2Re[Z||(pω0)]). (2.6)

Here λ(pω0) is the frequency domain representation of λ(z) and Z||(pω0) the longitudinalimpedance of the structure, the particle bunch is travelling trough.Multiplying equation 2.6 with the frequency f0 leads to the power loss WL in this device [ZRR13].f0 thereby is the frequency with which the particle bunch is rotating trough an accelerator with thecircumference C. If the beam is approximated as a number of consecutive bunches nbunches, thatleads to the single bunch approximation (SBA) of the beam power loss:

WLSBA= nbunches(f0eNbunch)2

∞∑p=−∞

(|λ(pω0)|2Re[Z||(pω0)]). (2.7)

However, this formula is only valid if the wakefields induced by one bunch are assumed to vanishbefore the next bunch passes by. [ZRR13].If that is not the case, the beam spectrum has to be taken into account. This is done by replacingλ(ω) with the spectrum of the beam Λ(ω). Also the number of particles has to be adjusted to the

2.4. Kicker 13

total number of particles in the beam Nbeam = nbunches ·Nbunch. This changes lead to the powerloss of the beam of:

WL = (f0eNbeam)2∞∑

p=−∞

(|Λ(pω0)|2Re[Z||(pω0)]). (2.8)

2.4. Kicker

This section deals with the kicker device. Therefore, first its purpose and requirements are describedand after that its structure and function principle. In the end, the problem of heating and heatingreduction techniques, already broached in the introduction, are investigated in depth.

2.4.1. Purpose and requirements

As described before, the main purpose of a kicker is to deflect the beam into or out of an accelerator,using an electromagnetic field. Kickers for extraction and injection are situated within the acceler-ator itself in the so called injection or extraction regions of the ring, which physically include theconnection to the transfer lines between two accelerators.For the extraction case, the kicker imparts an angle to the beam which diverts it from the beampipes middle axis and eventually out of the accelerator [Hin08].In the injection case, the kicker deflects the beam onto the beam axis of the circular accelerators.Extraction and injection are usually done within a single turn. Thus, the kickers are only activeonce during the transfer of each beam / train and inactive during its acceleration.In the SPS, the extraction kicker is called MKE - Magnetic Kicker for Extraction. The injectionkicker is called MKP Magnetic Kicker for Protons.Another purpose of a kicker is to dump the beam when needed or desired. The MKD - MagneticKicker for Dumping in the SPS is designed for that [FHS73]. When fired, it steers the particlesagainst an absorber.Here we concentrate on the MKP kickers, as they cause the biggest heating problems at the moment(see figure 1.1). Also the rise time τ , in which a kicker has to be able to obtain it’s maximal fieldstrength, is the shortest for this type. As explained in section 2.2, the time between two bunch trainshas to be 225 ns. Now the scenario, that three trains are already in the SPS and a fourth is preparedin the PS, is considered. This set-up is clarified in figure 2.4. The MKP then has to inject the PSfill as a fourth train with 225 ns distance to the last bunch in the SPS. Thereby, it must not disturbthe already circulating particles. Thus, the complete magnetic field has to be reached in less then225 ns and has to stay constant over the train length. The price to pay for that fast rise time is, thathigh magnetic fields cannot be realised [Duc05]. The pulse should also show a flat top in order touniformly deflect the beam [FFH+76].

14 2. Essentials

SPS

PS

kick

erfi

eld

bunc

hin

tens

itybu

nch

inte

nsity

time

1800 ns

225 ns

72 bunches,25 ns spacing

train

Figure 2.4.: SPS MKP kicker field.

2.4.2. Structure and function principle

The kickers used in the SPS are fast pulsed transmission line kickers. They are called like that,because they are constructed to approximate the schematic of a coaxial cable [BDF+11]. Hence,the energizing current pulse is minimally distorted [Bar]. The basic task of a kicker is to create amagnetic field, perpendicular to the beam axis. As the beam consists of moving particles, travellingthrough that field, the Lorentz force deflects it perpendicularly to the beam axis and the kicker field.As discussed in the previous section, the field has to rise and fall within 225 ns. Thus, a ferritewhose magnetic field is created by a fast current pulse, is used. That is why a kicker is also calleda fast pulsed magnet. The ferrite is C-shaped and therefore also referred to as ferrite yoke. Thebeam is travelling in the aperture of the C, experiencing the ferrites field if it is active. The set-up isshown in figure 2.5. The kicker length is along the beam axis perpendicularly to the paper plane (asshown in figure 2.6). The plate on the left in figure 2.5, in the aperture, is called the high-voltage(HV) conductor. The plate on the right is the ground (GND) conductor. Both extend over the fullkicker length. The pulse, raising the magnetic field, travels over the HV-conductor and returnstrough the ground conductor. The pulse current is depicted in red in figure 2.5, the magnetic fieldin blue. Assuming proton particles, that results in a beam deflection to the right.To emulate a coaxial cable, the kicker is divided into cells [BCC+09]. One cell is consisting ofa ferrite core sandwiched between two metal plates, the so called HV-plates. That can be seenin figure 2.6. The number and length of the cells depend on the requirements of the kicker, asexplained later. The HV-conductor is connected to the HV-plates. These are continued outside theferrite. Between them, plates connected to ground are installed as shown in figure 2.6. That formsa decoupling capacitance to ground.The schematic circuit diagram of a transmission line kicker is shown in figure 2.7. Lc represents theinductance of a kicker cell and Cc its capacitance [BDF+11]. As two ferrites are separated by onemetal plate, a cell extends from the middle of one plate to the middle of the next. Consequently aninductance is connected to ground over Cc/2. Currents travelling on the HV-conductor experience

2.4. Kicker 15

BI

beam deflection

N

S

ferrite yoke

HV-conductor GND-conductor

Figure 2.5.: Kicker function principle. The magnetic field (blue) is set up by the current (red) anddeflects the beam (black). The north- (N) and south-pole (S) of the magnetic field arealso marked.

ferrite

HV-plates

GND-plates

HV-conductor

transitionpieces

Figure 2.6.: A CAD model of the MKP kicker, cut vertically through the ferrite yoke. The over-lapping of the HV-plates, continued outside the ferrite and of the plates connected toground can be seen. That construction creates a decoupling impedance to ground. TheHV-plates are connected to the HV-conductor. The GND-plates are connected to theGND-conductor. Courtesy Lorena Vega Cid.

16 2. Essentials

that electric circuit.Using the transmission line model, the characteristic impedance Z of one cell can be calculated by[BCC+09]:

Z =

√Lc

Cc

. (2.9)

Lc Lc Lc Lc

Cc/2 Cc/2 Cc/2 Cc/2 Cc/2Cc/2 Cc/2 Cc/2

Figure 2.7.: Schematic circuit diagram of a transmission line kicker. Source: [BCC+09]

In order to rise the magnetic field, the left side of the HV-conductor is connected over a transmissionline and a switch to the pulse forming network whose task it is to create the fast rising pulse. Ithas to be matched to the impedance of the kicker in order to avoid reflections, as these reflectionscould miss-deflect the beam. The right side of the conductor is then terminated over an impedanceto ground.The filling time is the delay the current pulse needs to travel trough the whole kicker with n cells.Every cell delays the pulse with [BCC+09]:

τc =√Lc ·Cc. (2.10)

For a kicker with a HV-conductor, terminated in its characteristic impedance, the rise time τ canbe expressed as the time the edge of the pulse needs to travel through the kicker. When the edgereaches the end of the kicker, the magnetic field can be considered as completely built up. Thus,the whole kicker’s rise time can be written as τ = n · τc + tpulse where tpulse describes the currentpulses rise time.The pulse should not be degraded while travelling trough the kicker. Fast rise times require sharppulse edges. This leads to high frequencies. Due to the presence of L and C the kicker structureacts as a filter for pulses running on the HV-conductor. This is why the kicker’s cut-off frequencyfc, the pulse experiences, has to be high. Another benefit of a high fc is, that the flat-top rippleof the pulse reduces [Bar]. That is important for a consistent deviation of the beam. In reality, aparasitic inductance Lcs occurs, associated in series with Cc. fc can be calculated by [Duc05]:

fc =Z

π ·√

(Lc + 4Lcs) ·Lc

. (2.11)

2.4. Kicker 17

Lc is highly dependent on the cell length and gets higher the longer the cell gets. In order to allowsteep pulse edges, the cells have to be small. But as cells get smaller, the risk of voltage breakdownsbetween the HV-plates and the interleaved GND-plates gets higher: Another drawback is, that thecost and complexity of a kicker also increases. Hence, there is a limit in shortening the cells.Due to these restrictions and the requirements discussed before, the SPS kickers have differentdimensions [FFH+76]. The MKE and the MKD have longer cells than the MKP. The cell length ofa MKE for example is 24.5 cm but a MKP cell only measures 3.1 cm. That leads to a shorter τ forthe MKP.There are two MKP versions. They differ in the size of the aperture and length. The MKP-Lthereby has a large aperture (width 14.15 cm, height 5.4 cm) combined with 22 cells, whereasthe MKP-S a small aperture (width 10 cm, height 6.1 cm) and 17 cells. The different versionshave been developed due to space constraints in the accelerator tunnel. The complete MKP kickersystem consists of 7 MKP-S magnets and 4 MKP-L magnets. The MKP-S magnets are housed in2 vacuum tanks, one with 5 MKP-S magnets and the other with 2 MKP-S magnets. The 4 MKP-Lmagnets are in a single vacuum tank [Bar].

2.4.3. Heating issues

As described in section 2.1, wakefields are created by the beam when the structure, or the materialit passes, changes. Travelling through a kicker magnet, a beam sees a change between ferrite andmetal all the time. Thus, wakefields are created. These fields magnetize the ferrite. This can bedescribed as an alignment of the magnetic dipoles in the ferrite. This aligning creates thermal lossesin the ferrite and heats it up. A beam in the SPS revolves with a frequency of frSPS

= 43.4 kHz.So the beam passes through the kicker over 43 thousand times in a second and induces wakefieldsevery time. Therefore, the kicker is heated up.The parasitic field, induced by the beam, has to be strictly separated from the magnetic field createdby the pulse. Whereas the first only creates heat, the second steers the beam. It can be argued that,as the pulse also induces a magnetic field, it also heats up the magnet. But as the pulse is onlypresent once every fill, this effect is negligible.

Problems caused by the heating

The ferrite utilized in the kickers is Ferroxcube 8C11. As seen in appendix B, the Curie temperatureTc8C11

of that material is 125C. The high temperature induced during an accelerator run alreadycauses problems [ABC+04]. As plotted in figure 1.1, the temperature in one kicker tank rose about10C over a 14 hour run of the machine. Hereby the tank houses the vacuum, the kicker is situatedin. It has to be mentioned that the temperature probe is situated ca. 10 cm over the kicker aperture.Hence, it is possible that the temperature already exceeded Tc8C11

around the beam, where theheating is at its peak. Simulations investigating this are executed in parallel to this thesis [Bar].Heating the kicker up over Tc would lead to a temporary loss of ferrimagnetism.Another direct consequence of the heating is that the ferrite material starts to outgas. Out-gassing

18 2. Essentials

describes the effect of the desorption of molecules from the surface due to the high temperature[BCC+09]. This degrades the vacuum (shown in figure 1.1) and leads to unwanted collisions withthe beam in the SPS potentially degrading the beams lifetime.Looking at equation 2.8, it is obvious that the higher the beam intensity, the higher the powerloss gets. As the heating is proportional to the power loss, [ZRR13] that causes a problem. Forthe High-Luminosity LHC (HL-LHC) project, the intensities in all the pre-accelerators have torise [VAB+14]. This shall be achieved during the LHC Injectors Upgrade (LIU) [VAB+14]. Atthese intensities the effects the beam induced impedance has on the accelerator, already limit theoperation of the SPS [HDD+14]. Operating the machine constantly under these unprecedentedconditions is not possible without applying further heating reduction methods. Those are describedin the the following.

Heating reduction techniques

Several strategies have been pursued in order to reduce the temperature, or the heating of the ferritekickers. The MKP has not been equipped with any form of heating reduction yet, as the problemsonly occurred in recent runs.One way to get rid of the produced heat, is an active water cooling system as the MKE kickers havebeen equipped with [TBGU06]. Due to limited space around the MKPs (presence of GND-plates),this method cannot be applied to them.Also high Curie temperature ferrites (Ferroxcube 4E2) have been applied and tested [GCD+07].However, this type has a significantly lower relative permeability as the 8C11. To save costs, onegoal for measures to reduce the heating, is to reuse the already existing material [Bar]. Therefore,the approach of introducing new ferrite materials is no longer pursued.Another approach is not to get rid of the heat itself, but to prevent its cause. That means preventingunnecessary, strong wakefields from being generated. To do that, every abrupt change of materialin the kicker has to be hidden from the beam. The straight forward approach would be to cover theferrite with a conducting layer. That would enable the induced fields to follow the beam withoutproblems. Yet, the problem would be, that the layer would degrade the rise time of the magneticfield. The time the field needs to penetrate the layer would add up to the rise time [BFA+12]. Also,the HV-plates would be short circuited and lead to a non functioning kicker [Bar].To avoid this problem, a structure is employed that allows the induced fields to follow the beam bycoupling over the ferrites. As the HV-plates are not short circuted any more, the kickers operationability is not restricted. In the MKE this coupler is directly printed on the ferrite as 30µm thickstripes, using silver paste. A photo of this is shown in figure 2.8. This procedure and also the re-sulting heat reduction technique is called serigraphy [GCD+07]. Coupling over the serigraphy, theinduced fields bypass all sudden changes in material and do not create strong wakefields at almostall frequencies. To work properly, all ferrite surfaces exposed to the beam have to be equipped withserigraphy.This last explained heat reduction technique is also the approach that will be pursued in this thesisto reduce beam induced heating in the MKP kickers. Because of the different cell lengths, the trans-fer of the MKE serigraphy to the MKP is not trivial. Whatever the solution to reduce the heating

2.4. Kicker 19

Figure 2.8.: This photo shows a MKE kicker applied with serigraphy during assembly. The C-shaped HV-plates separating the cells are visible. The GND-conductor can be seen onthe left hand side of the picture. The serigraphy is also printed on the ferrite surfaceexploited to the beam from the top. Source: [BDF+11]

looks like in the end, it must not significantly impair the kickers performance.

20 2. Essentials

3. Electromagnetic simulations of the MKPs

The aim is to reduce the power loss of a kicker for a given beam intensity and spectrum. The revo-lution frequency of the accelerator as well as the charge of a proton are fixed. Looking at formula2.8 it becomes obvious that the only factor that can be changed in order to reduce the power loss isthe impedance of the kicker.To get a first idea of the longitudinal impedances of the MKP kicker, simulations using the CSTSTUDIO SUITE R© (CST) have been carried out (for this thesis in the versions 2014 and 2015).As the beam in the accelerator, causing the impedance consists out of charged particles, the CSTPARTICLE STUDIO R© (CST PS) tool is utilized. This tool reverts to the solver technologies CSTMICROWAVE STUDIO R© (CST MWS) and CST EM STUDIO R© (CST EMS) [CST]. The wake-fields created by the particle beam are calculated using the wakefield solver (WAK). During postprocessing the impedances are calculated by Fourier transforming the wake functions into the fre-quency domain [CST].Simulations comparing the impedances calculated using the WAK, with impedances calculated outof values obtained from simulating the measured setup with the CST Transient solver, were carriedout in [ZRR13]. They showed very good agreement [ZRR13]. With this justification the simulatedimpedances are here directly compared to the measured ones.This chapter first treats the modifications applied to the existing model in order to get more realisticresults, compared to the measurements. Later simulations are carried out, investigating the offsetof the beam out of the kicker centre and the effects of the proposed serigraphy designs.

3.1. Kicker model for the simulation

The model of the kicker used for the simulation is based on the one used in [ZRR13]. In this contextmainly the MKE kicker was discussed. As this thesis focuses on the MKP kicker the dimensionshad to be adjusted. However, the first measurements in section 4.2 showed a major differencebetween the simulations and the measurements. For this reason the model has been improved. Thechanges are described in this section. The model is improved for the MKP-S, as that is also thekicker the measurements were carried out on. Later the changes are transferred to the MKP-Lmodel.

3.1.1. Initial model

The basic MKP-S CST kicker model contains 17 ferrite cells with the dimensions obtained fromthe technical drawing, attached in appendix A. These yokes are separated by 5 mm metal plates

21

22 3. Electromagnetic simulations of the MKPs

with the same dimensions. All metal is simulated as a Perfect Electric Conductor (PEC). The twometal conductors extend over the length of all cells and are spaced by 100 mm. The HV-plates areconnected to the HV-conductor. This arrangement is shown in 3.1 on the left side. The simulatedbeam is situated in the middle of the aperture parallel to the conductors.In order to be able to simulate the serigraphy applied to the kicker later, the mesh of the simulationhas to be small. Due to limited memory available for the simulations, the model should be kept assmall as possible. That is why the HV-plates are not extended over the ferrite and interleaved withGND plates as seen in figure 2.6. The influence of that is later investigated using lumped elements.The beam axis is defined as the Z-direction the horizontal axis as X and the vertical one as Y. Theorigin of the coordinate system lies at the far end of the kicker with +Z facing in kicker direction.In figure 3.1 that means out of the paper plane. The positive X-direction spreads towards the GND-conductor.

X

Y

Z

Figure 3.1.: Evolution of the CST models for the MKP-S kicker. On the left the initial version andon the right the improved version with the added transmission pieces.

The model boundaries in CST PS can be chosen out of electric, magnetic, open, open with addedspace, conducting and periodic [CST] for all six sides, as shown in figure 3.2. In the machine thekicker is situated in a vacuum tank. However, the dimensions of the tank are to big to be simulatedwith a sufficient mesh. The tank is made out of stainless steel. To take it into account, the bound-aries parallel to the beam direction are chosen as electric, as seen in figure 3.2. This boundary typeoperates like PEC [CST] and emulates stainless steel. Changing the boundaries to a conducting ma-terial with the conductance of stainless steel, did not lead to different results. The two boundariesperpendicular to the beam direction are chosen to open with added space. This is done because thebeam pipes attached to the kicker are assumed to have the same characteristic impedance and noreflections occur. In CST the open boundary is a perfectly matched layer [CST]. The added spaceis vacuum that is added in order to avoid problems on the direct transition from different materialsto the boundary.The material properties of ferrite used in the simulations are those from the Ferroxcube 8C11. In[ZRR13] the magnetic properties of the ferrite have been remeasured. These data is used to refinethe 8C11 model provided by the manufacture. The table with the measured values is imported into

3.1. Kicker model for the simulation 23

Figure 3.2.: Boundaries of the MKP-S kicker CST model. The ferrites, HV-plates and conductor,lie completely in the vacuum (blue). The GND-conductor can be seen on the right sideconnected to the electric walls surrounding the kicker parallel to the beam direction.The boundaries perpendicular to it are open with added space.

CST and the curves are fitted with a second order function. The curves of the real and imaginarypermeability µ′ and µ′′ as well as of the real and imaginary permittivity ε′ and ε′′ can be found inappendix C.The sum in formula 2.8 weights the impedance of a structure (here the kicker) with the square ofthe beam spectrum. Looking at figure 2.3 leads to the conclusion, that only the part until 800 MHz

is important, as the beam spectrum is only present there. For an accelerated beam the time domainbunch length gets smaller and the bunch length in frequency domain gets wider [ZRR13]. To beable to also take changes in the bunch length into account, here frequencies up to 1 GHz are con-sidered. Nevertheless it can be stated, that impedance values under 500 MHz have a high impacton the power loss because they are strongly weighted by the squared beam spectrum. Followingthat argumentation the consistence of the model and the measurements in that region should beimproved.In order to get an idea of the accordance of simulation and measurements, the impedance curvesare ploted in figure 3.3. Here always the real part of the impedance is plotted, because only thatis needed for the power loss calculation. The high impedance from around 700 MHz to 1 GHz

occurs due to the segmentation of the ferrites [ZRR13]. The high permittivity and permeability inthe ferrite leads to the occurrence of the cell length in this frequency range. The elevation of themeasured curve around 520 MHz does not contribute to the beam power loss as discussed in section4.2. Therefore it can be neglected. For frequencies above 650 MHz the simulation shows higherimpedance values. This can be justified with the fact that the calculation of the impedance out ofthe measured data has a tolerance, too (see chapter 4.1).Comparing the simulation results of the initial model described above (blue curve), with the mea-


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

100

200

300

400

500

600

700

800

900

Frequency [GHz]

Re

Z||

[Ω]

initial modelmeasurementsmodel with transition platesmodel with lumped element network

Figure 3.3.: Development of the CST MKP-S kicker model.

surements (black curve) in the high weighted region it is obvious that between 100 MHz and300 MHz the impedance values differ. The cause of that is investigated in the next paragraph.

3.1.2. Influence of the transition pieces

The tank, the measurements were executed in, is equipped with so called transmission pieces. Theywere installed in order to shield the cavity between the vacuum tank and the kicker [CMT00]. Thepieces are connected between the tank and the kickers, as well as between the kickers in a tank andconnected to GND, as also the tank itself. To avoid voltage breakdowns they end 10 mm beforethe HV-plates of the kicker. Also they are only applied above and beneath the beam and not on itssides. Thereby, their edge aligns with the aperture edge. The transition pieces are also implied infigure 2.6, connected to the two thicker GND-plates sandwiching the whole kicker.To refine the model these transition pieces are now taken into account. Also HV-plates are attachedto the two outer ferrites to get a more realistic model. In the model the transition plates are con-nected to the GND-conductor because the GND-plates are not taken into account. The changes onthe model can be seen in figure 3.1 on the right.Applying the plates changes the kicker impedance by reducing it between 100 MHz and 300 MHz.That can be seen in figure 3.3, where the red curve represents the simulated impedance of the kickerwith transition plates.

3.1. Kicker model for the simulation 25

Kicker type Cc Lc Lcs fc Zc

MKP-S 220 pF 61.2 nH 100 nH 31 MHz 16.5 Ω

MKP-L 668 pF 104 nH 100 nH 17 MHz 12.5 Ω

Table 3.1.: Properties of the MKP types [Bar]. Zc and fc is obtained by plugging in the values informulas 2.9 and 2.11.

3.1.3. Influence of the decoupling network

The impedance simulation of the kicker shows a peak at 35 MHz which is not confirmed bythe measurements (see figure 3.3). The peak in the simulation can be explained with the HV-and GND-conductor allowing a TEM mode to spread. As the HV-conductor in the model is notconnected to anything it forms a resonator and causes the peak [ZRV12]. The connections of theHV-connector as described in section 2.4 has been left open in the measurements (see chapter 4).To investigate the peak the connection of the HV-conductor to the GND-conductor via Cc and Lcs

(see section 2.4) is taken into account, using lumped element networks between the HV-plates andthe GND-conductor. Employing lumped elements, CST connects the two conductors electricallybut not physically by a LC series circuit [CST]. The values for the MKP-S can be found in table3.1. Simulating the model with the attached lumped element networks leads to the green curvein figure 3.3. The simulated impedance curve now shows the same low frequency peaks as themeasurements. Due to the simulated LC network the TEM mode is shifted to 115 MHz, which isalso not consistent with the measurements. This inconsistency can be explained by the fact thatthe network, simulated here as lumped elements, consist out of distributed elements that are veryhard to characterize. Especially Lcs is very hard to determine and the value shown here only anapproximation for low frequencies [Bar].The lumped element network mainly influences the TEM mode on the HV-conductor. As there isno real improvement of the simulation results, but an enlargement of simulation time, the modelwithout lumped elements is used for the further simulations.

3.1.4. Transfer on MKP-L model

The MKP-L kicker CST model is now created in the same way as the MKP-S model before. TheMKP-L consists of 22 cells. The dimensions of the ferrites can be found in appendix A. Thetransmission plates and the lumped element network are attached. The lumped element network isincluded with the values for the MKP-L out of table 3.1. The simulated impedance curves for thesame evolution steps as for the MKP-S can be found in figure 3.4. Due to the higher amount ofcells the maximal impedance of the MKP-L is higher than the one of the MKP-S. Equipped withthe transition plates and the lumped element network the model shows similar effects as the MKP-S model. But due to the different length the TEM mode occurs at 20 MHz without the lumpedelement networks attached and at 100 MHz with them attached. Argumenting as above, the modelwith transition plates is used for further simulations.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

200

400

600

800

1000

1200

1400

1600

1800

Frequency [GHz]

Re

Z||

[Ω]

initial modelmodel with transition platesmodel with lumped element network

Figure 3.4.: Development of the CST MKP-L kicker model.

3.1.5. Influence of two kickers in series

The measured tank houses two kickers. Thus, the effect of two kickers in series to the beam, con-nected through transmission plates, is investigated using simulations. It turns out that the impedanceof two kickers in series is almost exactly the double of the impedance of one kicker. That is shownin figure 3.5. There the impedance curve of one kicker with transmission plates is shown in blackand the double of that curve in blue. The red curve shows the results of the impedance simulationfor two kickers back to back, connected via the transmission plates. It can be seen that the bluecurve and the red curve are nearly identical. With this justification the simulated values are multi-plied by two in order to compare them to measurements, or the measured values are divided by twoto compare them to the simulations.

3.2. Effect on impedance of the beam offset

In this section the offset of the beam from the centre of the kicker aperture is simulated. The beam isthereby offset in positive X-direction towards the GND-conductor, clarified in figure 3.6. In theorythat results in an impedance reduction as a larger part of the fields induced by the beam can flowthrough the GND-conductor, the closer the beam approaches it. As the GND-conductor is uniformover the whole kicker length less wakefields are created. The executed simulations confirm thetheory as seen in figure 3.7.The same simulations are effected for the MKP-L kicker model. Figure 3.8 shows the results. Sim-

3.2. Effect on impedance of the beam offset 27

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

200

400

600

800

1000

1200

1400

1600

1800

Frequency [GHz]

Re

Z||

[Ω]

impedance of two kickersimpedance of one kicker2 x impedance of one kicker

Figure 3.5.: Comparison of the simulated impedance of two MKP-S kicker models in series, withthe double impedance of one kicker model.

GND-conductorHV-conductor

ferriteX

Y

Z

beam offset

Figure 3.6.: Beam offset principle.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

100

200

300

400

500

600

700

800

900

Frequency [GHz]

Re

Z||

[Ω]

−7 mm 0 mm 5 mm10 mm20 mm30 mm40 mm

Figure 3.7.: Simulation of the MKP-S kicker with the beam offset by a given value from the aperturecenter, a positive displacement is in the direction of the ground conductor.

ilar to the MKP-S the simulated beam offset in the MKP-L also leads to an impedance reduction.

3.3. Effect on impedance of the serigraphy

Now the influence of the serigraphy on the impedance of the kicker is investigated using simu-lations. The serigraphy is implemented in CST as a tabulated surface impedance material. Itsthickness is 30µm and the conductivity is 106 S/m.

3.3.1. MKE serigraphy applied to the MKP-S

In order to get a first idea of its influence the serigraphy of the MKE is transferred onto the MKP.The result for one cell is shown in figure 3.9. The same serigraphy is installed on the inner topand bottom of the ferrite C and connected to the HV-plates as seen in figure 2.8. However, dueto the shorter length of the MKP cells the finger length of its serigraphy is only a tenth. Theimpedance simulation results can be seen in figure 3.10. The frequency of the maximum impedanceis shifted down to 420 MHz. The serigraphy thus worsens the power loss problem: It shifts the mainimpedance peak to frequencies where the beams spectrum is present. This effect occurs becauseof insufficient coupling between the serigraphy fingers due to the reduced length. Reducing the

3.3. Effect on impedance of the serigraphy 29

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

200

400

600

800

1000

1200

1400

1600

1800

Frequency [GHz]

Re

Z||

[Ω]


Figure 3.8.: Simulation of the MKP-L kicker with the beam offset by a given value from the aper-ture center, a positive displacement is in the direction of the ground conductor.

distance between the fingers in order to get a better coupling did not result in a major changedimpedance. Changing the finger width had had almost no effect on the impedance. To be applicableto the real kicker [Bar], 2 mm has been chosen for the width of all the serigraphy fingers.

serigraphy fingerdistance between fingers

GND-conductorHV-conductor HV-plateferrite

Figure 3.9.: MKP-S model cell with the MKE serigraphy. The cell is cut in the X-Z-plane to allowa view on the inner side of the ferrite yoke. The narrow spaced horizontal lines indicatethe cut.

3.3.2. Longitudinal serigraphy coupler

In order to reduce the impedance significantly a new serigraphy designed is needed. To achieve agood coupling, the serigraphy fingers should be as long as possible. The resonance frequency of


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

100

200

300

400

500

600

700

800

900

Frequency [GHz]

Re

Z||

[Ω]

Figure 3.10.: The simulated impedance of the MKP-S kicker with the MKE serigraphy (red). Theimpedance of a MKP-S kicker without serigraphy is plotted in a dashed black line asa reference.


the implied coupler should not lie on one of the beam frequency peaks seen in figure 2.3, in orderto lower the power loss. Also the HV-plates separating the ferrites must not be short circuited.Otherwise the pulse current which creates the magnetic field, would be able to travel between themand would impair the magnetic field [Bar].The resonance of the serigraphy can be calculated by considering it as a micro-strip line and theferrite as the isolator. As the ferrite is much thicker than the serigraphy width, the effective permit-tivity εeff (f) and the effective permeability µeff (f) can the be calculated by [Poz12]:

εeff (f) =ε′r(f) + 1

2and µeff (f) =

µ′r(f) + 1

2. (3.1)

These equations approximate uniform material properties surrounding the serigraphy what allowsto calculate the λ resonance of its overlapping length L using formula 3.2 [KCG07].

λ =c

f√εeff (f)µeff (f)

. (3.2)

In order to get a λ resonance at 15 MHz (ε′r ≈ 12, µ′r ≈ 400), far away from the first beam peak,the overlapping length of the serigraphy has to be around 550 mm. That is as long as the wholekicker. To employ a serigraphy with a finger length as long as the kicker, efforts to shield it from theHV-plates have to be made. Recent calculations show that the MKP-S has 7 mm of space availableon the top and bottom of the aperture and the MKP-L, due to its lower aperture, 5 mm [Bar]. Thisspace can be used to employ isolating plates where the serigraphy is printed on. This way theserigraphy can extend over the whole kicker length without short cutting the HV-plates.

serigraphy finger

distance between fingers GND-conductor

HV-conductor HV-plateferrite

transition pieces

Figure 3.11.: MKP-S kicker model with the serigraphy over the whole kicker length and connectedto the first and last HV-plates. The kicker is cut in the X-Z-plane to allow a view onthe inner side of the ferrite yokes.

Considering formula 3.2 it is obvious that the resonant length and thus the resonant frequency arehighly dependent on the electric and magnetic properties of the material, the serigraphy is situatedon. The isolation material is not chosen yet and has to fulfil special requirements to not influence thebeam [Bar]. However it will most likely be non magnetic (µ′r(f) = 0). In order to be independent


of the used material the serigraphy is simulated directly on the ferrite and the short cutting ofthe HV-plates is avoided by trimming them. The trimmed space is filled by vacuum. Executedsimulations showed that trimming the plates has no recognizable effect on the kickers impedance.This procedure has the advantage that the length can still be calculated using formula 3.2. Once thematerial is known, the resonance frequency peak of the serigraphy coupler can be placed betweentwo beam spectrum peaks by adjusting the fingers overlapping length.The long serigraphy is attached on the first and the last HV-plates and thus coupling over the wholekicker length. That set-up can be seen in figure 3.11. The distance between the finger is set to12 mm, in order to avoid voltage breakdowns between the fingers. These voltage breakdowns, couldionize the vacuum and thus lead to a voltage breakdown between HV and GND-conductor whatwould miss deflect the beam [Bar]. The influence of the serigraphy finger distance is investigatedlater.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

100

200

300

400

500

600

700

800

900

Frequency [GHz]

Re

Z||

[Ω]

Figure 3.12.: Simulated impedance of the MKP-S kicker with the serigraphy over the whole kickerlength and connected to the first and last HV-plates (red). The impedance of a MKP-Skicker without serigraphy is plotted in a dashed black line as a reference.

The results of the simulation are shown in figure 3.12. A big peak occurs at 60 MHz together withtwo smaller peaks at 14 MHz and 28 MHz (see figure 3.13). The 14 MHz and 28 MHz peaks are theλ and λ/2 resonances of the serigraphy (λ resonance expected at 15 MHz). The peak at 60 MHz

is suspected to occur due to the discontinuities between the transition pieces and the kicker. Thewakefields created there contribute to the impedance and show at 60 MHz. Thus, the cavity betweenthe transition pieces and the kicker has to be shielded to get rid of the peak at 60 MHz.


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5−50

0

50

100

150

200

250

300

350

400

450

500

Frequency [GHz]

Re

Z||

[Ω]

Figure 3.13.: Simulated impedance of the MKP-S kicker with the serigraphy over the whole kickerlength and connected to the first and last HV-plates (red) for the first 500 MHz. Theimpedance of a MKP-S kicker without serigraphy is plotted in a dashed black line asa reference.


3.3.3. Longitudinal serigraphy coupler between transition pieces

serigraphy finger

distance between fingers GND-conductor

HV-conductor HV-plateferrite

transition pieces

Figure 3.14.: MKP-S kicker model with the serigraphy between the transition pieces. The kicker iscut in the X-Z-plane to allow a view on the inner side of the ferrite yokes.

The next design proposed here is to extend the serigraphy from the first to the second transitionplate as seen in figure 3.14. Their ends are thus connected by the GND-conductor allowing couplingover the whole kicker length. The advantage of this design is, that it not only shields the ferrite butalso the cavity between transition plate and kicker. From an impedance reduction point of viewit would be best to connect the transition plates, which are both grounded by a conducting stripewithin the aperture: This would provide a continuous path for the fields induced. However, thefast rising magnetic field in the kicker would result in a significant current being induced in a loopformed by this strip and the GND-conductor. This current would produce a field in oppositionto the kickers magnetic field, which can lead to a significant increase in the field rise time [Bar].The simulated impedance of this arrangement can be found in figure 3.15. The resonance peak ofthe serigraphy can be found at 15 MHz as expected above. However the fingers only overlap by510 mm. This difference is explainable that calculating the serigraphy length by formula 3.2 onlygives an approximation for it.The distance between the finger is set to 12 mm, as before to avoid voltage breakdowns between thefingers. Changing the distance between the fingers leads to no major differences in the simulatedimpedances. As the coupling is still strong enough. That is supported by figure 3.16, where thesimulated impedance curves for the different finger distances are plotted for the first 500 MHz.The same serigraphy has been simulated on the MKP-L. As it is longer the overlapping length ofthe serigraphy fingers is now 667 mm, what should lead to a lower resonance frequency as before.The simulation of the serigraphy between the transition pieces adjusted on the MKP-L shows thesame impedance reduction effect as for the MKP-S. That is shown in figure 3.17. Figure 3.18, werethe frequency range up to 500 MHz is plotted. The resonance peak is now located at 10 MHz. Thiswas expected due to the longer overlapping of the finger.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

100

200

300

400

500

600

700

800

900

Frequency [GHz]

Re

Z||

[Ω]

Figure 3.15.: Simulated impedance of the MKP-S kicker with the serigraphy between the transitionpieces (red). The impedance of a MKP-S kicker without serigraphy is plotted in adashed black line as a reference.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0

50

100

150

200

250

300

350

400

Frequency [GHz]

Re

Z||

[Ω]

3 mm 6 mm 9 mm12 mm

Figure 3.16.: Simulated impedance of the MKP-S kicker with the serigraphy between the transitionpieces for different distances between the serigraphy fingers for the first 500 MHz.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

200

400

600

800

1000

1200

1400

1600

1800

Frequency [GHz]

Re

Z||

[Ω]

Figure 3.17.: Simulated impedance of the MKP-L kicker with the serigraphy between the transitionpieces. The impedance of a MKP-L kicker without serigraphy is plotted in a dashedblack line as a reference.


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0

100

200

300

400

500

600

Frequency [GHz]

Re

Z||

[Ω]

Figure 3.18.: Simulated impedance of the MKP-L kicker with the serigraphy between the transitionpieces for the first 500 MHz. The impedance of a MKP-L kicker without serigraphyis plotted in a dashed black line as a reference.


3.3.4. Longitudinal serigraphy coupler with wires

A way to cross the HV-plates without using an isolation plate between them is to used so calledbonding wires. These wires connect the serigraphy strips, directly attached on the ferrite, by bridg-ing over the HV-plate as seen in figure 3.19. The serigraphy is attached to the first and last HV-plate.The distance between the serigraphy fingers is again chosen to 12 mm. Simulating this approachleads to a similar impedance curve as the continuous serigraphy connected to the first and lastHV-plate, as figure 3.20 shows. Similar resonance frequencies as in figure 3.12 appear. With thesame argumentation as for the longitudinal coupler connected to the HV-plates, they are suspectedto occur because of the cavity between the transition plate and the kicker. The main peak is nowlocated at 58 MHz. The two smaller peaks, occurring because of the coupling length are situated at14 MHz and 27 MHz.



wire

Figure 3.19.: MKP-S model cells with the longitudinal wire coupler. The cells are cut in the X-Z-plane to allow a view on the inner side of the ferrite yoke. The wires bend extends inY-direction.

The wires are not applicable in the accelerator. The risk of them getting lose and then movingaround uncontrolled in the beam pipe is to high [Bar]. Thus this serigraphy design is not furtherpursed.

3.3.5. Transversal serigraphy coupler

Another idea was to implement a micro-strip coupler, coupling over the ferrite in transversal direc-tion. The coupler on one cell can be seen in figure 3.21. The serigrahy is directly attached onto theferrite. The simulated impedance, shown in figure 3.22, introduces a peak at 155 MHz and reducesthe impedance around 900 MHz by approximately 200 Ω. The impedance peak could be influencedby optimizing the coupler. But as the results are not very promising, this approach was not pursued.Also note, that the coupler already covers too much of the ferrite surface [Bar] and would not befeasible.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

100

200

300

400

500

600

700

800

900

Frequency [GHz]

Re

Z||

[Ω]

Figure 3.20.: Simulated impedance of the MKP-S kicker with the serigraphy, bridging the HV-plates by wires (red). The impedance of a MKP-S kicker without serigraphy is plottedin a dashed black line as a reference.


Bonding wires could be used to achieve better coupling [Poz12]. But as discussed before they arenot applicable to the machine.



Figure 3.21.: MKP-S model cell with the transversal coupler. The cell is cut in the X-Z-plane toallow a view on the inner side of the ferrite yoke.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

100

200

300

400

500

600

700

800

900

Frequency [GHz]

Re

Z||

[Ω]

Figure 3.22.: Simulated impedance of the MKP-S kicker with the transversal coupler serigraphy(red). The impedance of a MKP-S kicker without serigraphy is plotted in a dashedblack line as a reference.

4. Bench measurements of the MKP-Simpedance

To evaluate the simulations, impedance measurements have been executed. Measuring theimpedance of the kicker in the accelerator with the beam is not possible. With the beam onlythe overall impedance of the machine can be determined [KCG07], although it is possible to detectthe locations of the main impedance sources [BAA+13]. To measure the impedance of the kicker aspare vacuum tank, housing two MKP-S kickers is used. This spare tank is also a reserve in case theone installed in the machine breaks down. For this reason and also because the vacuum seal is veryexpensive and destroyed once the cap is removed, the opening of the tank was prohibited. Thus,two kickers had to be measured in the tank. Simulations with two kickers in series were executedto examine the impact of the second kicker. They show that the impedance simply doubles for thiscase, as described in chapter 3.

horizontal wire position adjustmentmechanism

HV-port

vacuum port

Figure 4.1.: Photo of the vacuum tank housing the kickers connected to the VNA.

41

42 4. Bench measurements of the MKP-S impedance

4.1. Measurement setup

Consisting of flying protons, the beam can be described as an ideal current source. For the mea-surements it is approximated by a pulsed current over a wire. The wire should have a diameter assmall as as possible to achieve a high line impedance, which approximates an ideal current source.But also it has to be thick enough to not sag under its own weight, as it has to be stretched throughnearly 1.7 m of vacuum tank. To achieve a relatively low losses, in the measurements a silver coatedcopper wire with a diameter of 0.5 mm has been used, as it constituted the best compromise.The wire is mounted in the middle of the kicker’s aperture where normally the beam would travel.It has to be installed in a way that it is not sagging in the middle. The ends of the wire are thenguided through the flanges of the tank and attached to a connector where the measurement equip-ment can be connected.For the measurements an Agilent Technologies E5071C vector network analyser (VNA) has beenused. The VNA is connected to the wire by a 10 dB attenuator at each end. The analyser creates adefined pulse which then travels over the wire, to simulate the beam in the kickers. Resistors willbe attached between the connectors and the wire to matched the characteristic impedance of theVNA with the cables (Z0 = 50Ω) and the kicker. In order to calculate the value of the matchingresistor the characteristic impedance ZDUT , of the wire in the device under test (DUT) has to bedetermined. In this case of the DUT is the vacuum tank with the 2 kicker magnets. ZDUT is ob-tained by connecting the VNA only to one side of the wire in the tank and leaving the other endopen and without attenuators. By considering the reflection Scattering parameter (S-parameter) S11

in the time domain, the reflection factor Γ can be determined. As the characteristic impedance ofthe VNA is known using the formula

Γ =ZDUT − Z0

ZDUT + Z0

(4.1)

the characteristic impedance of the DUT can be calculated [TWK98]. The resistance to match thewire is then calculated by Rm = ZDUT − Z0.A way to analytically determine ZDUT is to approximate the kicker as a coaxial cable. The in-ner radius d thereby represents the wires radius whereas the outer radius D is represented by thedimension of the kicker aperture. There formula to calculate ZDUT then is [Poz12]:

ZDUT/Ω = 60 · lnD

d(4.2)

The VNA measures the S-parameters of the the whole tank. To compare the measurements with thesimulations these S-parameters have to be convert into the longitudinal impedance. This is doneduring post processing using the so called log formula [Jen00]:

Z|| = −2 ·ZDUT · ln (S21). (4.3)

Where S21 is the measured forward voltage gain S-parameter. The exponential attenuation of thesignal over the distributed impedance leads to the logarithm in the formula. The derivation can befound in [KCG07].

4.2. Initial impedance measurements 43

VNA tank

MKP-S I MKP-S II

wire (0.5mm)

transition pieces

attenuator matchingresistor

Figure 4.2.: Sketch of the measuring configuration.

The complete measuring configuration can be seen in figure 4.2. As seen in the sketch the mea-surements are executed in a tank with transition pieces installed between the two kickers and alsobetween the tank and the kickers. A photo with the tank connected to the VNA connected is shownin figure 4.1. Two high voltage ports for the two kickers in the tank are underneath the tank. Also,the flanges for the vacuum pumps are visible. The HV-ports on the tank have been left open onboth sides for the measurements.The intermediate frequency (IFBW) of the VNA was set to 300 Hz for all measurements. Thefrequency resolution is 0.6 MHz.

4.2. Initial impedance measurements

Initial longitudinal impedance measurements have been executed to evaluate the simulations. Forthe power loss calculation only the real part of the longitudinal impedance is necessary. That iswhy figure 4.3 shows the real part of the longitudinal impedance measured in the configuration asdescribed above.The comparison to the simulation of one kicker can be seen in figure 3.3.As there is still a gap between the transition pieces connected to ground and the first HV-plate ofthe kicker, electromagnetic waves are able to spread between the tank and the kicker. This createsthe 520 MHz peak seen in the measurements. However, in reality this does not contribute to thepower loss as it is not a beam behaviour [ABC+04]. So the peak can be neglected.The difference in magnitude of the simulated and measured curves can be attributed to two mainreasons. First the ferrite model used for the simulations. As the measurements of the ferrites ma-terial properties have a tolerance of 20 to 30%, so do the simulations [Zan]. Second, the errortransforming the S-Parameter into the impedance values gets higher the bigger the total value of Zgets [Jen00]. Applying the improved log formula proposed in [Jen00] did not lead to any improve-ment. Nevertheless the position of the peaks over 400 MHz for measurements and simulation arein accordance.The ripple in the measurement comes from parts of the wave spreading in the ferrite, being delayedand interfering with the wave travelling in the aperture [KCG07].


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

200

400

600

800

1000

1200

1400

1600

Frequency [GHz]

Re

Z||

[Ω]

Figure 4.3.: Measured real longitudinal impedance of the vacuum tank housing two MKP-S kickers.

As discussed in section 3.1 the peaks under 20 MHz are created by the decoupling network betweenGND-connector and HV-connector introduced in section 2.4.

4.3. Beam offset impedance measurements

The simulations predict that offsetting the beam from the middle in the direction of the groundconductor brings a reduction of the longitudinal impedance. That is due to the fact that a largerpart of the wakefields travels in the ground conductor instead of the ferrite. This effect shall nowbe confirmed by measurements. Therefore the wire is moved out of the middle of the aperture bya known amount of millimetres. This adjustment mechanism can be seen in figure 4.1 on the tanksfront flange.The simulated effect of impedance reduction achieved by offsetting the beam is confirmed by themeasurements as seen in figure 4.4. Figure 4.5 shows only the offsets of 10 mm and 30 mm forlow frequencies. The transformation of the S-Parameter to the Z|| values is responsible for the non-physical negative values at the beginning of the measurement curves. It is also responsible for thebigger difference between measurements and simulations the higher the impedance value gets.In figure 4.4 a high discrepancy between simulated and measured values occurs around 520 MHz

and can be neglected as discussed above. Figure 4.5 shows that the first 350 MHz are in goodaccordance except for the simulated TEM mode peak at 35 MHz.

4.3. Beam offset impedance measurements 45

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

100

200

300

400

500

600

700

800

900

Frequency [GHz]

Re

Z||

[Ω]


Figure 4.4.: Comparison between simulation (solid) and measurements (dashed) for the beam(wire) offset from the center of the aperture, in the direction of the ground conduc-tor.


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0

50

100

150

200

250

300

350

400

Frequency [GHz]

Re

Z||

[Ω]

10 mm30 mm

Figure 4.5.: Comparison between simulation (solid) and measurements (dashed) for the beam(wire) offset from the center of the aperture, in the direction of the ground conduc-tor for the first 500 MHz.

4.4. Serigraphy impedance measurements 47

4.4. Serigraphy impedance measurements

In order to confirm the serigraphy simulations a serigraphy setup has been measured. A rectangulartube manufactured from glass epoxy, a material that is considered reasonably invisible for thefrequency range the measurement is executed in, is used. The serigraphy is painted on the inner topand bottom with the same material (silver paste) the MKE serigraphy was painted on the ferrite.The design that was chosen to measure, is the one where the serigraphy goes from the first transitionplate trough the whole kicker to the second. The sides are left untouched to not screen the HV andGND conductors. The tube is as long as the tank. The tube, seen in figure 4.6, is placed into thekickers aperture between HV and GND-conductor. The connection to GND is achieved by applyingbraids to the structure. They are later attached to the flanges. To measure the impedance of oneserigraphed kicker, the serigraphy is only pained in the region of the first kicker. The rest of thetube length is completely painted, top and bottom, to screen the second kicker. Thus, measurementsshould only show the impedance of one kicker equipped with serigraphy.

Figure 4.6.: Serigraphy insertion for MKP-S tank. The tube with the attached braids is shown in thebig picture. The painted serigraphy structure inside the tube can be seen in the upperright corner. Courtesy Lorena Vega Cid.

The measurements show the impedance reduction for the kicker shielded with serigraphy as thesimulations suggested. That can be seen in figure 4.7 where the measurements of the kicker withoutserigraphy and with it are plotted. Also the simulated impedance of the kicker with the sameserigraphy is plotted. The serigraphy shields the cavity between the transition plates and the kicker,the peak at 520 MHz does not occur. That is why the frequency range between 400 MHz and


600 MHz is in reasonable agreement for simulations and measurements.The sinusoidal overlay on the measured curve over 600 MHz appears due to imperfect matching inthat frequency area.Figure 4.8 shows the same curves as figure 4.7, focused on the first 500 MHz. The peaks created bythe decoupling network at 7 MHz and 15 MHz are visible. Due to the different dielectric propertiesof the inlay material the serigraphy resonance occurs at around 40 MHz. The higher measuredimpedance from 20 MHz to 50 MHz is suspected to be in context with the inlay used to measurethe serigraphy. Thus, this can be neglected, as a constuction like this cannot be exposed to thebeam [Bar] and should only evaluate the simulations. However it becomes obvious that whenchoosing the material isolating the serigraphy from the high voltage plate attention has to be paidon the properties of the material. Once a material is known, by adjusting the finger length of theserigraphy the resonance can be shifted to a frequency that does significantly not affect the powerloss.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

100

200

300

400

500

600

700

800

Frequency [GHz]

Re

Z||

[Ω]

kicker without serigraphy measuredkicker with serigraphy simulatedkicker with serigraphy measured

Figure 4.7.: Impedance measurement of the MKP-S kicker with the serigraphy inlay (red). Com-pared with the simulated impedance of the kicker with the same serigraphy (green) andthe measurement of the kicker without the serigraphy (black).

4.4. Serigraphy impedance measurements 49

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0

50

100

150

200

250

300

350

400

Frequency [GHz]

Re

Z||

[Ω]

kicker without serigraphy measuredkicker with serigraphy simulatedkicker with serigraphy measured

Figure 4.8.: Impedance measurement of the MKP-S kicker with the serigraphy inlay (red). Com-pared with the simulated impedance of the kicker with the same serigraphy (green) andthe measurement of the kicker without the serigraphy (black) for the first 500 MHz.

5. Power loss reduction in the MKPs

In this chapter the power loss reduction trough the proposed impedance reduction techniques shallbe discussed. The power loss is calculated using formula 2.8 for a beam with 288 bunches anda bunch intensity of 1.7e11 protons, as it was used in may 2015 [Rum]. The bunch spectrum isassumed to be Gaussian, with a standard deviation of the bunch length of 0.2 m. Thus, the bunchand the beam have the same spectra as plotted in figure 2.3.

5.1. Effect of the beam offset

The effect on the power loss by the impedance reduction through offsetting the beam and throughthe serigraphy is investigated. To be consistent only the simulated curves are used for the calcula-tions. In order to see the effect on the power loss, the power deposition following an impedancereduction technique is always given in proportion to a reference. This reference is always the modelof the kicker as it is employed in the machine at the moment. For the MKP kickers that means with-out serigraphy and with the beam in the centre of the aperture. Therefore, values smaller than onesignify a reduction of power loss, whereas values bigger than one signify an increase of power loss.The heating of the ferrite is dependent on the power loss [ZRR13] and power loss reduction leadsdirectly to heating reduction.In table 5.1 the power deposition ratio values for offsetting the beam out of the center of the MKP-Lkicker are listed. The impedance curves, the values base on, can be found in figure 3.8. As expectedfrom the impedance curves, the power loss gets less, the larger the offset gets, the nearer the beamapproaches the GND-conductor. In the machine the maximal achievable beam offset for the MKP-

Beam offset ↓ WLdx/WL0↓

dx = −7 mm 0.99dx = 5 mm 0.98dx = 10 mm 0.94dx = 20 mm 0.83dx = 30 mm 0.66dx = 40 mm 0.46

Table 5.1.: Calculated power deposition ratio through beam offset for the MKP-L kicker. The val-ues are always set in relation to the power loss of the beam in the center of the apertureof the MKP-L kicker (WL0).

L is 30 mm. At this offset the beam may already hit the accelerator in case of a miss kick [Bar].

51

52 5. Power loss reduction in the MKPs

So according to the simulations supported by the measurements, the power loss can be reduced bymaximal 34% by offsetting the beam. As the LIU project aims to increase the bunch intensity by30% [HDD+14] and the power loss depends on the square of the bunch intensity [ZRR13], this isnot enough.The gain through power loss reduction by offsetting the beam in the MKP-S kicker is even biggeras table 5.2 shows. That is due to the smaller aperture of the kicker (see section 2.4), leading tocloser distances to the GND-conductor. As the focus of heating reduction lies on the MKP-L at themoment, calculations determining the maximal beam offset for the MKP-S have not been done yet[Bar]. Assuming a feasible beam offset of 20 mm the power loss would already nearly be halved.

Beam offset ↓ WLdx/WL0 ↓

dx = −7 mm 0.93dx = 5 mm 0.86dx = 10 mm 0.77dx = 20 mm 0.56dx = 30 mm 0.32dx = 40 mm 0.11

Table 5.2.: Calculated power deposition ratio through beam offset for the MKP-S kicker. The valuesare always set in relation to the power loss of the beam in the center of the aperture ofthe MKP-S kicker (WL0).

An MKP-S kicker has a power deposition of approximately one-quarter of an MKP-L. But becausea larger aperture is required for the kicker magnet at the end of the MKP chain (see section 2.4),where the deflected beam exits the magnets, the replacement of all MLP-L kicker is not possible[Bar].

5.2. Effect of the serigraphy options

Now the power deposition reduction by applying the different simulated serigraphy designs is cal-culated. The resulting values, given in proportion to the MKP-S kicker without serigraphy, can befound in table 5.3. The MKE serigraphy applied to the MKP-S nearly doubles the power depo-sition, as it introduces a big impedance peak at 420 MHz (see figure 3.10). The other serigraphydesigns, with a power deposition ratio bigger than 1, also lead to more heating, as they introducewide frequency peaks at low frequencies (see figures 3.12, 3.20 and 3.22).The only serigraphy simulated that leads to a power loss reduction for the MKP-S, is the one ap-plied between the transition pieces, as shown in figure 3.14. Due to its low impedance values inthe weighted spectrum (see figure 3.15), which have been supported by measurements, it leads to apower deposition ratio of 0.55. Thus, it nearly halves the power loss in the kicker. The same serig-raphy design applied to the MKP-L kicker (simulated impedance curve in figures 3.17 and 3.18)leads to a power power deposition ratio of 0.27. Employing that serigaphy design on the MKP-L

5.2. Effect of the serigraphy options 53

Serigraphy design ↓ WLser/WL0 ↓MKE serigraphy transfered to the MKP-S 1.98Longitudinal serigraphy coupler attached to the HV-plates 1.22Longitudinal serigraphy coupler attached to the transition plates 0.55Longitudinal serigraphy coupler with wires 1.12Transversal serigraphy coupler 1.22

Table 5.3.: Calculated power deposition ratio for the different serigraphy designs applied to theMKP-S. The values are always set in relation to the power loss the MKP-S kicker with-out any serigraphy (WL0).

kickers would reduce the power loss by 70%.

54 5. Power loss reduction in the MKPs

6. Conclusion

The improved CST model of the kicker presented in this thesis allows a better understanding of thelongitudinal beam coupling impedance of the measurements performed. Using it, the effect of theproposed power loss reduction techniques have been deeply investigated.Employing the model, the effect of transition pieces applied to the kicker magnet has been identifiedand validated in measurements. Also, it has been found that the decoupling network betweenHV and GND-conductor creates frequency peaks at low frequencies, which are also seen in themeasurements.Several options to reduce the beam induced power loss in the SPS injection kickers (MKP-S andMKP-L) have been shown. Offsetting the beam offers limited power loss reduction and may notbe suited to sufficiently reduce the beam induced heating in the longer term: The new proposedserigraphy design is far more promising. The calculated power loss reduction can be as high as45% for the MKP-S and as high as 70% for the MKP-L: Making this a very promising solution forthe heating problem.Once the isolation material, which will support and insulate the serigraphy, is decided on, theproposed serigraphy pattern will be adjusted to its electromagnetic properties. The overlappinglength of the serigraphy fingers will be chosen in a way that the occurring low frequency resonancepeak is in a position where the beam spectrum exhibits no peak. This serigraphy on the isolatingplate is planned to be installed in one kicker in the accelerator during the technical stop end of theyear 2016 to be tested with beam. If proven successful, the solution could then be retrofitted to theother injection kickers, if needed also on the extraction and dumping kickers.

55

56 6. Conclusion

A. Ferrite dimensions

57

58 A. Ferrite dimensions

Figure A.1.: Technical drawing of the C-core ferrite of an MKP-L cell.

59

Figure A.2.: Technical drawing of the C-core ferrite of an MKP-S cell.

60 A. Ferrite dimensions

B. Ferrite Ferroxcube 8C11 data sheet

61

62 B. Ferrite Ferroxcube 8C11 data sheet

DATA SHEET

Supersedes data of September 2004 2008 Sep 01

FERROXCUBE

8C11Material specification

Figure B.1.: Page one of Ferroxcube 8C11 data sheet.

63

2008 Sep 01 270

Ferroxcube

Material specification 8C11

8C11 SPECIFICATIONS

High permeability specialty NiZn ferrite only used in large toroids and machined products mainly for scientific particle accelerators operating at frequencies up to 1 MHz.

SYMBOL CONDITIONS VALUE UNIT

µi 25 °C; ≤10 kHz; 0.25 mT

1200 ±20%

B 25 °C; 10 kHz; 1200 A/m

≈ 310 mT

100 °C; 10 kHz; 1200 A/m

≈ 210

ρ DC; 25 °C ≈ 105 Ωm

TC ≥ 125 °C

density ≈ 5100 kg/m3

Fig.1 Complex permeability as a function of frequency.

handbook, halfpage

MBW452

1 10 102

104

f (MHz)

µ's ,µ''s

103

102

1010−1

8C11

µ''s

µ's

Fig.2 Initial permeability as a function of temperature.

handbook, halfpage2000

50 50 2500

MBW453

150

500

1000

1500

µi

T ( oC)

8C11

Fig.3 Typical B-H loops.

handbook, halfpage

50 100 1000

500

0

MBW454

500

100

200

300

400

500H (A/m)

B(mT)

8C1125 oC

100 oC

Figure B.2.: Page two of Ferroxcube 8C11 data sheet.

64 B. Ferrite Ferroxcube 8C11 data sheet

2008 Sep 01 271

Ferroxcube

Material specification 8C11

DATA SHEET STATUS DEFINITIONS

DISCLAIMER

Life support applications These products are not designed for use in life support appliances, devices, or systems where malfunction of these products can reasonably be expected to result in personal injury. Ferroxcube customers using or selling these products for use in such applications do so at their own risk and agree to fully indemnify Ferroxcube for any damages resulting from such application.

PRODUCT STATUS DEFINITIONS

DATA SHEET STATUS

PRODUCT STATUS

DEFINITIONS

Preliminary specification

Development This data sheet contains preliminary data. Ferroxcube reserves the right to make changes at any time without notice in order to improve design and supply the best possible product.

Product specification Production This data sheet contains final specifications. Ferroxcube reserves the right to make changes at any time without notice in order to improve design and supply the best possible product.

STATUS INDICATION DEFINITION

PrototypeThese are products that have been made as development samples for the purposes of technical evaluation only. The data for these types is provisional and is subject to change.

Design-in These products are recommended for new designs.

PreferredThese products are recommended for use in current designs and are available via our sales channels.

SupportThese products are not recommended for new designs and may not be available through all of our sales channels. Customers are advised to check for availability.

Figure B.3.: Page three of Ferroxcube 8C11 data sheet.

C. Ferrite material properties for the simulation

65

66 C. Ferrite material properties for the simulation

010

020

030

040

050

060

0

0

100

200

300

400

500

600

Freq

uenc

y [M

Hz]

µ’, µ’’

µ’fi

t

µ’’ fi

t

µ’m

easu

red

µ’’ m

easu

red

Figure C.1.: Magnetic properties of ferrite 8C11.

67

010

2030

4050

6070

8090

100

0

100

200

300

400

500

600

Freq

uenc

y [M

Hz]

µ’, µ’’

µ’fi

t

µ’’ fi

t

µ’m

easu

red

µ’’ m

easu

red

Figure C.2.: Magnetic properties of ferrite 8C11 for the first 100 MHz.

68 C. Ferrite material properties for the simulation

010

020

030

040

050

060

0

024681012

Freq

uenc

y [M

Hz]

ε’, ε’’

ε’ ε’’

Figure C.3.: Electric properties of ferrite 8C11.

Bibliography

[ABC+04] Gianluigi Arduini, T Bohl, Friedhelm Caspers, E H Gaxiola, T Kroyer, M Timmins,L Vos, and J Uythoven. Beam Induced Heating of the SPS Fast Pulsed Magnets. Pro-ceedings of EPAC 2004, Lucere, Switzerland, (CERN-AB-2004-038):4 pages, 2004.

[BAA+13] N Biancacci, G Arduini, T Argyropoulos, H Bartosik, R Calaga, K Cornelis, S Gi-lardoni, E Métral, N Mounet, Y Papaphilippou, S Persichelli, G Rumolo, B Sal-vant, G Sterbini, R Tomàs, R Wasef, M Migliorati, and L Palumbo. Beam Cou-pling Impedance Localization Technique Validation and Measurements in the CERNMachines. Proceedings of IPAC2013, Shanghai, China, (CERN-ACC-2013-0120):3pages, May 2013.

[Bar] Mike Barnes. Private communication. 2015.

[BCC+09] M J Barnes, Friedhelm Caspers, K Cornelis, L Ducimetière, E Mahner, G Papotti,G Rumolo, V Senaj, and E Shaposhnikova. Measurement and analysis of SPS kickermagnet heating and outgassing with Different Bunch Spacing. Proceedings of PAC09,Vancouver, BC, Canada, (CERN-ATS-2009-017):4 pages, Jul 2009.

[BDF+11] M J Barnes, L Ducimetière, T Fowler, V Senaj, and L Sermeus. Injection and ex-traction magnets: kicker magnets. Proceedings of CAS - CERN Accelerator School:Specialised course on Magnets 2009, Bruges, Belgium, (arXiv:1103.1583):26 pages,2011.

[BFA+12] M J Barnes, T Fowler, M G Atanasov, T Kramer, and T Stadlbauer. Effect of a met-allized chamber upon the field response of a kicker magnet: simulations results andanalytical calculations. Conf. Proc., (CERN-ATS-2012-217):4 pages, Aug 2012.

[Cha93] A.W. Chao. Physics of Collective Beam Instabilities in High Energy Accelerators.Wiley Series in Beam Physics and Accelerator Technology. Wiley, 1993.

[CMT00] Friedhelm Caspers, A Mostacci, and H Tsutsui. Impedance Evaluation of the SPSMKE Kicker with Transition Pieces between Tank and Kicker Module. TechnicalReport (CERN-SL-2000-071-AP), CERN, Geneva, Oct 2000.

[CMTZ13] Alexander Wu Chao, Karl Hubert Mess, Maury Tigner, and Frank Zimmermann.Handbook of accelerator physics and engineering; 2nd ed. World Scientific, Sin-gapore, 2013.

[CST] CST. CST STUDIO SUITE R© 2015 Help.

[Duc05] Laurent Ducimetière. Advances of Transmission line kicker magnets. Proceedings ofPAC 2005, Knoxville, USA, (CERN-AB-2005-023):4 pages, Jun 2005.

[FFH+76] Paul E Faugeras, E Frick, C G Harrison, H Kühn, V Rödel, G Schröder, and J P

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70 Bibliography

Zanasco. The SPS fast pulsed magnet systems. Technical Report CERN-SPS-BT-76-1,CERN, Geneva, Mar 1976.

[FHS73] Paul E Faugeras, C G Harrison, and G H Schröder. Design study of the SPS beamdumping system. Technical Report CERN-OPEN-2013-015. CERN-LabII-BT-INT-73-5, CERN, Geneva, Jul 1973.

[GCD+07] E Gaxiola, Friedhelm Caspers, L Ducimetière, P Faure, T Kroyer, B Versolatto, andG Vossenberg. The SPS Fast Extraction Kicker System in LSS6. Proceedings of EPAC2006, Edinburgh, UK, (CERN-LHC-Project-Report-913):4 pages, Jul 2007.

[HDD+14] K Hanke, H Damerau, A Deleu, A Funken, R Garoby, S S Gilardoni, N Gilbert, B God-dard, E B Holzer, A M Lombardi, D Manglunki, M Meddahi, B Mikulec, E Shaposh-nikova, and M Vretenar. Status of the LIU project at CERN. Proceedings of IPAC2014,Dresden, Germany, (CERN-ACC-2014-0125):4 pages, Jun 2014.

[Hin08] Frank Hinterberger. Physik der Teilchenbeschleuniger und Ionenoptik : mitdurchgerechneten Beispielen und 105 Übungsaufgaben mit vollständigen Lösungen.Springer, Berlin, 2. aufl. edition, 2008.

[Jen00] E Jensen. An improved log-formula for homogeneously distributed impedance. Tech-nical Report CERN-PS-RF-NOTE-2000-001, CERN, Geneva, Jan 2000.

[KCG07] T Kroyer, Friedhelm Caspers, and E Gaxiola. Longitudinal and Transverse Wire Mea-surements for the Evaluation of Impedance Reduction Measures on the MKE Extrac-tion Kickers. Technical Report CERN-AB-Note-2007-028, CERN, Geneva, Jul 2007.

[Poz12] David M. Pozar. Microwave engineering. Wiley, Hoboken, NJ, 4th edition, 2012.

[Rum] Giovanni Rumolo. Private communication. 2015.

[TBGU06] M Timmins, A Bertarelli, E Gaxiola, and J Uythoven. SPS extraction kicker mag-net cooling design. Technical Report CERN-AB-Note-2004-005-BT. CERN-TS-Note-2004-001-MME, CERN, Geneva, 2006.

[TWK98] Manfred K. A. Thumm, Werner Wiesbeck, and Stefan Kern. Hochfrequenzmeßtechnik: Verfahren und Meßsysteme. Teubner, Stuttgart, 2., durchges. aufl. edition, 1998.

[Uma89] K. Umashankar. Introduction to Engineering Electromagnetic Fields. Advanced seriesin electrical and computer engineering. World Scientific, 1989.

[VAB+14] FM Velotti, O Aberle, C Bracco, E Carlier, F Cerutti, K Cornelis, L Ducimetiere,B Goddard, V Kain, R Losito, C Maglioni, M Meddahi, F Pasdeloup, V Senaj, andGE Steele. Performance Studies of the SPS Beam Dump System for HL-LHC Beams.Proceedings of IPAC2014, Dresden, Germany, (CERN-ACC-2014-0239):4 pages, Oct2014.

[Wid28] R. Wideröe. Über ein neues Prinzip zur Herstellung hoher Spannungen. ElectricalEngineering (former Archiv für Elektrotechnik), Volume 21(Issue 4), 1928.

[Wie15] Helmut Wiedemann. Particle Accelerator Physics. Graduate Texts in Physics SpringerLink : Books. Springer, Cham, 4th edition, 2015.

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[Zan] Carlo Zannini. Private communication. 2015.

[ZRR13] Carlo Zannini, Leonid Rivkin, and Giovanni Rumolo. Electromagnetic Simulation ofCERN accelerator Components and Experimental Applications. PhD thesis, EcolePolytechnique, Lausanne, Mar 2013. Presented 15 Apr 2013.

[ZRV12] C Zannini, G Rumolo, and VG Vaccaro. Effect of the TEM Mode on the kickerImpedance. Conf. Proc., (CERN-ATS-2012-134):3 pages, May 2012.

72 Bibliography

List of Figures

1.1. Vacuum degradation and temperature rise in the MKP.11955 vacuum tank. . . . . . 21.2. Principle of the Widerøe LINAC. . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3. The CERN accelerator chain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1. Creation of wakefields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2. The 25 ns SPS-beam composition in the time domain. . . . . . . . . . . . . . . . . 112.3. The 25 ns beam spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4. SPS MKP kicker field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5. Kicker function principle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.6. A CAD model of the MKP kicker. . . . . . . . . . . . . . . . . . . . . . . . . . . 152.7. Schematic circuit diagram of a transmission line kicker. . . . . . . . . . . . . . . . 162.8. Serigraphy applied in the MKE kicker. . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1. Evolution of the CST models for the MKP-S kicker. . . . . . . . . . . . . . . . . . 223.2. Boundaries of the MKP-S kicker CST model. . . . . . . . . . . . . . . . . . . . . 233.3. Development of the CST MKP-S kicker model. . . . . . . . . . . . . . . . . . . . 243.4. Development of the CST MKP-L kicker model. . . . . . . . . . . . . . . . . . . . 263.5. Two MKP-S kickers in series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.6. Beam offset principle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.7. Beam offset simulations in the MKP-S. . . . . . . . . . . . . . . . . . . . . . . . 283.8. Beam offset simulations in the MKP-L. . . . . . . . . . . . . . . . . . . . . . . . 293.9. MKP-S model cell with the MKE serigraphy. . . . . . . . . . . . . . . . . . . . . 293.10. Simulated impedance of the MKP-S with the MKE serigraphy. . . . . . . . . . . . 303.11. MKP-S kicker model with the serigraphy over the whole kicker length and con-

nected to the first and last HV-plates. . . . . . . . . . . . . . . . . . . . . . . . . . 313.12. Simulated impedance of the MKP-S kicker with the serigraphy over the whole

kicker length and connected to the first and last HV-plates. . . . . . . . . . . . . . 323.13. Simulated impedance of the MKP-S kicker with the serigraphy over the whole

kicker length and connected to the first and last HV-plates for the first 500 MHz. . . 333.14. MKP-S kicker model with the serigraphy between the transition pieces. . . . . . . 343.15. Simulated impedance of the MKP-S kicker with the serigraphy between the transi-

tion pieces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.16. Simulated impedance of the MKP-S kicker with the serigraphy between the transi-

tion pieces for different finger distances. . . . . . . . . . . . . . . . . . . . . . . . 35

73

74 List of Figures

3.17. Simulated impedance of the MKP-L kicker with the serigraphy between the transi-tion pieces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.18. Simulated impedance of the MKP-L kicker with the serigraphy between the transi-tion pieces for the first 500 MHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.19. MKP-S model cells with the longitudinal wire coupler. . . . . . . . . . . . . . . . 383.20. Simulated impedance of the MKP-S kicker with the serigraphy, bridging the HV-

plates by wires. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.21. MKP-S model cell with the transversal coupler. . . . . . . . . . . . . . . . . . . . 403.22. Simulated impedance of the MKP-S kicker with the transversal coupler serigraphy. 40

4.1. Photo of the vacuum tank housing the kickers connected to the VNA. . . . . . . . 414.2. Sketch of the measuring configuration. . . . . . . . . . . . . . . . . . . . . . . . . 434.3. Measured real longitudinal impedance of the vacuum tank housing two MKP-S

kickers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.4. Beam offset measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.5. Beam offset measurements first 500 MHz. . . . . . . . . . . . . . . . . . . . . . . 464.6. Serigraphy insertion for MKP-S tank. . . . . . . . . . . . . . . . . . . . . . . . . 474.7. Serigraphy measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.8. Serigraphy measurements for the first 500 MHz. . . . . . . . . . . . . . . . . . . . 49

A.1. Technical drawing of the C-core ferrite of an MKP-L cell. . . . . . . . . . . . . . . 58A.2. Technical drawing of the C-core ferrite of an MKP-S cell. . . . . . . . . . . . . . . 59

B.1. Page one of Ferroxcube 8C11 data sheet. . . . . . . . . . . . . . . . . . . . . . . . 62B.2. Page two of Ferroxcube 8C11 data sheet. . . . . . . . . . . . . . . . . . . . . . . . 63B.3. Page three of Ferroxcube 8C11 data sheet. . . . . . . . . . . . . . . . . . . . . . . 64

C.1. Magnetic properties of ferrite 8C11. . . . . . . . . . . . . . . . . . . . . . . . . . 66C.2. Magnetic properties of ferrite 8C11 for the first 100 MHz. . . . . . . . . . . . . . . 67C.3. Electric properties of ferrite 8C11. . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Mario BeckMaster Thesis: Simulation, measurement and mitigation of the beam induced power loss inthe SPS injection kickersZeitraum: 01.04.2015 – 23.09.2015Betreuer: Prof. Dr.-Ing. John Jelonnek , Dr. Giovanni Rumolo

Abstract:The kickers, used to impart fast deflection to the beam in an accelerator, may suffer from high heat-ing due to beam induced power loss created by their large impedance. In order to reduce the powerloss in the SPS injection kickers (MKP-S and MKP-L), their impedance is investigated using theCST Wakefield Solver.Therefore in this work, the existing model of the MKP-S kicker is compared to measurements andthen refined. The influence of transition pieces, installed inside the measured tank, is investigatedemploying simulations. The impact of the decoupling network, between the HV-conductor and theGND-conductor, is investigated using lumped element networks in the simulation. The effect onthe impedance of measuring two kickers in series is investigated executing simulations. The im-provements made to the MKP-S model are translated to the MKP-L model.The power loss reduction achievable through offsetting the beam out of the centre of the kickersaperture in the direction of the ground conductor is investigated by simulations for both kickers.The results are validated through measurements on the MKP-S: An MKP-L was not available formeasurements. Calculations show that the maximal power loss reduction achievable by that mea-sure for the MKP-L is 30%.Several serigraphy designs are introduced, simulated and their feasibility is discussed. The mostpromising concept, including also the transition pieces and thus shielding the cavities betweenthemselves and the kicker, is realised as a prototype and measured. The measurements prove theimpedance reduction through the serigraphy design. Calculations show that this serigraphy couldreduce the power loss in the MKP-S by 45% in the MKP-L by 70%.

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