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Effect of Insertion Devices Tapering Mode of Operation on the MAX IV Storage Rings

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Effect of Insertion Devices Tapering Mode of Operation on the MAX IV Storage Rings LUND UNIVERSITY MASTER THESIS MAXM30 Effect of Insertion Devices Tapering Mode of Operation on the MAX IV Storage Rings Author: Georgia PARASKAKI Supervisors: Sverker Werin Hamed Tarawneh June 4, 2018 Abstract Tapering is a mode of operation of insertion devices that allows the users to perform scanning in a range of photon energies. NanoMAX, BioMAX and BALDER are all beamlines of the 3 GeV MAX IV storage ring and will provide this special mode of operation for their users. In this thesis, the spectra of NanoMAX and BioMAX while operating with tapering were studied and feed forward tables that cancel out the closed orbit distortion caused by the insertion devices were generated. Moreover, a study of the nature of the closed orbit distortion was performed, aiming at simplifying the feed forward table measurements that can currently be quite time consuming. In addition, the effect of BALDER, which is a wiggler and currently the strongest insertion device in the storage ring, on the electron beam was studied. Apart from the feed forward table that corrects for the closed orbit distortion, BALDER induces a beta beat and tune shift which has to be eliminated in order to make the insertion device transparent to the electron beam. This correction is needed in order to keep the beam life time unaffected and ensure a stable operation. For this reason, a two-stage correction scheme was proposed. First, a local correction with the quadrupoles adjacent to BALDER was performed in order to eliminate the beta beat induced by the wiggler. As a second step a global correction was applied. The aim of the global correction is to bring the tune back to the design values. Contents 1 Introduction 3 2 Background 5 2.1 Beam Dynamics . 5 2.1.1 Coordinate system . 5 2.1.2 Optics of charged particle beams . 7 2.2 Response Matrix . 9 2.3 Insertion Devices . 10 2.3.1 Physics of Insertion Devices . 10 2.3.2 Tapering mode . 12 2.3.3 Effects of Insertion Devices on the electron beam . 14 2.4 The MAX IV Laboratory . 16 2.5 The MAX IV beamlines . 16 2.5.1 NanoMAX . 16 2.5.2 BioMAX . 16 2.5.3 BALDER . 17 2.5.4 BLOCH . 17 3 Methods 18 3.1 SPECTRA . 18 3.2 Accelerator Toolbox . 18 3.3 Matlab Middle Layer . 18 3.4 LOCO . 19 4 Modelling and correction strategy 20 4.1 Spectrum study . 20 4.2 Neutralizing the effect of IDs on the electron beam . 20 4.2.1 Feed Forward table generation . 20 4.2.2 Field integral study . 21 4.2.3 Modelling BALDER’s effect on the storage ring . 22 4.2.4 Optics correction for BALDER . 23 5 Results 25 5.1 Spectrum study . 25 5.2 Neutralizing the effect of IDs on the electron beam . 29 1 5.2.1 Feed Forward table generation . 29 5.2.2 Field integral study . 29 5.2.3 Simulation of BALDER’s effect on the storage ring . 30 5.2.4 Optics correction for BALDER . 31 6 Discussion 33 6.1 Spectrum study . 33 6.2 Neutralizing the effect of IDs on the electron beam . 34 6.2.1 Feed Forward Table generation . 34 6.2.2 Field integral study . 34 6.2.3 Simulation of BALDER’s effect on the storage ring . 34 6.2.4 Optics correction for BALDER . 35 7 Outlook 36 2 Chapter 1 Introduction Light sources are accelerators dedicated to the production of light. Synchrotron radiation (SR), the light emitted when charged particles are accelerated, was first discovered in 1947 at the General Electric Research Laboratory in a 70 MeV synchrotron [1]. Until the 1970’s, synchrotrons were mostly dedicated to nuclear and high energy physics experiments for which SR was only a limiting factor in achieving higher energies. That was the first generation of light sources. Early in 1980s synchrotrons started being dedicated to the production of X-rays using bending magnets. This was the second generation of light sources. In the middle of 1990s the first light sources using insertion devices (IDs), a special type of magnets, to produce light were built in Europe, the so called third generation of light sources [1]. The full capabilities of this generation has not yet reached its limit. However, at the same time, we are moving towards the fourth generation of light sources; the free electron lasers (FELs) and low emittance storage rings. FELs are linac-based light sources the aim of which is to produce fully coherent light of higher brightness with very short pulse duration [1]. MAX IV is a Swedish national accelerator laboratory that was inaugurated on the 21st of June 2016 and is expected to provide users with the most brilliant X-rays in the world with its light sources. In order to produce light for the experiments, electron beams are circulated in accelerators, called storage rings. In these storage rings the light is produced with IDs. Even though the insertion devices are essential for the light production, they introduce changes to beam parameters or orbit that need to be corrected. The two problems to be corrected are the closed orbit distortion (COD) and the optics distortion. 3 Figure 1.1: The MAX IV facility. The aims of this thesis are to: • Study a special mode of operation of the insertion devices, called tapering mode. • Generate feed forward tables to correct the COD for tapered and nontapered insertion de- vices. • Investigate the nature of COD in order to simplify the measurement method. • Correct the optics distortion caused by BALDER, the strongest insertion device of the MAX IV storage rings. In this thesis, first there is an introduction to the accelerator physics theory and a description of the tools used. Later, the tapering mode of operation is studied. Following, the effect of the insertion devices on the electron beam is studied and the proposed corrections are presented. Finally, there is a discussion of the results and possible future steps. 4 Chapter 2 Background 2.1 Beam Dynamics 2.1.1 Coordinate system In order to describe the state of a particle, a 6D coordinate system can be used (x, x0, y, y0, z, δ). The coordinates x and y are the transverse displacements from the reference particle that follows the design orbit, x0, y0 the transverse angles, z the longitudinal displacement from the reference particle and δ is the relative momentum offset from the reference particle [3]. As expected, the coordinates of the reference particle in this system are (0, 0, 0, 0, 0, 0). The motion of particles in the transverse plane can be described by Hill’s equation [4]: 00 x (s) + Kx(s)x(s) = 0; 00 (2.1) y (s) + Ky(s)y(s) = 0; where Kx and Ky are functions of the magnets’ properties that are periodic with the circumference of the ring and s is the coordinate along the beam direction [2]. Since the equations for the hori- zontal and the vertical plane are similar, we can limit us to the study in the horizontal plane. The general solution to the equation of motion is: p p x(s) = β(s)cos(Ψ(s) + Ψ0): (2.2) The solution indicates that the particles perform harmonic oscillations which are called betatron oscillations. In Eq. 2.2 β(s) is the beta function, also known as the amplitude function, which describes the amplitude of betatron oscillations and is a measure of the transverse size of the beam. When performing betatron oscillations, the amplitude of the oscillations is position dependent [2]: p E(s) = pβ(s): (2.3) 5 Figure 2.1: Coordinate system in the vicinity of the reference particle [2]. Therefore, the trajectories of the particles are included in the envelope E(s) which defines the range of their oscillation. We can also define α(s) and γ(s) [2] as: β0(s) α(s) = − ; 2 (2.4) 1 + α2(s) γ(s) = : β(s) The beta function β(s) along with α(s) and γ(s) are called twiss parameters and they will be interpreted later in this section. Ψ, which appears in Eq. 2.2, is the phase advance [2]: I ds Ψ(s) = ; (2.5) β(s) and is a constant of motion called the Courant-Synder invariant also known as emittance [2]: = γ(s)x2(s) + 2α(s)x(s)x0(s) + β(s)x02(s): (2.6) This is the equation of an ellipse in the x−x0 plane which is also called phase space. The emittance is the area of this ellipse divided by π, and based on Liouville’s theorem it is an invariant of motion [2]. The twiss parameters introduced previously describe the orientation of this ellipse in phase space. At this point, the tune of the machine can be defined as shown in Eq. 2.7 [2]. The tune expresses the number of oscillations an electron performs in one revolution along a circular accelerator. 1 I 1 Qx=y = ds: (2.7) 2π βx=y(s) 6 2.1.2 Optics of charged particle beams Optics in accelerator physics concerns the use of magnetic fields in order to force the electron beam, in our case, to follow the design orbit while being focused [5]. The force acting on a particle of charge e with velocity u in an electromagnetic field (E, B) is the Lorentz force shown in Eq. 2.8 [2]: F = eu × B: (2.8) Since the transverse displacement of the beam is quite small, it is possible to expand the magnetic field in the vicinity of the nominal orbit [2]: @B @2B @3B B (x) = B + y x + y x2 + y x2 + ::: (2.9) y y0 @x @x2 @x3 p Dividing all the terms in Eq.
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