Simulation of storage ring injection of HLS II

Simulation of storage ring injection of HLS II 1 first-author 1 corresp Corresponding author, lshang@ustc.edu.cn Corresponding author, lshang@ustc.edu.cn lshang@ustc.edu.cn 1 1 National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, China National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, China The Hefei Light Source (HLS) has been upgraded into HLS II, with increased brightness and stability. In this paper, the new injection system is described. Elegant program is used to simulate the particles motion in 6-D phase space. In the process of tracking simulation of electrons, the system tolerances and magnet errors are introduced. Influences to the injection efficiency from beam injection deviation are studied. These provide important reference for realizing the Top-up injection. Injection system Bump orbit Injection simulation Beam deviation Injection efficiency 1 Introduction 1 Hefei Light Source, of 800 MeV electron beam energy, has been upgraded into HLS II [ 1 1 ] with increased number of straight sections (from four to eight) by changing the magnet focusing structure of the storage ring, of the same circumference as before. The aim is to install more insertion devices and improve brightness of the light source. The main specifications of HLS II are listed in Table 1 Table 1 . Where, ε x is the horizontal emittance, ν x / ν y is the betatron tune, ξ xN / ξ yN is the natural chromaticity, α is the momentum compaction, τ is the damping time, J is the damping partition number, δ is the energy spread and β xy is the beta-function. 1 1 Specifications 1 1 Values 1 1 ε x (nm rad) 1 1 37.14 1 1 ν x / ν y 1 1 4.445/2.316 1 1 ξ x N / ξ y N 1 1 -7.42/-7.43 1 1 α 1 1 0.0158 1 1 τ x / τ y / τ s (ms) 1 1 19.5/21.0/10.9 1 1 J x / J y / J s 1 1 1.076/1/1.924 1 1 δ 1 1 0.00047 1 1 β xy |max 1 1 19.49/14.78 1 1 β xy |min 1 1 1.81/1.61 1 1 β xy |ave 1 1 6.26/5.82 1 1 η x |max 1 1 1.22 For future development of the Top-up mode, a major transformation of the injection system of storage ring was done. According to characteristics of HLS, the distributed four-kicker bump orbit scheme was adopted [ 2 2 , 3 3 , 4 4 , 5 5 ]. This scheme can reduce the kicker strength and improve flexibility of adjusting the shape of bump orbit. Figure 1 Figure 1 shows a layout of the new injection bump orbit system. Considering beam orbit distortion, beam size and other factors, the height of orbit bump is 24 mm and the septum inside is 29 mm from the equilibrium orbit. To have a good field region, the electron beams are injected at 2 mm away from the septum outside and 33 mm to equilibrium orbit. The horizontal aperture of vacuum chamber is 22% smaller than that of the HLS before upgrading. This reduces the demand for magnet aperture. Figure 2 Figure 2 shows the horizontal phase space of injection system at injection point. In order to achieve the required height of bump orbit, we need to calculate the deflection angles of four kickers. According to the conditional expression of four-kicker bump orbit [ 6 6 ] with zero angle at injection point: <math display="block" id="M1"><mrow><msub><mi>θ</mi><mn>1</mn></msub><mo>=</mo><mo stretchy="false">[</mo><mi>b</mi><mo>/</mo><mo stretchy="false">(</mo><msub><mi>β</mi><mn>0</mn></msub><msub><mi>β</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo stretchy="false">(</mo><mi>cos</mi><mi>Δ</mi><msub><mi>Ψ</mi><mrow><mn>02</mn></mrow></msub><mo>−</mo><msub><mi>α</mi><mn>0</mn></msub><mi>sin</mi><mi>Δ</mi><msub><mi>Ψ</mi><mrow><mn>02</mn></mrow></msub><mo stretchy="false">)</mo><mo>/</mo><mi>sin</mi><mi>Δ</mi><msub><mi>Ψ</mi><mrow><mn>01</mn></mrow></msub><mn>,</mn></mrow></math> <math display="block" id="M2"><mrow><msub><mi>θ</mi><mn>2</mn></msub><mo>=</mo><mo stretchy="false">[</mo><mi>b</mi><mo>/</mo><mo stretchy="false">(</mo><msub><mi>β</mi><mn>0</mn></msub><msub><mi>β</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo stretchy="false">(</mo><mi>cos</mi><mi>Δ</mi><msub><mi>Ψ</mi><mrow><mn>01</mn></mrow></msub><mo>−</mo><msub><mi>α</mi><mn>0</mn></msub><mi>sin</mi><mi>Δ</mi><msub><mi>Ψ</mi><mrow><mn>01</mn></mrow></msub><mo stretchy="false">)</mo><mo>/</mo><mi>sin</mi><mi>Δ</mi><msub><mi>Ψ</mi><mrow><mn>21</mn></mrow></msub><mn>,</mn></mrow></math> <math display="block" id="M3"><mrow><msub><mi>θ</mi><mn>3</mn></msub><mo>=</mo><mo stretchy="false">[</mo><mi>b</mi><mo>/</mo><mo stretchy="false">(</mo><msub><mi>β</mi><mn>0</mn></msub><msub><mi>β</mi><mn>3</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo stretchy="false">(</mo><mi>cos</mi><mi>Δ</mi><msub><mi>Ψ</mi><mrow><mn>40</mn></mrow></msub><mo>−</mo><msub><mi>α</mi><mn>0</mn></msub><mi>sin</mi><mi>Δ</mi><msub><mi>Ψ</mi><mrow><mn>40</mn></mrow></msub><mo stretchy="false">)</mo><mo>/</mo><mi>sin</mi><mi>Δ</mi><msub><mi>Ψ</mi><mrow><mn>43</mn></mrow></msub><mn>,</mn></mrow></math> <math display="block" id="M4"><mrow><msub><mi>θ</mi><mn>4</mn></msub><mo>=</mo><mo stretchy="false">[</mo><mi>b</mi><mo>/</mo><mo stretchy="false">(</mo><msub><mi>β</mi><mn>0</mn></msub><msub><mi>β</mi><mn>4</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo stretchy="false">(</mo><mi>cos</mi><mi>Δ</mi><msub><mi>Ψ</mi><mrow><mn>40</mn></mrow></msub><mo>−</mo><msub><mi>α</mi><mn>0</mn></msub><mi>sin</mi><mi>Δ</mi><msub><mi>Ψ</mi><mrow><mn>30</mn></mrow></msub><mo stretchy="false">)</mo><mo>/</mo><mi>sin</mi><mi>Δ</mi><msub><mi>Ψ</mi><mrow><mn>43</mn></mrow></msub><mn>,</mn></mrow></math> where α and β are the twiss parameters in the horizontal direction, Δ ij is the phase-advance from i to j , and b is height of the bump orbit. Deflection angles (in mrad) of the four injection kickers (K1–K4) are 6.4825, 3.4583, 3.4583 and 6.4825, respectively, calculated at the design height of bump orbit with the orbit angle being zero at injection point. Figure 3 Figure 3 shows the shape of local bump orbit. The septum thickness is 2 mm, due to limitation of the pulse septum technology. Considering orbit distortion and size of the injected beam, the ideal launching condition for an injected beam center in 6-D phase space is set to ( x , x’ , y , y’ , s , δ ) = (33 mm, 0, 0, 0, 0, 0). A multiparticle beam of Gaussian distribution is used for tracking simulalations of injection process [ 7 7 , 8 8 ]. Various system and project errors are included to obtain realistic simulations of injection process. 2 Injection simulation 1 The simulations using Elegant were carried out [ 9 9 , 10 10 ]. Through analysis of numerical simulation results, performance of the new injection system could be determined. Practically, alignment and rotation errors of the magnets were considered in the simulation. And, errors of the new injection system, such as amplitude jitter, time jitter, alignment and rotation errors, etc. ( Table 2 Table 2 ), were considered, too. For all the errors, a multiparticle beam of Gaussian distribution is used for tracking simulations of the injection process. Figure 4 Figure 4 shows the first seven turns of particles tracking for an injected beam in the horizontal phase space. 1 1 Error source 1 1 Value 1 1 Quadrupole alignment Δ x /Δ y /Δ z (mm) 1 1 0.08/0.08/0.50 1 1 Quadrupole rotation Δ (mrad) 1 1 0.20 1 1 Sextupole alignment Δ x /Δ y /Δ z (mm) 1 1 0.08/0.08/0.50 1 1 Sextupole rotation ΔΦ (mrad) 1 1 0.20 1 1 Kicker alignment Δ x /Δ y /Δ z (mm) 1 1 0.20/0.20/0.20 1 1 Kicker rotation Δ (mrad) 1 1 0.5 1 1 Kicker field time jitter (ns) 1 1 2.0 1 1 Kicker field amplitude jitter (%) 1 1 0.15 The waveform of kicker field is a half-sine wave and pulse width is 1.32 μs. The injection time is selected on the falling edge of half sine wave at 0.88 μs relative to the initial time. Figure 5 Figure 5 shows the waveform of kicker field and the injection time point. It is obvious that the bump orbit shrinks faster. The HLS storage ring is 66.13 m in circumference, with a beam bunch cycling period of 0.22 μs [ 6 6 , 11 11 ]. The orbit bump shall disappear completely after running 2 cycles. Table 3 Table 3 lists the main parameters of the kickers and pulse septum. 1 1 Parameters 1 1 Kickers 1 1 Pulse septum 1 1 Maximum injection energy 1 1 1 GeV 1 1 1 GeV 1 1 Maximum deflection angle 1 1 8 mrad 1 1 105 mrad 1 1 Integral field 1 1 0.027 Tm 1 1 0.35 Tm 1 1 Peak field strength 1 1 1050 G 1 1 8750 G 1 1 Yoke physical length 1 1 200 mm 1 1 400 mm 1 1 Aperture size 1 1 80×54 mm 1 1 10 mm 1 1 Magnetic inductance 1 1 0.47 μH 1 1 4.2 μH 1 1 Excitation current peak 1 1 4514 A 1 1 5570 A 1 1 Half-sine width 1 1 1350 ns 1 1 60 μs The oscillation amplitude [?] in vertical direction is derived from the vertical injection angle and position deviation of the injected beam. The rotating angle errors of kickers and the transverse coupling caused by rotation errors of other components are also important influence factors. Compared with the horizontal oscillation amplitude, the vertical beam emittance caused by these errors is far less than those caused by the ring vertical aperture. We used 1000 electrons to represent an injected beam bunch. From the moment of injection starting, we tracked the electrons for 1000 cycles and determined the injection efficiency by observing the number of missing particles. The initial state of an injected beam depends on parameters at the end of transfer line. The twiss parameters at the end of transport line are β x =7.917 m, β y =5.718 m, α x =0.067, α y =-0.725, ε x = ε y =25.56 nmrad, and ε =0.0048. Errors of the existence of transport line and injection system cause variations in launching condition of transverse phase space for an injected beam. We respectively scanned the initial value of injected beam on x , x’ , y , and y’ directions, and checked the beam capture efficiency. Figure 6 Figure 6 shows the injection efficiency under the condition of four types of injection deviation. Deviation ranges of the injected beam to ideal condition are Δ x (mm) = [0.0, 4.6], Δ x’ (mrad) = [-0.985, 0.99], Δ y (mm)= [-1.87, 2.4], and Δ y’ (mrad)= [-1.4,0.4], when the injection efficiency is above 80%. 3 Conclusion 1 The Top-up mode injection of HLS II requires high injection efficiency and beam stability of the injection system. Through numerical simulation for the injection process of the new injection system, we determined the tolerance of errors. This provides an important reference for improving the injection efficiency and stability of HLS II. Later, high injection efficiency can be achieved by adjusting the parameters of transport line and septum according to the results. So it can be a steppingstone for the commissioning and operation of Top-up in the future. References Hwang I , Huang J Y , Kim M , et al . Top-up operation at Pohang Light Source-II . Rev Sci Instrum , 2014 , 85 : 055113 . 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J Korean Phys Soc , 2013 , 63 : 2072 - 2079 . DOI: 10.3938/jkps.63.2072 http://doi.org/10.3938/jkps.63.2072 Tracking study of transient behaviors at beam injection of the PLS-II ring 10.1007/s41365-016-0007-8 Supported by National Natural Science Foundation of China (No. 11175181) 2015-02-09 2015-04-01 2015-04-09 2016-02-27 2016-02-20 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2016 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-016-0007-8 http://dx.doi.org/10.1007/s41365-016-0007-8 . 2016 Nuclear Science and Techniques 01 27