Comparison between Simulation and Experiment on Injection Beam Loss and Other Beam Behaviours in the SPring-8 Storage Ring Presented by Hitoshi TANAKA,Contributors: Jun SCHIMIZU, Kouichi SOUTOME, Masaru TAKAOJASRI/SPring-81

Contents 1. Motivation2. Simulation Model 3. Comparison between Simulation and Experiments4. Summary5. Tentative FMA Results2

1. MotivationIn ideal top-up operation, reduction of injection beam loss and suppression of stored beam oscillation by frequent beam injections are critically important.3Aiming at understanding of mechanism of injection beam loss and its suppression, a precise simulation model has been developed.Key: Precise simulation of particle motion with a large amplitude (x=~10mm)

2. Simulation Model 42.1. Hamiltonian Refs.[1] D.P. Barber, G. Ripken, F. Schmidt; DESY 87-036 [2] G. Ripken; DESY 87-036 (1)

52.2. Components and their Simplectic Integration (a) Bending MagnetEquation (1) is integrated without expanding the square root part.Analytical solutions derived by E. Forest are used for rectangular and sector magnet integration.Ref. [3] E. Forest, M.F. Reusch, D.L. Bruhwiler, A. Amiry; Particle Accel.45(1994)65.

62.2. Component Model and Simplectic Integration (2) (b) Quadrupole and Sextupole MagnetsIn this case, Eq. (1) has a separating form of A(p) +V(x).4th order explicit integration method is adopted. Sextupoles are treated as thick elements.Refs. [4] E. Forest and R.D. Ruth; Pysica D 43 (1990)105.[5] H. Yoshida; Celestial Mechanics and Dynamical Astronomy 56 (1993) 27.

72.2. Component Model and Simplectic Integration (3) (c) Other Magnets (except for IDs)All other magnetic components are treated as thin kicks.Multi-pole up to 20 poles available. (d) RF CavitiesCavities are treated as thin elements. (Ref. [1])

82.2. Component Model and Simplectic Integration (4) (e) Radiation EffectsNormalized photon energy spectrum + random number ranging from 0 to 1Radiation from BMs, QMs, SMs and IDs are considered.(f) Fringe FieldsLowest order effect is only considered for BMs, QMs and SMs.BM fringe ->(Ref. [3])Ref. [6] M. Sands; Report SLAC-121 (1970).

92.3. Magnetic Errors (a) Normal and Skew Quadrupole Errors236 Q-error kicks and 132 SQ-error kicks are considered. These strengths are estimated by fitting measured beam response with 4x4 formalism.Systematic errors lower than 20 poles are considered. 10pole for BM and 12pole for QM.(b) Multipole errorsRef. [7] J. Safranek; NIMA 388 (1997)27.[7]

102.4. ID Model For ID integration, the square root of Eq.(1) is expanded and the lowest order parts are only integrated by means of a generating function. Refs. [8] K. Halbach; NIM 187(1981)109.[9] E. Forest and K. Ohmi; KEK Report 92-14 (1992).

113.1. Amplitude Dependent Tune Shift 3. Comparison between Simulation and Experiments

123.2. Smear of Coherent Oscillation Refs. [10] K. Ohmi et.al.; PRE 59 (1999)1167.

[11] J. Schimizu et.al.; Proc. of EPAC02 (2002) p.1287.

133.3. Nonlinear Momentum Compaction Ref. [12] H. Tanaka et.al.; NIMA 431(1999)396.

143.4. Nonlinear Dispersion h(d)=h1 + h2d + h3d2 + h4d3 + h5d4 .Ref. [12]

153.5. 3D Closed Orbit

163.6. Injection Beam Loss3.6.1. Parameters of Injection Beam and Injection schemeex=220 nmrad, (ey/ex)=0.002sd=0.0013, st=63 psecOptical Functions at IP bx=~13.5m, ax=-0.11 by=~13.7m, ay=-0.20Septum Inner wall: -19.5mm Chamber Aperture 70(H) / 40(V) mmIn-vacuum ID Vert. Lim.: min.7mm Injection Beam ParametersInjection Point: Dx=-24.5mmBump height=~14.5mmBump Pulse Width=~8usec(Revolution=~4.7usec)Injection Bump SystemAperture Limitex=2.8~6.6 nmrad, Coupling(ey/ex)=0.002sd=0.0011, st=13 psec nx=40.15, ny=18.35Optical Functions at IP bx=~23m, ax= -0.2 by=~7.5m, ay=-0.45Ring Parameters

173.6.2. ID Parameters(1)# Min.Gap KxKyPowerType [mm] [kW] 19121.835In-Vacuum Long2072.114In-Vacuum Hybrid99.62.18.8In-Vacuum Standard109.62.29.6In-Vacuum Standard119.62.29.9In-Vacuum Standard129.62.29.6In-Vacuum Standard139.62.29.8In-Vacuum Standard1612.92.47.4In-Vacuum229.982.912.3In-Vacuum249.61.31.44In-Vacuum Figure-8298.82.411.2In-Vacuum Standard3592.310.8In-Vacuum Standard3782.613.3In-Vacuum Standard 398.62.310.9In-Vacuum Standard 408.31.11.03.5In-Vacuum Helical419.62.08.1 In-Vacuum Standard 4492.310.9In-Vacuum Standard 4581.71.4In-Vacuum Vertical tandem4681.58.1 In-Vacuum Hybrid 479.62.19.1In-Vacuum Standard

183.6.2. ID Parameters(2)825.51.111.218.04Out-Vacuum Elliptical Wiggler1520.02.25.4Out-Vacuum Revolver (Linear) 20.03.43.45.6Out-Vacuum Revolver (Helical)2530.04.84.62Out-Vacuum Helical tandem2737.03.95.46.6Out-Vacuum Figure-82336.03.43.4Out-Vacuum APPLE-II (Circular)36.05.8Out-Vacuum APPLE-II (Linear)36.04.2Out-Vacuum APPLE-II (Vertical)17*20.0Installed but under commissioning

* ID 17 was recently installed in the ring. Gap of ID 17 is usually closed. The phase is shifted so that the magnetic field is cancelled out at the center. The field is no zero and nonlinear at the off-center.# Min.Gap KxKyPowerType [mm] [kW]

193.6.3. Behaviour of Injection Beam (1-Calc) In simulation, particles are mainly lost : Septum wall (Hori.) LSS beta-peak (Vert.) IDs (Vert.)

203.6.3. Behaviour of Injection Beam (2-Calc) Observation Point:Entrance of ID19

213.6.4. Beam Loss v.s. Gap of ID47(1)

223.6.4. Beam Loss v.s. Gap of ID47(2)

233.6.5. Beam Loss v.s. Symmetry restoration of Optics

243.6.6. Beam Loss v.s.Initial Condition (Calc) Lost particles have clear correlation with horizontal emittance .

253.6.7. Beam Loss v.s. Beam Collimation (1)Planner type IDs are only considered in the simulation.

263.6.7. Beam Loss v.s. Beam Collimation (2)Planner type IDs are only considered in the simulation.Injection orbit is shiftedto septum wall by 2mm

4. Summary(1) Developed simulator well describes nonlinear particle motion in a storage ring. However, the simulator can not explain injection beam loss quantitatively. 27Possible causes are:Ambiguity in injection beam distributionIncorrect ID Modeling at especially large amplitudeNonlinearity not included in the model Some mistake in calculation, etc

4. Summary(2) Frequency Map Analysis (FMA) could be a powerful tool to investigate mechanism of injection beam loss.28To use FMA effectively, we need a precise ring model.

5. Tentative FMA Results 29Tune modulation in damping of injection beam

30FMA of Normal Optics w/o ErrorsChromaticity (+8, +8)3nx-2ny=84=4*214nx-2ny=124=4*31

Stability Map of Normal Optics w/o ErrorsChromaticity (+8, +8)31

FMA of Normal Optics with ErrorsChromaticity (+8, +8)32

Stability Map of Normal Optics with ErrorsChromaticity (+8, +8)33