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L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al:

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1 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 1 Experiences of Bunch Shape Monitoring at GSI Peter Forck, Christoph Dorn, Timo Milosic, Benjamin Zwicker GSI Helmholtz-Zentrum für Schwerionenforschung, Darmstadt Lund, February 11 th, 2013 The GSI facility and FAIR Overview of two installations at UNILAC  Particle detectors setup - Used for ToF-based longitudinal emittance measurement - Installed at 1.4 MeV/u section  Cavity for transversal beam deflection  Older Experiences....  Non-destructive monitor  see talk by Benjamin Zwicker  Comments to Cavity Bunch shape Monitor for slow electrons  Recent paper in PRST-AB Partly sponsored by:

2 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 2 The present Accelerator Facility at GSI SIS FRS ESR Ion sources all elements UNILAC Synchrotron, Bρ=18 Tm E max p: 4.7 GeV U: 1 GeV/u Achieved e.g.: Ar 18+ : 1·10 11 U 28+ : 3·10 10 U 73+ : 1·10 10 ESR: Storage Ring, Bρ=10 Tm Atomic & plasma physics Radiotherapy Nuclear Physics UNILAC: all ions p – U : 3 – 12 MeV/u, 50 Hz, max. 5 ms Up to 20 mA current (with 0.1 ms pulses) Pulse-to-pulse variation possible  different ion species, energy, target location…

3 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 3 UNILAC at GSI: Overview MEVVA MUCIS PIG RFQ IH1 IH2 Alvarez DTL HLI: (ECR,RFQ,IH) Transfer to Synchrotron 2.2 keV/u β = 0.0022 120 keV/u β = 0.016 11.4 MeV/u β = 0.16 RFQ, IH1, IH2 Gas Stripper U 4+ U 28+ Alvarez DTL Single Gap Resonators All ions, high current, 5 ms@50 Hz, 36&108 MHz Foil Stripper To SIS ↑ Constructed in the 70th, Upgrade 1999,  Injector for FAIR ion operation 1.4 MeV/u β = 0.054 10mm f rf = 36 MHz f rf = 108 MHz

4 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 4 GSI and FAIR in Future FAIR: Extension of GSI facilities and its experimental program + antiproton research Accelerator facility: Synchrotron for high current heavy ion beams Cooler rings for low emittance beams Challenges for LINACs:  Efficient acceleration  High current, in particular of heavy ions  low emittance i.e. high brilliance  new p-LINAC and evtl. Heavy Ion LINAC GSI FAIR

5 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 5 The Facility for Antiproton and Ion Research UNILAC & SIS18 as injector for ions after upgrade p-LINAC: high current 70 mA, 70 MeV SIS100: 100Tm, s-c magnets 2T, 1-29 GeV/u fast ramping 4 T/s, length 1084 m design: p 3*10 13, U 28+ 5*10 11 S-FRS: RIB production 100-fold higher acceptance CR: stochastic cooling of RIB and pbar HESR: acc. of pbar to max. 14 GeV, pellet target, stochastic & e-cooling pbar FLAIR: HITRAP LSR:30→0.3MeV/u USR:0.3→0.02MeV NESR RESR: accumulation of pbar, NESR: versatile experimental ring RIB, pbar e-cooling, gas-target, e-A collider FLAIR: decelerators of RIB, HCI, pbar  Will be realized later > 2020 Challenges for LINACs:  Efficient acceleration  High current, in particular of heavy ions  low emittance i.e. high brilliance

6 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 6 Proton Linac Overview 45 m Beam energy Beam current (op.) Beam current (des.) Beam pulse length Repetition rate Rf-frequency Tot. hor. emit. (norm.) Tot. mom. spread Linac length 70 MeV 35 mA 70 mA 36 µs 4 Hz 325.224 MHz 2.1 / 4.2 µm ≤ ± 10 -3 ≈ 35 m Main feature of p-LINAC:  CH-structures with high gradient  KONUS beam dynamics… General Requirements for BD:  High current  non-destructive BD  Machine protection: transformer based interlock  Dynamic range 60 dB, i.e. 0.3 mA or 1 % I nom (UNILAC >100 dB)  CH-structures: sensitive beam dynamics  high precision measurements for longitudinal phase space required

7 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 7 Requirements for Bunch Shape Measurements Requirements:  1 o of phase resolution: 77ps@36MHz, 26ps@108MHz and 8.6ps@325MHz  Beam characterization during commissioning: Test bench after each LINAC cavity  Change of ion species: Measurement for critical settings desirable But: no standard method established, only installation at 3 locations at UNILAC  High current of heavy ions  short penetration depth: non-destructive method preferred  Cost: not such important due to installation at few locations only  Wish of operation team: Measurement of longitudinal emittance Features of LINACs at GSI :  IH- and CH-structures with high gradient for heavy ion  KONUS beam dynamics with 0 o reference particle phase  non-Gaussian bunch shape

8 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 8 Particle Detector for 1.4 MeV/u Beams for Bunch Shape and longitudinal Emittance

9 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 9 UNILAC at GSI: Overview MEVVA MUCIS PIG RFQ IH1 IH2 Alvarez DTL HLI: (ECR,RFQ,IH) Transfer to Synchrotron 2.2 keV/u β = 0.0022 120 keV/u β = 0.016 11.4 MeV/u β = 0.16 RFQ, IH1, IH2 Gas Stripper U 4+ U 28+ Alvarez DTL Single Gap Resonators All ions, high current, 5 ms@50 Hz, 36&108 MHz Foil Stripper To SIS ↑ Constructed in the 70th, Upgrade 1999,  Injector for FAIR ion operation 1.4 MeV/u β = 0.054 10mm f rf = 36 MHz f rf = 108 MHz

10 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 10 Installation of the device at 1.4 MeV Matching Section MCP-Dia2.: d=80cm T. Milosic (GSI) et al., Proc. DIPAC‘09 Macro-pulse :0.1 ms < t < 5 ms  fast detector required

11 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 11 Longitudinal Emittance using two Particle Detectors Arrival time and time-of-flight between two particle detectors: 2 detectors for 1.4 MeV/u ions: Arrival at diamond detector compared to acc. f rf Bunch shape: Time resolution:  100 ps ⇔ phase resol. 1 0 for 36 MHz Energy: different arrival times ⇔ energy resolution 0.03%  E/E= -2* (t MCP - t Diamond )/t tot t tot = 48 ns Conversion factor:  E/E = 0.1%   t = 24 ps Intersecting material: Reduction of beam intensity e.g. by de-focusing or collimation Conclusion: suited for bunch shape meas. at accelerators with f rf < 100 MHz Difficult to achieve sufficient time resolution for long. emittance measurement

12 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 12 Beam Attenuation by Rutherford Scattering Particle attenuation via Rutherford scattering in 120  g/cm 2 Ta foil:  Single particle detection Influencing processes:  Finite solid angle   10 -4 (Lab.-system)  resolution better for light ions  Straggling by electronic stopping (Bethe-Bloch)  resolution better for heavy ions

13 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 13  10 mm Diamond detector, thickness 185 µm Least significant bit: 25 ps Resolution  30 ps double pulse res.  10 ns Detector Setting: Poly crystalline Diamond as 2 nd Detector Single particle signal Analog electronics Timing by double threshold disc. Digitalization by TDC CAEN V1290 Principle: Interval counter 1 ns/div 50 mV/div diamond disc. out Pulse width:  1 ns Count rate: up to 100 MHz broad pulse high distrib.

14 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 14 beam Detector Setting: Multi Channel Plate as 1 st Detector MCP  18 mm 50  anode Analog pulses: the good one the bad one 4 kV 2 kV 0 kV Installation for scattered ions Electric potential: 4 kV on foil, 2 kV on MCP front

15 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 15 Example of Measurement: Current dependent long. Distribution Example: Different low and high current Ar beam  The effect of the emittance blow-up due to the large space-charge forces. I = 5 mA I = 0.1 mA

16 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 16 Example of Measurement: Comparison to Theory Phase space measurement: Bunch shape: t dia Velocity from t dia – t MCP Particle detection,  10 min Result:  Non-Gaussian bunch shape,  Gaussian energy distribution  Comparison to theory: Too low correlation i.e. α Resolution:  Very good for bunch shape  Sufficient for total energy  In-sufficient for phase space Never-the-less: Used diagnostics for bunch shape & energy distribution (i.e. Twiss parameter  and  ) measure theory 1 o @108MHz =25.7 ps

17 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 17 Resolution Result:  Comparison to theory: Too low correlation i.e. α Resolution:  Bunch shape  good  Total energy  sufficient  Phase space  insufficient (10-fold better resolution required) Improvement: De-convolution using Gaussian approximation  Trustable results, but too indirect method Quantitative background suppression Innovative ‘Minimum Covariance Determinant Estimator’

18 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 18 Example of Measurements Reference setting: bunch  b = 0.43 ns, energy:  E = 1.4 % IH2 Phase shift 5 o :  t = 0.63 ns,  E = 1.3 % Tendency: Strong variation of bunch shape but energy width is measured as constant  not consistence measurement  correlation  = /  is wrong

19 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 19 Example of Measurements Due to the sensitive scattering foil an attenuation is required: Variation of slits width after stripping foil  Bunch shape ok for nominal setting  for low slit width wrong measurement Possible reason: Straggling of ions in slit knives ??? Must be investigated..... slit  5 mm slit  4 mm slit  3 mm slit  2 mm slit  1 mm slit .5mm

20 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 20 Limiting Factors for Emittance Measurement Uncertainty for detector effects & electronics: Poly-crystal diamond: discrimination: 50 ps Diamond: propagation time: 10 ps MCP: disc. of ugly pulses (for  E/E): 100 ps MCP: tilt of Al-foil: 25 ps TDC resolution & logical electronics: 30 ps  E/E uncertainty for scattering at Ta-foil : Straggling for Argon: 0.12 % Straggling for Uranium: 0.10 % Finite solid angle for Rutherford scat.: 0.03 % All processes are independent  Gaussian error propagation For actual device:  E/E = 0.1%   t = 24 ps Additional uncertainties:  Texture of foils  horizontal-longitudinal coupling after bend Requirements:  77 ps for bunch shape,  0.3 % for energy, but  0.03 % for phase space  prolongation of distance MCP – diamond does not improve the resolution  10 mm

21 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 21 Single Crystal Diamond Detector Measurement of arrival time and energy within one detector  single crystal diamond detector with energy resolution SC diamond manufactures specification: Size: 4.5 x 4.5 mm 2 Thickness: 100  m leakage current: 0.1 nA Energy resol. for  ’s: 1 % Test due by storing the pulse with 20 GSa/s, 2.5 GHz oscilloscope Typical diamond detector problem: Decrease of amplitude during irradiation  fit of slope for compensation

22 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 22 Single Crystal Diamond Detector Reconstruction of phase space via baseline restoring and pulse integration: Conclusion:  Well suited for bunch shape  Energy resolution at the boarder  Distribution of ‘stream’ due to scattering at slits as determined from the ToF Slit-Detector

23 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 23 Transverse Ion Beam Deflection at 11.4 MeV/u Test setup for longitudinal Emittance Determination

24 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 24 Longitudinal Emittance within dispersive Section Sketch by P. Gerhard Beam behind dispersive section Rhomb aperature dE dt „Pencil“ like beam from core of main beam Vertical chopper Luminescent screen & CCD camera or SEM-Grid SlitGrid Idea: Energy spread by dispersion Phase width by vertical deflection with ‘rf-buncher’:

25 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 25 Results of longitudinal Emittance Measurement: Alvarez Buncher Alvarez Bunchers „Off“Alvarez Bunchers „On“ 1 st buncher  focusing 2 nd buncher  defocusing

26 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 26 Conclusion Particle detector realization:  relatively simple technical installation  intercepting device, here scattering foil  not suited for high intensities  time resolution for entire signal processing chain  50 ps (poly-crystal diamond)  better time resolution of single-crystal device  total energy measurement possible, but detector resolution just sufficient  longitudinal phase space measurement not possible fro GSI parameter  time domain method: Suited for f rf < 100 MHz to have 1 o resolution Transverse deflection technology:  complex and expensive installation  requires special beam optical environment  can visualize longitudinal phase space  no dedicated tests done so far at GSI Thank you for your attention!

27 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 27 Just for Discussion (not a GSI Contribution!) Bunch Shape Measurement behind a photo-cathode:

28 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 28 Just for Discussion (not a GSI Contribution!) Bunch Shape Measurement behind a photo-cathode: Short cavity such that only TM 0n0 modes are possible, 1 ≤ n ≤ 12, 100 < Q < 1000 f 010 = 1550 MHz B. Roberts et al.

29 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 29 Just for Discussion (not a GSI Contribution!) Reconstructed signal Time domain Laser pulse B. Roberts et al.

30 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 30 Spare transparencies

31 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 31 Bunch Shape and longitudinal Emittance  Particle Detectors  Non-invasive Monitor

32 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 32 Novel Type of non-intercepting Bunch Shape Measurement Scheme for non-intercepting device:  Secondary electrons from residual gas  Acceleration by electric field (like for Ionization Profile Monitor)  Target localization by apertures and electro-static analyzer (Δy = 0.2 to 2 mm, Δz=0.2 to 1 mm)  rf-resonator as ‘time-to-space’ converter λ/4 resonator, Q 0  300, P in =50 W max.  Readout by MCP + Phosphor + CCD  Measurement done within one macro-pulse (presently: few pulses due to background)  Some improvements required  Conclusion: Quite complex device !

33 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 33 Realization for non-intercepting Bunch Shape Monitor E-field box and energy-analyzer: The installation for beam based tests:

34 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 34 Other Types of Bunch Shape Monitors (not used at GSI) x-ray created in a solid traget or gas-jet: Intercepting foil or Design by Argonne Nat. Lab, see P. Ostroumov et al., PAC’09. Design presently foreseen for Spiral2, presented by R. Revenko at this workshop Feschenko-Monitor: Micro-strip 50 Ω Faraday Cup: e.g.design: C. Deibele (SNS) Used at FNAL

35 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 35 Beam Diagnostics for FAIR p-LINAC Beam Para.Device # Non-dest.Remark CurrentTransformer 9Yes Dynamic transmission interlock Faraday Cups 4No Used as beam dump ProfileSEM-Grid 4No Standard, requires trans. control BIF (fluorescence) 1Yes For test only (during comm.) Transversal emittance Slit-Grid LEBT: Allison Scanner 3No Standard CEA/Saclay design PositionBPM 15Yes Online display Mean energyBPM (15)Yes Time-of-flight or phase Bunch shapeNon intersecting BSM Yes/No Under development Charge states behind source Wien Filter 1No From CEA Saclay

36 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 36 Beam Diagnostics at UNILAC and their Usage Control system: Data acquisition and presentation on 50 Hz pulse repetition Beam Para.Device#Non-dest.Remark CurrentTransformer 51 Yes Dynamic transmission interlock Faraday Cup (beam dump) 65 No High current: as beam dump ProfileSEM-Grid 81 No Requires transmission control BIF (fluorescence) 4 Yes Recently operable IPM (ionization products) 1 Yes Presently for test only Transversal emittance Slit-Grid 9 No Standard Pepper-pot 1 No Problem: Scintillation screen PositionBPM 25 Yes Online display Mean energy BPM (same as for position) 25 Yes Time-of-flight Bunch Shape Particle Detector 1 No Complex, requires low current Non-intercepting BSM 1 Yes Under development Screen:dispersion&deflection 1 No Only at one position possible

37 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 37 Example of Measurements 1 o @108MHz =25.7 ps Reference setting  Bunch shape  t =250 ps IH2 Phase shift 5 o   t  750 ps

38 L. Groening, Sept. 15th, 2003 GSI-Palaver, Dec. 10 th, 2003, A dedicated proton accelerator for p-physics at the future GSI facilities P. Forck: et al: Bunch Measurement at GSI Lund, February 11 th, 2013 38 Combined 0° Structure Overview and Definition of the Longitudinal KONUS Lattice Period lattice period: : long. phase advance of KONUS period i i-1 ii+1 IH cavity of the GSI HLI injector beam envelope From G. Clemente


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