1. Longitudinal Beam Diagnostics with the LBS Line 17. November 2009 Linac4 Beam Coordination Committee Meeting Thomas Hermanns

2. Thomas Hermanns 17. November 20092 Geographical Overview LT.BHZ20 LTB.BHZ40 Transfer Line Linac4 and Dump Line LBE Line LBS Line LBE Line LBS Line (1)(2) (3) Slit (1) Spectrometer Magnet (2) SEM Grid (3) Beam Dump

3. Thomas Hermanns 17. November 20093 Introduction LBS line: Diagnostics line close to PS Booster injection point Measurement of the Linac4 beam energy and energy spread  Correlation between beam energy and vertical beam position induced by spectrometer magnet Subject of this presentation (1) Proposal for a spectrometer line for Linac4 operation (2) Physical performance of the proposed line (3) List of requirements and functional specifications for LBS line upgrade

4. Thomas Hermanns 17. November 20094 Energy Distribution (behind slit) 159.204 MeV dEdE160.6 keV E kin (min.)158.9 MeV E kin (max.)159.5 MeV

5. Thomas Hermanns 17. November 20095 Experimental Principle Experimental quantity: Fitted vertical spatial particle distribution on SEM grid  Maximum Value  Mean beam energy (from calibration function)  Beam Size  Energy/Momentum spread Install SEM grid at position where beta-function has a local minimum Reduce vertical emittance by vertical slit Analyze particles by strong magnet with large bending angle (high dispersion) Local dispersion function from simulations

6. Thomas Hermanns 17. November 20096 Simulation Tools Definition of line layout with envelope code (Trace 3-D)  Position of slit, spectrometer magnet, and SEM grid  Parameters of spectrometer magnet  Proposal for a LBS line layout Implementation of the LBS line layout in particle tracking code (Path)  Single particle tracking through line  Create output particle distribution at SEM grid position to analyze  Simulation of measurements errors Data evaluation with analysis package (ROOT)  Physical performance and functional specifications

7. Thomas Hermanns 17. November 20097 Proposed Optical Parameters Slit  Position: 4089mm behind LTB.BHZ40  Aperture: 148mm (horizontal)  1mm (vertical)  Length: 200mm (absorption length of H - -ions at 160 MeV in carbon: 85mm) Spectrometer Magnet  Position: 6286mm behind slit exit  Radius: 1500mm (B=1.27T)  Bending Angle: 54°  Edge angles: 10° SEM grid  Position: 4139mm from mid-point of magnet  Wire clearance: 0.75mm (energy resolution 57 keV)  About 20% of all incident particle arrive at SEM grid (I  13mA)

8. Thomas Hermanns 17. November 20098 Simulation Results Correlation factor: -99.7% Determination of maximum value  (Wire-)binned projection on spatial axis to fit 2 nd order polynomial Current per wire: few µA to several 10 µA  Lower limit 5.5 nA  time-differentiated readout seems possible at MHz-rate Correlation for Nominal Energy“SEM Grid Simulation” and Data Fit dE/dy  82 keV/mm dE per wire  13-14 keV

9. Thomas Hermanns 17. November 20099 Results for Mean Energy Shift manually energy within  1MeV Linear Correlation between fitted position and central energy value Energy shifts determine vertical length of SEM grid

10. Thomas Hermanns 17. November 200910 Results for Energy Spread (reference value 160.6 keV) Validity of approximation  Ratio of total beam size to beam size for virtual beam with dp/p=0: 11.918   =0.0842  Perturbation less than 1% Reconstructed Energy Spread Reconstructed157.9 keV Deviation-1.7%

11. Thomas Hermanns 17. November 200911 Uncertainties Alignment errors  Slit, magnet and SEM grid displaced by  1mm Manufacturing errors  Magnet edge angles:  0.5°  Vertical slit aperture:  5% (equivalent to 50µm) Spectrometer B-field:  0.1% Variation of vertical slit width Variation of slit length Variation of input parameters at LTB.BHZ40

12. Thomas Hermanns 17. November 200912 Mean Energy (reference value 159.204 MeV) Maximum position shifted by... ... error on fit parameter ... systematic error due to deviations from nominal line design Intrinsic Error: Energy spread on one wire due to finite vertical slit width Mean Position Nominal Fit -0.2938  0.1020 mm Sys. Error3.4976 mm Total Error Mean Energy (with dE/dy  82 keV/mm) Absolute 8.4 keV (fit)  286.5 keV (sys.)  13-14 keV (intrinsic) Relative 1.8  10 -3

13. Thomas Hermanns 17. November 200913 Beam Size and Vertical Dispersion (reference value 158.2 keV) Beam Size  Statistical error of beam size measurement  Systematic error due to deviation from nominal line design Vertical Dispersion Value  Systematic error due to deviation from nominal line design Total Error Dispersion Absolute0.6 keV (sys.) Relative 0.4  10 -2 Total Error Beam Size Absolute 2.7 keV (stat.)  0.9 keV (sys.) Relative 1.8  10 -2

14. Thomas Hermanns 17. November 200914 Error on Energy Spread (reference value 158.2 keV) Total error on energy spread  Error on beam size and dispersion  Intrinsic Error: Energy spread on one wire due to finite vertical slit width Total Error Energy Spread Absolute 2.9 keV (Beam Size)  0.6 keV (Dispersion)  13-14 keV (intrinsic) Relative 8.3  10 -2 - 8.9  10 -2 Example for Gaussian distributions with energy width 14 keV and energy difference 57 keV

15. Thomas Hermanns 17. November 200915 Perturbation Coefficient  (reference value 0.0842) Systematic error due to deviation from optimal design Perturbation still remains below 1% if error is included Difference between energy spread neglecting and respecting  well below other sources of errors dE (  = 0) − dE (  << 1) = 0.5 keV Total Error Perturbation Coefficient  Absolute0.0064 (sys.) Relative 7.6  10 -2

16. Thomas Hermanns 17. November 200916 Additional Studies I Variation of slit length (select more dense material than carbon)  Perturbation coefficient increases by 0.5% if slit length is reduced to 20 mm  Transmitted current through slit increases by 6%  No significant influence on line design Variation of vertical slit aperture  Change vertical aperture by factor k=0.5 and k=2  Perturbation coefficient and intrinsic resolution scales with 1/k  Transmitted current scales with k  Lower aperture  Reduction of perturbation and better resolution, but production more challenging (accuracy and potentially cooling)  Larger aperture  Beam size must potentially be corrected for contribution from beta-function to obtain true energy spread (result becomes more dependent on simulation code)

17. Thomas Hermanns 17. November 200917 Additional Studies II Variation of beam input parameters  Input beam at LTB.BHZ40 approximated by Gaussian distributions  Vertical Twiss-parameters and vertical emittance separately set to half and twice of their nominal values  Values of perturbation coefficient  coincide to each other  Slit acts as a kind of “equalizer”  Contribution to total beam size due to evolution of beta-function remains less than 1%  Transmitted current varies by a factor of up to 2  Effect on design of beam dump behind SEM grid  Could be compensated by variable slit aperture

18. Thomas Hermanns 17. November 200918 LBS Line with Quadrupoles (based on an initiative by C. Carli) Build LBS line with a pair of quadrupole magnets instead of slit to create local minimum of beta-function  Avoid construction of a slit, which gets activated  Full beam dump required at the end of line Specifications for spectrometer magnet and SEM grid similar Energy spread sampled per wire  50 keV (compared to 13-14 keV)  Intrinsic error at the order of required resolution  Further systematic error study missing Total beam size contains a 10% contribution due to evolution of beta- function (compared to 1 %)  Technical advantages, but reduced physical performance  First steps towards an alternative scenario available

19. Thomas Hermanns 17. November 200919 Summary (reference values E=159.204 MeV and dE=160.6 keV) Mean Energy Measurement Absolute Error286.9 - 287.0 keV Relative Error 1.8  10 -3 Energy Spread Measurement Offset-2.7 keV (-1.7 %) Absolute Error13.3 - 14.3 keV Relative Error 8.3  10 -2 - 8.9  10 -2

20. Thomas Hermanns 17. November 200920 LBS Line --- List of Wishes LTB.BHZ40 (keep present deflection angle)  Increase current to 111 A for LBS line and 179 A for LBE line (I max = 210 A)  In principle power supply can provide 250 A  Water-cooled magnet, needs to check if flow sufficiently high for higher current Slit (reference point of alignment at exit of slit)  Vertical aperture 1mm (precision of a few 10 µm tolerable)  Sufficiently long to absorb incident particles (simulations between 20 and 200 mm done)  If cooling necessary check in experimental area if enough space is available Spectrometer magnet (not yet designed)  Bending angle: 54°  Radius: 1500 mm (B=1.27 T)  Edge angles: 10°  Beam size at entrance: 5.1 mm  2.0 mm (  horizontal   vertical )  dB/B  dE kin /  p  2  10 -4  Power supply (and cooling infrastructure?)  NMR probe for B-field measurement

21. Thomas Hermanns 17. November 200921 LBS Line --- List of Wishes II SEM grid  Extension 1:  5 mm to sample the entire distribution at nominal energy  Extension 2:  17 mm to allow for energy shifts by  1 MeV  Wire spacing: 0.75 mm  Time-resolved readout with about 1MHz to measure resolve longitudinal energy painting  Check option of to steer beam to high-resolution centre in case of energy shifts (avoid high costs for large grid with small clearance) Beam Dump  Installation at ceiling height of experimental area  Beam size at SEM Grid: 3.0 mm  2.0 mm (  horizontal   vertical )  Beam angle at SEM Grid: 0.6 mrad  0.7 mrad (  horizontal   vertical )  Current to be absorbed (up to 20 mA)  Pulse length 100 µs Transformer (presently three are installed)  Keep/upgrade at least one behind slit and one behind spectrometer magnet

22. Thomas Hermanns 17. November 200922 LBS Line --- List of Wishes II Interlocks  Temperature sensors (LTB.BHZ40, slit, spectrometer magnet, beam dump)  Power supply sensors (B-field controlling) for LTB.BHZ40 and spectrometer magnet  Transformer signals ... Software  Data display  Data fit and beam size simulations  Calculation of mean energy and energy spread

23. Thomas Hermanns 17. November 200923 Merci vielmals! Thanks a lot for patient explanations, valuable assistance, and intense discussions to Giulia Bellodi, Christian Carli, Mohammad Eshraqi, Klaus Hanke, Alessandra Lombardi, Bettina Mikulec, Uli Raich

24. Backup Slides

25. Thomas Hermanns 17. November 200925 Initial Bias of the Measurement Measurement is unbiased  Correlation factor: 0.4% Selecting a beam slice by slit does not favour a certain energy interval Correlation for Nominal Energy at the Entrance of the Slit

26. Thomas Hermanns 17. November 200926 Acceptance-Rejection-Method Beam size from fit function to SEM grid signal by statistical approach Acceptance-rejection method  Generate pairs of random numbers and decide to accept/reject with fitted curve Projection of accepted numbers to vertical position axis RMS of distribution = Beam Size Series of ten repetitions with 10 7 random numbers  Statistical error O(10 -4 ) acceptance region

27. Thomas Hermanns 17. November 200927 Error on SEM Grid Resolution (reference value 57 keV) Error sources  Systematic error due to deviation from nominal line design  Manufacturing error on wire distance Total error dominated by error on wire distance  Length L between spectrometer magnet and SEM grid is much larger than wire distance s  s/L=O(10 -4 ), but error differ only by one order of magnitude Error SEM Grid Resolution ds = 0.1 mm7.6 keV ds = 0.02 mm1.5 keV ds = 0.01 mm0.8 keV

28. Thomas Hermanns 17. November 200928 Results Additional Studies I Beam Size  dE/dydE per wireI behind Slit Slith Width 0.5 mm1.9672 mm0.045281.8 keV/mm7-8 keV6.1 mA 1.0 mm1.9593 mm0.084281.9 keV/mm13-14 keV13.2 mA 2.0 mm1.9828 mm0.162978.5 keV/mm26-27 keV25.6 mA Slit Length 200 mm1.9593 mm0.084281.9 keV/mm13-14 keV13.0 mA 150 mm1.9587 mm0.085481.9 keV/mm13-14 keV13.2 mA 100 mm1.9579 mm0.086781.9 keV/mm13-14 keV13.4 mA 50 mm1.9586 mm0.088381.8 keV/mm13-14 keV13.6 mA 20 mm1.9601 mm0.089181.8 keV/mm13-14 keV13.8 mA

29. Thomas Hermanns 17. November 200929 Results Additional Studies II For modification of input ellipses beam in Gaussian approximation Beam Size  dE/dydE per wireI behind Slit Modified Input Parameters Nominal1.9593 mm0.084281.9 keV/mm13-14 keV13.0 mA Nominal (Gauß) 1.8664 mm0.084381.9 keV/mm13-13 keV10.9 mA 0.5   0 1.8816 mm0.085981.8 keV/mm13-14 keV7.3 mA 2.0   0 1.8708 mm0.078582.0 keV/mm12-13 keV21.3 mA 0.5   0 1.8527 mm0.082081.9 keV/mm12-13 keV16.6 mA 2.0   0 1.8713 mm0.086982.2 keV/mm13-14 keV5.4 mA 0.5   0 1.8627 mm0.085082.0 keV/mm13-13 keV15.6 mA 2.0   0 1.8788 mm0.082182.1 keV/mm12-13 keV7.5 mA