1. Simulation Techniques in Beam Instrumentation Adam Jeff CERN & University of Liverpool

2. adam.jeff@cern.ch A ‘typical’ diagnostic instrument…

3. adam.jeff@cern.ch Contents LHC Longitudinal Density Monitor – Synchrotron Light (SRW) – Instrument Response (C++) Off-axis Undulator Radiation for CLIC – Magnet field (CST) – Synchrotron Light (SRW) – Light Propagation (ZEMAX) Focusing a neutral gas jet – ‘Optics’ (ZEMAX) – Mechanical strength (ANSYS)

4. adam.jeff@cern.ch LHC Longitudinal Density Monitor

5. adam.jeff@cern.ch Longitudinal Density Monitor ProtonsLead Ions Maximum beam energy (2010-11)3.5 TeV3.5 x 82 TeV / ion Revolution period89 μs RF period2.5 ns Minimum bunch spacing25 ns100 ns Maximum number of bunches2808592 Bunch population (ultimate)1.7 x 10 11 8.2 x 10 9 charges [10 8 ions] 9 out of 10 buckets should be empty… …but they’re not.

6. adam.jeff@cern.ch Longitudinal Density Monitor APD TDC synchrotron light LHC turn clock Electrical pulse Arrival time Single Photon Counting Profile is built up over many turns A very high dynamic range can be achieved with a long integration time But all systematic effects need to be corrected for

7. adam.jeff@cern.ch Longitudinal Density Monitor Synchrotron Radiation Workshop (SRW) SRW computes the radiated field from ‘first principles’ First, we define our beam: Why simulate? Well-known analytical expressions for dipoles and ‘ideal’ undulators The LHC sync. light monitor uses a short undulator (2 periods) ‘Edge radiation’ from the fringe field of the dipole is also important I lied!

8. adam.jeff@cern.ch Longitudinal Density Monitor Magnetic field SRW allows the radiation to be simulated from magnetic field map or from trajectory Neither is ideal for our case – undulator field is constant while dipole field ramps with beam energy Fortunately, SRW allows flexible programming so the field can be defined for each energy

9. adam.jeff@cern.ch Longitudinal Density Monitor <- Define the sampling space Set the simulation parameters -> “The independence, to a given precision, of the results on the simulation parameters is a necessary but not sufficient condition for the validity of the simulation”

10. adam.jeff@cern.ch Longitudinal Density Monitor1 / 17

11. adam.jeff@cern.ch Longitudinal Density Monitor Undulator Dipole

12. adam.jeff@cern.ch Longitudinal Density Monitor

13. Why simulate? The LHC filling pattern is complex. The correction will not be the same for all bunches, since the deadtime due to photon counts from a bunch affects many following bunches Nominal LHC filling scheme

14. adam.jeff@cern.ch Longitudinal Density Monitor We set up a Monte Carlo simulation Photons arrive stochastically and trigger the detector deadtime Each counted photon may cause an afterpulse The photon counts are collected in a histogram A second procedure performs a correction on the histogram The corrected histogram is then compared to the original profile

15. adam.jeff@cern.ch Longitudinal Density Monitor

16. Bunch number -> Total counts per bunch

17. adam.jeff@cern.ch Longitudinal Density Monitor Deadtime correction successfully benchmarked in lab tests using pulsed LED

18. adam.jeff@cern.ch Longitudinal Density Monitor Main bunch Satellites Afterpulsing Deadtime Ghost bunches

19. adam.jeff@cern.ch Longitudinal Density Monitor Corrected for deadtime

20. adam.jeff@cern.ch Longitudinal Density Monitor Corrected for deadtime and afterpulsing Corrected for deadtime Achieved a dynamic range > 10 5 thanks to correction algorithm Only LHC instrument capable of measuring ghost and satellite bunches Crucial for calculation of true LHC luminosity

21. adam.jeff@cern.ch Off-axis undulator radiation for the CLIC DriveBeam

22. adam.jeff@cern.ch Undulator Radiation Why Simulate? Need to take into account imperfections of a short, wide-gap undulator Non-intercepting diagnostic for high-intensity Drive Beam linac Observe the off-axis component of SR from an undulator Undulator period adjusted for each position (energy) on the linac, to produce UV on-axis and visible light at ~3 mrad

23. adam.jeff@cern.ch Undulator Radiation A ‘high quality’ undulator generally needs gap width < period length In this case, the large aperture of the beam pipe ≈ period Use CST magneto-static solver to compute field quality Side view End view

24. adam.jeff@cern.ch Undulator Radiation A ‘high quality’ undulator generally needs gap width < period length In this case, the large aperture of the beam pipe ≈ period Use CST magneto-static solver to compute field quality Looks OK – but what is the effect on the synchrotron radiation?

25. adam.jeff@cern.ch Undulator Radiation Import the field map from CST into SRW to compute radiation SRW only takes a ‘line’ field map Separate simulations for on-axis and off-axis particles Again, looks OK less than 5% variation between on-axis and off-axis particles But what about depth-of-field effects?

26. adam.jeff@cern.ch Undulator Radiation SRW contains an optics propagation module but it is limited and not user-friendly. Instead, we transfer the synchrotron radiation computed by SRW into ZEMAX for optical simulation. We need to write the full wavefront as a.zbf ZEMAX beam file Include some ‘padding’ around the edges to stop ZEMAX treating the edge of the file as an aperture Can then use ZEMAX Physical Optics Propagation (POP) PSF smallest for shorter undulator

27. adam.jeff@cern.ch Undulator Radiation SRW contains an optics propagation module but it is limited and not user-friendly. Instead, we transfer the synchrotron radiation computed by SRW into ZEMAX for optical simulation. We need to write the full wavefront as a.zbf ZEMAX beam file Include some ‘padding’ around the edges to stop ZEMAX treating the edge of the file as an aperture Can then use ZEMAX Physical Optics Propagation (POP) Small improvement if horizontal polarisation is used

28. adam.jeff@cern.ch Focusing a neutral Gas Jet

29. adam.jeff@cern.ch Gas jet focusing To measure the profile of very intense beams, we would like to build a ‘gas jet scanner’ A thin jet of gas will be scanned through the beam like a wire scanner To generate a sufficiently narrow jet, we use interference on the de Broglie wavelength of the gas molecules Fresnel Zone Plate The path difference between each successive light ring is equal to 1 wavelength (at the focal point) constructive interference. Each zone is equal in area Focal spot size is roughly the width of the narrowest (outer) zone Compared to traditional lens: no spherical aberration, large chromatic aberration DeBroglie wavelength ≈ 0.05 nm for Helium jet Outer zones need to be very small – and zone plate must be thin

30. adam.jeff@cern.ch Gas jet focusing Photon Sieve replaces clear zones of an FZP with a series of holes + Sharper focusing - Lower transmission + Easier to manufacture Apodised Photon Sieve reduces higher order diffraction, increases central maximum

31. adam.jeff@cern.ch Gas jet focusing Why Simulate? Many variations on the photon sieve: varying the hole size, placement, apodisation, etc. Little research on which one is better for different situations Evaluate different sieves according to various figures of merit: Peak Intensity in the focal spot. Ultimately, signal strength will depend on this. Transmitted power. A measure of how ‘open’ the plate is. The higher the better. FWHM of focal spot. As small as possible for resolution. However, all the designs produce spots which are plenty small enough. In reality this will be dominated by chromatic effects (not investigated yet). % encircled in 10 μm or 100 μm. Maybe the most important – shows what fraction is spread out into higher order and ‘zeroth order’ diffraction.

32. adam.jeff@cern.ch Gas jet focusing Design DescriptionPeak irradianceTransmitted powerFWHM of focal spot% in 0.01mm% in 0.1mm micrometers Sieve, size 1, first zone 1, 10 rings755.60E-040.355997 Sieve, size 1.35, first zone 1, 10 rings77.67.50E-040.355097 Sieve, size 1.5, first zone 1, 10 rings718.40E-040.354898 Random Angle Sieve, size 1, first zone 1, 10 rings514.70E-040.355697 Random Angle Sieve, size1.35, first zone 1, 10 rings496.00E-040.354897 Random Angle Sieve, size 1.5, first zone 1, 10 rings436.80E-040.354898 Sieve, size 3.5 holes, first zone 3, 6 rings8.71.10E-030.33099 Sieve, size 3.5 holes, first zone 2, 6 rings9.41.20E-030.352799 Sieve, size 3.5 holes, first zone 1, 5 rings6.99.80E-040.46.699 Apodised Sieve, size 1, first zone 1, Gaussian 0.8,15,0835.90E-040.355797 Apodised Sieve, size 1, first zone 1, Gaussian 0.8,15,81959.20E-040.356496 Apodised Sieve, size 1, first zone 2, Gaussian 0.8,15,81808.80E-040.356496 Apodised Sieve, size 1, first zone 1, Gaussian 0.8,8,0222.90E-040.554798 Equal holes sieve, 1 micron, 16 rings612.20E-030.32297 Equal holes sieve, 2 micron, 10 rings102.50E-030.32798 Equal Holes sieve, 5 micron, 6 rings1.32.50E-0355099 Zone Plate, first zone 0, 6 rings1449.20E-040.56499 Zone Plate, first zone 0.5, 6 rings1449.10E-040.56299 Zone Plate, first zone 1, 6 rings1449.10E-040.45699 Zone Plate, first zone 1.5, 6 rings1449.10E-040.45399 Zone Plate, first zone 2, 6 rings1449.20E-040.45399 Evaluate different sieves according to various figures of merit:

33. adam.jeff@cern.ch Gas jet focusing Evaluate different sieves according to various figures of merit:

34. adam.jeff@cern.ch Gas jet focusing Will such a thin sheet withstand the pressure of the gas jet? Simulation using ANSYS mechanical: Define the geometry (procedurally!) Fix outer edge and apply uniform pressure

35. adam.jeff@cern.ch Gas jet focusing Will such a thin sheet withstand the pressure of the gas jet? Simulation using ANSYS mechanical: Pressure 10 -4 mbar 0.2 micron Silicon Nitride Stress << material tolerances

36. adam.jeff@cern.ch Gas jet focusing Will such a thin sheet withstand the pressure of the gas jet? Simulation using ANSYS mechanical: Pressure 10 -4 mbar 0.2 micron Silicon Nitride Deformation << thickness

37. adam.jeff@cern.ch Gas jet focusing ‘Atomic sieve’ currently in production!

38. adam.jeff@cern.chConclusions Conclusions Optimisation of beam instrumentation often involves simulations in a number of different fields Usually no single program can solve all needs Where possible simulations can be combined by passing results from one program to the next You can lie to your simulations – but be aware that they might lie back !

39. Thank you for your Attention