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Emittance Measurement Methods: Practical Considerations and Mathematical Treatment

This presentation covers various methods for measuring emittance in accelerator systems, focusing on practical considerations and mathematical treatments. Topics include beam ellipse, beam transport, emittance normalization, laser wire usage, and measurement techniques. It explores the importance of emittance in determining luminosity and beam quality in accelerators, with an emphasis on methods like pepperpot, transverse beam profiling, and laser wires. The presentation also delves into skew correction, beam matrix reconstruction, and H- neutralization processes. The summary underscores the significance of emittance for accelerator operations and highlights key measurement techniques.

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Emittance Measurement Methods: Practical Considerations and Mathematical Treatment

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  1. G A Blair 1st DITANET School, at Royal Holloway Univ. London 2nd April 2009 Beam Emittance • Introduction • Mathematical treatment • Proton emittance • H- machines • ILC emittance measurement • Laser-wire – practical considerations • Summary

  2. Luminosity - Emittance Luminosity is dominated By the spot-sizes

  3. Conjugate Variables View from the top: Instantaneous motion is described by a point in “phase space”:

  4. Motion on a horizontal plane

  5. Consider a parabolic groove: View from the top: Individual particles will travel on elliptical trajectories in phase space

  6. General Solution where with a similar result for y constants to be determined from initial conditions determined by the beam-line

  7. Beam Ellipse H. Braun

  8. Beam Transport H. Braun

  9. Transport of Twiss Parameters H. Braun

  10. Effect of Acceleration on ε Normalised emittance: is preserved during acceleration “geometric” emittance H. Braun

  11. Common Units for ε H. Braun

  12. ε Measurement - I H. Braun

  13. Derivation of Twiss params: H. Braun

  14. ε Measurement - II H. Braun

  15. Change quad strength: H. Braun

  16. Need 3 or more measurements: H. Braun

  17. Formalism H. Braun

  18. H. Braun

  19. Pepperpot

  20. Principle and technical set up of the pepper pot emittance instrument. Copper block Scintillator screen Fast CCD Camera H- Ion Beam H- Beamlets Tungsten screen The linear shift mechanism mounted to the main flange. Adjustable camera mount. C. Gabor

  21. Longitudinal Emittance Conjugate variables E (→p), z

  22. Measurement in linac H. Braun

  23. Measuring the Transverse Beam Profile • Traditional method is to sweep a solid wire across the beam. • Measure background vs relative position of wire and beam. • Micron-scale precision required for LC • Solid wires would not stand the intense beams of the LC • Solid wires could ablate, harming SC surfaces nearby. • So: replace wire with a laser beam. • Count Comptons downstream.

  24. Laserwire

  25. y u x Skew Correction: x-y coupling ILC LW Locations Eb = 250 GeV Error on coupling term:

  26. Linac ILC

  27. Laser wire : Measurement precision Phys. Rev. ST Accel. Beams 10, 112801 (2007) I. Agapov, G. B., M. Woodley The Goal: Beam Matrix Reconstruction NOTE: Rapid improvement with better σy resolution Reconstructed emittance of one ILC train using 5% error on σy Assumes a 4d diagnostics section With 50% random mismatch of initial optical functions The true emittance is 0.079 m rad

  28. H- Neutralisation The process has threshold energy ~0.75 eV so it can be driven by a Nd:YAG laser operating at 1060 nm. A focussed laser beam can thus be used to • Measure emittance of H- beam • Enable proton production by laser-induced stripping. All the previous technical issues apply…

  29. Schematic Operation Front End Test Stand (RAL) – electrons + neutrals SNS (detect electrons)

  30. SNS laser-wire system Laser e- detector dipole to extract e-

  31. Higher Order Modes TM01 Their presence increases the effective “emittance” of the laser (M2>1) pure TM00 property of a realistic laser

  32. Summary • Emittance is an important parameter for accelerators • Determines the final luminosity of a collider • Determines the quality of a beam in a light source • Determines the aperture of a beam at any location, given a known set of optics. • Measurement: • Pepperpot for low energy protons • Transverse beam profile plus knowledge of optics: e.g. quad scans • Laser-wires for electron/positron and H- • Shintake monitor for 10s nm scale beams

  33. Thanks to: • A. Assadi • H. Braun (CAS 2008) • P. Forck • K. Wittenburg • C. Gabor Whose ideas I have used and whose slides I have borrowed! Enjoy the problem set !

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