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

Luminosity - Emittance Luminosity is dominated By the spot-sizes

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

Motion on a horizontal plane

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

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

Beam Ellipse H. Braun

Beam Transport H. Braun

Transport of Twiss Parameters H. Braun

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

Common Units for ε H. Braun

ε Measurement - I H. Braun

Derivation of Twiss params: H. Braun

ε Measurement - II H. Braun

Change quad strength: H. Braun

Need 3 or more measurements: H. Braun

Formalism H. Braun

H. Braun

Pepperpot

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

Longitudinal Emittance Conjugate variables E (→p), z

Measurement in linac H. Braun

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.

Laserwire

Skew Correction: x-y coupling ILC LW Locations Eb = 250 GeV x(m) y (m) opt(°) u (m) 39.9 2.83 86 3.99 17.0 1.66 84 2.34 81 3.95 39.2 1.69 88 2.39 7.90 3.14 68 4.13 44.7 2.87 4.05 Error on coupling term:

Linac ILC

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

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…

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

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

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

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

Whose ideas I have used and whose slides I have borrowed! 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 !