1. 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

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.
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

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. 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:

26. Linac
ILC

28. Laser wire : Measurement precision
Phys. Rev. ST Accel. Beams 10, (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 m rad

29. 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…

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

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

32. 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

33. 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

34. 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 !