# Presentation: 222527

## Lepton Beam Emittance Instrumentation

- Igor Pinayev
- National Synchrotron Light Source
- BNL, Upton, NY

## Outline

- Motivation and Definitions
- Invasive methods
- Three screens
- Wire scan
- Quadrupole and solenoid scan
- Non-invasive methods
- Visible light imaging
- Pinhole camera
- Imaging with zone plate
- Interferometric method
- Undulator radiation
- Optical diffraction radiation
- Conclusions

## Emittance Definition

- Emittance is a measure of area occupied by a beam in phase space
- It affects major operational parameter: brightness, luminosity, gain length, coherency, etc.

- x’

- Area = 

- For uncoupled beam

- The invariant emittance ellipse is given by

## Matrix Gymnastics

- Particle propagating from point to another
- can be described by the transport matrix

- Twiss parameters transform as follows

- For drift space with length L

- For thin lens

## Three Screens Method

- Requires long drift space
- Sensitive to optical magnification errors
- Space charge effects can be significant
- Shot-to-shot variations

- S0

- S1

- S2

## Wire Scan

## Factors Affecting Accuracy of Wire Scan

- tilt angle of wire
- dispersion in transfer line
- beam jitter
- scan non-uniformity

## Quadrupole Scan

- Beam parameters are extracted from the dependence of observed beam size vs. quadrupole strength
- Change in the upstream quadrupoles strength may be required because quadrupole focuses in one plane and defocuses in another

- Quadrupole (0, 0, 0)

- beam

- Screen (S)

## Extracting Data from the Quadrupole Scan

- For the thin quadrupole and drift with length L transport matrix is

## Solenoid Scan

- Similar to the quadrupole scan
- Solenoid introduces beam rotation (coupling)
- Low energy
- Radial symmetry can be used

## Imaging with Visible Radiation

- Used mostly for storage rings with well known -functions
- Versatile and easily realized
- Can be used for real-time beam measurements

- Synchrotron radiation

- Iris

- Lens

- Bandpass
- filter

- Neutral
- filter

- Camera

- Mirror

- Source length should be accounted for
- Mirror should provide minimal distortion under the heat load

## Pinhole Camera

- At ESRF 10 μ pinhole provides resolution of 13 μ for beam size

## Imaging with Fresnel Zone Plate

- source

- double crystal monochromator

- zone plate

- screen

- Monochromator is required due to the strong chromatic aberrations of zone plate
- SPring-8 achieved 4 μ resolution for beam size with the help of X-ray zooming tube
- Observed transient in the beam size during top-off operation

## Laser “Wire”

- Replaces solid “wire” with laser beam
- Can reach micron level resolution (waist 12 μ)

## Laser “Harp” 

- Standing wave interference pattern is generated by two crossing laser beams
- Electron beam is moved across the pattern and modulation in the intensity of Compton scattered photons is observed

## Interference Method

- Similar to Michelson stellar interferometer
- Measures dependence of contrast of interference fringes on slit separation

- For Gaussian beam

## Set-up KEK-ATF

## Undulator Radiation

- screen

- The nth harmonic wavelength

- Emittance of 0.2 nm was measured with 30 keV X-ray photons

*l*

- Undulator (LU)

## Undulator Spectrum

## Calculated vs. Measured

- SRW Calculations

- Measured

- 3

- 4

- 5

## Optical Diffraction Radiation

- =2500  y=0, 30 μm

- Dependence of contrast
- vs. beam size at different
- wavelengths

## Conclusions

- The emittance measurement technique became state-of-the-art capable to satisfy most requirements
- Wide variety of methods is used
- Some methods require thorough theoretical consideration
- Some has experimental complexity
- New methods will appear as improvements in beam quality will require more precise instrumentation

- mrad = meter·radian

## Optical Klystron Spectrum

- Spectrum is interference of two wave packets
- Fringes visibility is defined by energy spread
- Only longer wavelength part of the spectrum is affected by non-zero emittance
- Horizontal emittance is obtained

- Undulator 1

- Undulator 2

- Buncher

## source

- screen

- mask

- L