# Presentation: 211318

## Bunch length measurements at JLab FEL using coherent transition and synchrotron radiation

- _P. Evtushenko_, J. Coleman, K. Jordan, M. Klopf, G. Neil, G. Williams

## JLab FEL (layout and longitudinal matching)

- Requirements on phase space:
- Long bunch in linac
- high peak current (short bunch) at FEL
- bunch length compression at wiggler
- “small” energy spread at dump
- energy compress while energy recovering
- “short” RF wavelength/long bunch
-  get slope *and curvature* right

## Bunch length measurements using coherent radiation

- Transition (synchrotron) radiation is produced when the electron bunch passes a boundary of two media
- 	(magnetic field).
- Response time is zero. Shape of the radiation pulse is a “copy” of the electron bunch shape.
- When the wave length of the radiation becomes more than the bunch length the radiation becomes
- 	_COHERENT_.  (   L )
- Power is proportional to:
- 		intensity of incoherent radiation  N
- 		intensity of coherent radiation     N2
- Measurements of the radiation spectrum give information about  the bunch length.
- An interferometer could be used to measure the spectrum.

- at 135 pC
- N  8.4108

## Interferometers 

- We use two different interferometers;
- essentially both are a modification
- of the Michelson interferometer.
- The two interferometers differ in
- implementation;
-    Beam splitter
-    Polarizer
-    Detector
-    Focusing element
-    _Mirror position measurements!_

- Modified Marin-Puplett interferometer:
- (step scan device 2 min/scan)
-   beam splitter & polarizer (wire grids)
-   detector (Golay cell)
-   focusing (Plano-convex lens)
-   mirror position is set by
-   _step motor_
**Used with CTR**

- Michelson interferometer:
- (rapid scan device 2 sec/scan)
-   beam splitter (silicon)
-   detector (pyroelectric)
-   focusing (parabolic mirrors)
-   mirror position is measured by
-   _another built-in interferometer_
**Used with CSR**

## Mathematics of Michelson interferometer 

- the _autocorrelation function_ is
- measured with the help of an
- interferometer

- The Wiener-Khintchine theorem says:
- “the Fourier transform of the _autocorrelation_ function
- is the _power spectrum_”.

- longitudinal field profile
- at the MPI entrance

- longitudinal field profile
- at the _MPI_ exit

- detectors measure
- intensity IE2

## Interferogram example & corresponding spectrum

- raw data – interferogram

- Fourier transform of the interferogram

## Bunch length estimation

- the Gaussian shape
- of the bunch is assumed

- its power spectrum is
- also Gaussian

- low frequency cut-off
- diffraction on the
- detector input window
- the losses are
- approximated by

- The fit function is used

## Pulsed beam measurements; RMS 148 fs

- The mod. Martin-Puplett interferometer (the Happek device) measurements.

## CW beam measurements 0.31 mA; RMS 147 fs

## CW beam measurements 0.62 mA; RMS 151 fs

## CW beam measurements 1.25 mA; 163 fs

## CW beam measurements 2.51 mA; 145 fs

## Pulsed beam measurements vs. CW beam

- The bunch length does not change with beam current.

## Very short and very long bunches

- The bunch compression is optimized for the nominal (135 pC) bunch.
- It is also strongly bunch charge dependent.

## Beam stability

- The interferometer measurements also provide
- an information about the beam stability!

## Conclusion

- Further developments

- A modified Martin-Puplet interferometer and Michelson interferometer
- are routinely used at JLab FEL for bunch length measurements.
- Michelson interferometer (rapid scan device) provides non-invasive
- measurements with high current CW beam.
- Results of the measurements of two interferometers agree
- within 15%, when the same (frequency domain) data evaluation approach
- is applied.

- Make the Michelson interferometer to work with the pulsed beam.
- Also the modified Martin-Puplett interferometer could be used with the
- CW beam if another detector is used (with synchrotron radiation).
- To eliminate the water vapor absorption the Michelson interferometer
- will be operated in vacuum.