# Presentation: 726703

## Longitudinal Diagnostics of Electron Bunches Using Coherent Transition Radiation 

**Daniel Mihalcea**

- Northern Illinois University
- Department of Physics

- Fermilab, Jan. 16, 2007

## Outline:

** ****Michelson interferometer**
** ****Bunch shape determination**
** ****Experimental results**
** ****Conclusions**

_**Outline:**_

## Fermilab NICADD Photo-injector Laboratory

**Fermilab NICADD ****Photo-injector Laboratory**

**FNPL is a collaborative effort of several institutes and universities to operate a high-brightness photo-injector dedicated to accelerator and beam physics research.**
** ****Collaborators include:**

**U. of Chicago, U. of Rochester, UCLA, U. of Indiana, U. of Michigan, LBNL, NIU, U. of Georgia, Jlab, Cornell University **

**DESY, INFN-Milano, IPN-Orsay, CEA-Saclay**

## FNPL layout

**Michelson interferometer for longitudinal diagnostics**

## Michelson Interferometer

**Michelson Interferometer**
**(University of Georgia & NIU)**

- Autocorrelation = I1/I2

_**Detectors:**_** **

**- ****Molectron pyro-electric**
**- Golay cell (opto-acoustic)**

## Data Flow

**Data Flow**

- Get Q

- Get I1 and I2

_**LabView code:**_

-  Advances stepping motor between x1 and x2 with adjustable step size (50 m)
-  At each position there are N readings (5)
-  A reading is valid if bunch charge is within some narrow window (Ex: 1nC  0.1 nC)
-  Position, average values of I1 and I2 and their ’s are recorded.
-  Autocorrelation function is displayed.

## Basic Principle (1)

**Basic Principle (1)**

_**Ginsburg-Franck:**_

**Detector aperture ******** 1 cm**

_**Backward transition radiation**_

## Basic Principle (2)

**Basic Principle (2)**

- Intensity of Optical Transition Radiation:

**Coherent part ******** N****2**

- To determine (z) need to know  _**I(**__****__**)**_ and the _**phase of f(**__****__**)**_

**Kramers-Kröning technique**

## Coherence condition 

**Coherence condition**** **

**Due to detector sensitivity:**

_**Acceptable resolution:**__** **_

**Need bunch compression !**

## Bunch Compression 

**Bunch Compression**** **

- RF field in booster cavity

- Electron bunch before compression

- Energy-Position correlation

**Head**

**Tail**

- After compression

## Measurement Steps

**Measurement Steps**

**Ideal apparatus**

**FT**

**K-K**

## Experimental results (1)

**Experimental results (1)**

## Experimental results (2)

**Experimental results (2)**

**Golay detectors: no problem with interference !**

_**Still need to account for:**_

** ****low detector sensitivity at low frequencies**
** ****diffraction at low frequencies**
** ****absorption at large frequencies**

## Experimental results (3)

**Experimental results (3)**

_**Low detector sensitivity**_

**Diffraction**

**Absorption**

**Interference**

_**Apparatus response function:**_

## Experimental results (4)

**Experimental results (4)**

_**Molectron pyroelectric detectors**_

## Experimental results (5)

**Experimental results (5)**

-  Molectron pyroelectric detectors
-  Kramers-Kroning method

- Head

- Tail

- Parmela simulation

**Head-Tail ambiguity**

## Experimental results (6)

**Experimental results (6)**

** ****FT **
** ****Spectrum correction with R(********)**
** ****Spectrum completion for:**

**and**

**K-K**

_**Golay cell**_

**Start point**

- z  1ps

## Complicated bunch shapes

**Complicated bunch shapes**

- Stack 4 laser pulses

- Select 1st and 4th pulses (t 15ps)

- Before compression

- After compression

- (Parmela simulations)

##  K-K method may not be accurate for complicate bunch shapes ! 

**Experimental results (7)**

_**Double-peaked bunch shapes**_

** ****K-K method may not be accurate for complicate bunch shapes !**** **

## K-K method accuracy

**K-K method accuracy**

- R. Lai and A. J. Sievers, Physical Review E, **52**, 4576, (1995)

**Generated**

**Reconstructed**

**K-K method accurate if:**

-  Simple bunch structure
-  Stronger component comes first

**Calculated widths are still correct !**

## Other approaches

**Other approaches**

_**Major problem:**_** the response function is not flat.**

**1. Complete I(********) based on some assumptions at low and high frequencies.**
-     R. Lai, *et al.* Physical Review E, **50**, R4294, (1994).
-     S. Zhang, *et al. *JLAB-TN-04-024, (2004).
**2. Avoid K-K method by assuming that bunches have a predefined shape and make some assumptions about I(********) at low frequencies.**
**    **A. Murokh, *et al.* NIM **A410**, 452-460, (1998).
-     M. Geitz, et al. Proceedings PAC99, p2172, (1999).
**    **

**This work:**

- D. Mihalcea, C. L. Bohn, U. Happek and P. Piot, Phys. Rev. ST Accel. Beams **9**, 082801 (2006).

## Conclusions:

** ****Longitudinal profiles with bunch lengths less than 0.6 mm can**
** ****be measured.**
** ****Systematic uncertainties dominated by approximate knowledge of response function and completion procedure.**
** ****Golay cells are better because the response function is more uniform.**
** ****Some complicate shapes (like double-peaked bunches) can be measured.**