Optical Transition Radiation

Klara Insulander Björk,

Chalmers University of Technology,

Gothenburg, Sweden

Beam profile measurements with

Outline

• Beam diagnostics?

• Physical principle

• Mathematical description

• Beam profile measurement

• The BIBLE

• Summary

Beam diagnostics?• You need to know stuff about your beam:

- If it is there at all- Where it is- What size and shape it has- How it evolves in time- Its energy, etcetera…

• Measurements using Optical Transition Radiation (OTR) involve letting the beam pass through a foil

► It is mostly used for profile measurements

Physical principle

• A charged particle moves through vacuum with its accompanying Coulomb field

• It hits a foil of a medium having a different dielectric constant

• The Coulomb field adapts to the new medium

• The difference in fields is emitted as transition radiation

C am era

B eamO T R fo il

L en s

W in d o w

Mathematical description

zzzxx

zz

c

qI

22222

222

2

2

//sincos)cos1(

1cos

2

22

2222

)cossin1)(sin1cos1(

sin1cossin)cossin11(

zzzzxx

zxzxzxxzzz

zzzxx

zyzx

c

qI

22222

22242

2

2

sincos)cos1(

1coscos

222 )cossin1)(sin1cos1(

1

zzzzxx

The angular intensity distribution is given by:

212121 ),(),(),( ddIII beamzOTRz

The actual angular intensity distribution becomes:

Beam profile measurement• Put the camera in the image plane of the

optical system to get a geometrical image of the beam

• Information on transverse beam profile (beam size and shape)

• OTR is fast – resolution better than picosecond• Use a streak camera to get the longitudinal beam profile (bunch length and spacing)• Converts time variation into space variation

The BIBLE

• The acronym (of course) stands for Beam Instrumentation BookLEt, a pocket sized document for beam instrumentation users

• My work – the chapter on OTR• The same information is also

available as a webpage• Calculation of important

parameters can be done with a Matlab program

x [m]

y [m

]

-0.1 -0.05 0 0.05 0.1

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

Summary• You need to know stuff about your beam• Let it pass through a foil and you get OTR• Look at the angular distribution to get info on energy and

divergence• Look directly at the image of the beam to get information

on beam size, shape and position• Use a streak camera to get information on bunch length

and spacing• Read the BIBLE in case you forget what I just told you

Questions?