Sub-ps bunch length measurementsat the JLab FEL

with coherent transition radiation (CTR) and “Martin-Puplett” interferometer

Pavel Evtushenko, JLab

The key principles of the diagnostic

Operation of the Matrin-Puplett interferometer

An examples of data

Low frequency cut-off

Data Evaluation in frequency domain

Pulsed beam vs. CW beam measurements

ps and sub-ps bunch length measurements using CTR

1. Transition radiation is produced when the electron bunch passes a boundary of two media.

2. Respond time is zero. Shape of the radiation pulse is a

“copy” of the electron bunch shape.

3. When the wave length of the radiation becomes more than the bunch length the radiation becomes COHERENT. ( L )

4. Power is proportional to:incoherent radiation N coherent radiation N2

5. Measurements of the radiation spectrum give information about the bunch length.

Coherent radiation power spectrum

€

˜ E b(ω ) ∝ ˜ E S k(ω )e iωτ k

k

∑

€

Pb(ω ) = ˜ E b(ω ) ˜ E b*(ω ) = ˜ E S k(ω )e iωτ k ˜ E S

*j(ω )e−iωτ j

j

∑k

∑

€

Pb(ω ) = Ps(ω ) N e + e iω (τ k −τ j )

j ≠k

∑k

∑ ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

€

PS (ω ) = ˜ E S (ω ) ˜ E S*(ω )

€

e iωτ k

k

∑ ≡ N e fb(t)e iωtdt∫ = ˜ f b(ω )

€

Pb(ω ) = PS (ω ) N e − N e( N e +1) ˜ f b(ω )2

[ ]

€

˜ f b(ω )2

€

Eb(r r ,t) = ES k(

r r ,t −τk )

k

∑ - Coulomb field of electron bunch

- Fourier transform of the Coulomb field

- Power spectrum of the bunch

- Power spectrum of a single electron

- Bunch Form Factor (BFF)

The Martin-Puplett interferometer operation

The Martin-Puplett interferometer

The Martin-Puplett interferometer

)tt(g)t(gE2RT)t(E 0||out

dt)t(g)t(g)t(gRTE)(U 2

||2

o

)t(gE)t(E 0in

the autocorrelation function ismeasured with the help of the MPI

The Wiener-Khintchine theorem says: “the Fourier transform of the autocorrelation functionis the power spectrum”.

longitudinal field profileat the MPI entrance

longitudinal field profileat the MPI exit

detectors measureintensity IE2

The MPI scan

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Am

plitu

de o

f th

e G

olay

cel

l sig

nal,

V

mirror position, mm

Golay #1 Golay #2

Interferogram - the normalized difference

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0.0

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Inte

nsity

, a. u

.

mirror position, mm

The use of two detectors: raw data vs. interferogram

Bunch length reconstruction

2

t 2

t

t

e2c

Qtn

2teCP~

2t4

0 eCe1)(f fit

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

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1.0

diffraction on the Golay cell input window

4

0e1

2

0e1

Gol

ay c

ell a

pert

ure

tran

smis

sion

Frequency, THz

the Gaussian shapeof the bunch is assumed

its power spectrum isalso Gaussian

low frequency cut-offdiffraction on the Golaycell input window

two filter functionswere considered:

20e11F filter

40e12F filter

The fit function is used

Jlab FEL CTR interferogram

step size – 5 um, 128 steps

Jlab FEL CTR spectrum and the fit function

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

E

f

E

f

E

f

E

f

modified Martin-Puplettinterferometer (step scan)is used with CTR;only tune (pulsed) beam

Michelson interferometer(rapid scan)is used with CSR;CW beam

Interferometers

We use two different interferometers;essentially both are a modificationof the Michelson interferometer.

The two interferometers differ inimplementation; Beam splitter Polarizer Detector Focusing element Mirror position measurements

Modified Marin-Puplett interferometer:(step scan device) beam splitter & polarizer (wire grids) detector (Golay cell) focusing (Plano-convex lens) mirror position is set by step motorUsed 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 interferometerUsed with CSR

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.