sub-ps bunch length measurements at the jlab fel with coherent transition radiation (ctr) and...
TRANSCRIPT
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
∑
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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
16 17 18 19 20 210.05
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0.25
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0.35
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0.50
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
16 17 18 19 20 21
-0.2
-0.1
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
0.8
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.