Upload
others
View
5
Download
0
Embed Size (px)
Citation preview
Measuring high brightness beams
C.Limborg-Deprey
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 2
Introduction
Measuring e-beam properties
emittance, charge, monochromaticity, pulse duration …
𝐵 = 𝑄
휀𝑛,𝑥 휀𝑛,𝑦 휀𝑛,𝑧
𝐵 = 𝑄
휀𝑛,𝑥2 𝜎𝜏𝜎𝐸
Standard measurement techniques for tuning FELs
Some measurements of ultimate beam dimensions for colliders
and e-diffraction sources
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 3
Synopsis
• Emittance definition
• Transverse emittance measurements
• Beam size measurements
• Destructive
• Non-Destructive
• Bunch lengths
• Non-Destructive
• Destructive
• Longitudinal Phase space
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 4
6D-emittance
Evolution of a population of particles (~109 for 160 pC) in time
3D-space coordinates (x, y, z) and their canonical (Hamilton) conjuguates (𝑝𝑥,py, 𝑝𝑧)
6D phase space of non-interacting particles,
in a conservative dynamical system
is invariant
“Liouville theorem”
Volume 𝑉 = 𝜓(𝑥, 𝑝𝑥, 𝑦, 𝑝𝑦, 𝑦, 𝑧, 𝑝𝑧) 𝑑𝑥 𝑑𝑝𝑥 𝑑𝑦 𝑑𝑝𝑦 𝑑𝑧 𝑑𝑝𝑧 conserved
V referred to as emittance
J.D.Lawson “The physics of charge particle beams “ , Clarendon Press, Oxford, 1977
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 5
6D-emittance – more practical choice of coordinates
Particles travel along z with relativistic velocity 𝑣 = 𝛽𝑐 and 𝑝𝑧 = 𝛽𝛾𝑚𝑜𝑐
then 𝑝𝑥 = 𝑣𝑥𝛾𝑚𝑜 =𝑑𝑥
𝑑𝑧
𝑑𝑧
𝑑𝑡𝛾𝑚𝑜 = 𝑥′𝛽𝑐 𝛾𝑚𝑜
𝑝𝑥 → 𝑝𝑥𝑝𝑧𝑜
= 𝑥′
𝑝𝑦 → 𝑝𝑦
𝑝𝑧𝑜= 𝑦′
𝑧 → 𝑧 − 𝑧𝑜𝛽𝑐
= 𝜏
𝑝𝑧 → 𝛿 =𝑝𝑧−𝑝𝑧𝑜𝑝𝑧𝑜
or 𝛿 =𝐸−𝐸𝑜
𝐸𝑜
(x,x’) are the trace-space coordinates (not conjuguate quantities)
𝑥, 𝑝𝑥 , 𝑦, 𝑝𝑦, 𝑦, 𝑧, 𝑝𝑧 (𝑥, 𝑥′, 𝑦, 𝑦′, 𝜏,𝛿) (measured quantities)
z
𝑝𝑧𝑜 for centroid
subtleties of emittance conservation are discussed in K.Floettmann , “some basic features of
the beam emittance” PRST-AB Vol.3, 034202 (2003)
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 6
Geometric emittance / Normalized emittance
휀 = 𝑓(𝑥, 𝑥′, 𝑦, 𝑦′, 𝜏, 𝛿) 𝑑𝑥 𝑑𝑥′ 𝑑𝑦 𝑑𝑦′ 𝑑𝜏 𝑑𝛿
e geometric emittance
e conserved in the absence of acceleration
(e decreases with 1/ g3 when beam accelerated)
we introduce en = g3 e , normalized emittance en
en conserved in the presence of acceleration
--------------------------- Possible sources of emittance growth ------------------------------
Non-linear space charge forces
Non-linear forces from electromagnetic components
Synchrotron radiation emission
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 7
Emittance - Practical evaluation
2D emittance : area occupied by particles represented in 2D “trace space”
What is the “area” for points ?
arbitrarily define a contour
Typical distributions are gaussians,
or if not,
can be evaluated by their rms value ,
< 𝑢2 > ,< 𝑢′2>,< 𝑢𝑢′ >
u
u’
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 8
Emittance - Practical evaluation
• Determinant of the matrix of second order moments
< 𝑢2 > < 𝑢𝑢′ >
< 𝑢𝑢′ > < 𝑢′2>
1/2
휀 = < 𝑢2 >< 𝑢′2 >−< 𝑢𝑢′ >
Corresponds to 휀 = 𝐴
𝜋= 𝜎𝑀 𝜎𝑚
• Another definition : “Lapostolle”
휀 = 4 < 𝑢2 >< 𝑢′2 >−< 𝑢𝑢′ >
Corresponds to 𝐴∗
𝜋= 2𝜎𝑀 2𝜎𝑚
u
u’
used in our
community
u
u’
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 9
Emittance
Define Twiss parameters 𝛽, 𝛼, 𝛾 by
< 𝑢2 > = 𝛽휀
< 𝑢′2 > = 𝛾휀
< 𝑢𝑢′ > = −𝛼휀
𝛽, 𝛼, 𝛾 define the orientation of the ellipse
𝜋휀 defines the area
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 10
Courant-Snyder
Another approach to emittance
Particles (u,u’) subject to restoring forces K(s) u
𝑢′′ + 𝐾 𝑠 𝑢 = 0 Hill’s equation
Solution: 𝑢 𝑠 = 휀𝛽 𝑠 𝑠𝑖𝑛 𝜓 𝑠 + 𝜙𝑜
with 𝜓 𝑠 = 𝑑𝑠′
𝛽 𝑠′
𝑠
𝑠𝑜
휀 and 𝜙𝑜 are constants of integration
Defining : 𝛼 𝑠 = −1
2𝛽′ 𝑠 and 𝛾 𝑠 =
1+𝛼2 𝑠
𝛽2 𝑠
𝛾 𝑠 𝑢2 𝑠 + 2𝛼 𝑠 𝑢 𝑠 𝑢′ 𝑠 + 𝛽 𝑠 𝑢′2 𝑠 = constant (Courant-Snyder Invariant) = e
Also equation of an ellipse
Explains why choice of an ellipse is more than a mathematical convenience
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 11
Measuring emittance
휀 = < 𝑢2 >< 𝑢′2 >−< 𝑢𝑢′ >
Beam size Beam divergence Correlation
Position-angle
One method gives the 3 parameters in one shot : “Pepper pot”
but
destructive
only for low energy beam (E < 10 MeV)
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 12
Direct reading of trace space
𝑢′𝑚 = 𝑥′𝑚 =𝑢𝑚 − 𝑥𝑚
𝐿=𝑢𝑚 −𝑚𝑑
𝐿
𝜎′𝑚2= 𝜎𝑢,𝑚
2 − 𝑎
4
2
< 𝑥2 > = 𝐼𝑚𝑥𝑚
2
𝐼𝑚 ,
< 𝑥′2> =
𝐼𝑚 𝑥′𝑚,𝑜2 +
𝜎′𝑚2
𝐿2
𝐼𝑚 ,
< 𝑥𝑥′ > = 𝐼𝑚𝑥𝑚,𝑜𝑥′𝑚,𝑜
𝐼𝑚
With Im detected intensity for mth beamlet
Pepper pot
Transverse emittance , low energy
Destructive
Single Shot
M. Zhang, Report No. FERMILAB-TM-1988, 1996
S. G. Anderson, et al. Phys. Rev. ST Accel. Beams 5, 014201 (2002)
u Multislit in high Z material
𝜎𝑢,𝑚
d a
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 13
Pepper pot for thermal emittance
C.P Hauri , PRL 104, 234802 (2010)
Electron beam on YAG, with pepper pot in, Solenoid scan
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 14
Pepper pot based emittance oscillation
D.Alesini et al , “Experimental results with the
SPARC emittance-meter” MOOAAB02, PAC07
Emittance-meter
Variation of emittance along z after gun (at 5 MeV)
2mm thick W
7 slits of ~ 50 mm at 500 mm
Resolution ~ 100 mrad PITZ data
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 15
Photofield emission from tips : Nb/ Nb3Sn
A.Anghel et al , PRL , 108, 194801 (2012)
No explosive electron emission erosion
even if close to 1GW/cm^2 limit
Huge QE ~ 0.9 % (X 100)
en = 0.6 mm-mrad at 2500pC
Brightness better by ~ 100
than conventional PC guns
14326 filaments, f = 3.8 mm
2 laser spots
50 mm 100 mJ/cm2
160 mm 10 mJ/cm2
for 2 mJ , 6ps 266 nm laser
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 16
Pepper pot
• Difficult at high energy
scattering stopping length longer with energy :
𝐿𝑠[𝑐𝑚] =𝐸
𝑑𝐸𝑑𝑥 ≅
𝐸[𝑀𝑒𝑉]
1.5 𝜌 𝑔.𝑐𝑚−3
E > 10 MeV , Ls ~ 5 mm
• Unsuitable for extremely low emittance
slit thickness condition : 𝜎𝑥′ <𝑎
4𝑤
minimum emittance ∝ a (slit width) but S/N decreases
• Space Charge correction: low energy : analysis still often requires
space charge calculation
G. Anderson, et al. Phys. Rev. ST Accel. Beams 5, 014201 (2002)
a
w
Transverse emittance , low energy
Destructive
Single Shot
W Ta Cu
[g/cm3] 15.6 16.7 8.96
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 17
Measuring extremely low emittance <0.1 mm-mrad
Grid technique similar to pepper pot ,
multi knife edge measurement with info. on correlations
electrons hitting Cu bars scattered at wide angle
huge magnification M= 12.8 (from L =2 m)
M a > L s’m
a : bar width = 32 mm
L : distance grid to screen =2.1m
s’m : divergence of beamlet ~40 mrad
Grid for low emittance
Transverse emittance , low energy
Destructive
Single Shot
R.Li et PRST-AB 15, 090702 (2012) 30nm measured with 0.1 pC
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 18
Studying cigar shape :
linear space charge
R.Li et PRST-AB 15, 090702 (2012)
Grid for low emittance
Transverse emittance , low energy
Destructive
Single Shot
1.8ps
65fs
GPT Simulations Profile measured
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 19
Quadrupole/solenoid scan
𝑥𝑥′
= 1 𝐿0 1
1 0
−1
𝑓1
𝑥𝑜𝑥′𝑜
= 𝑅 𝑥𝑜𝑥′𝑜
𝑥 = 1 −𝐿
𝑓𝑥𝑜 + 𝐿𝑥𝑜
𝑥′ = −𝑥𝑜𝑓+ 𝑥′𝑜
𝑥2 = 1 −2𝐿
𝑓+𝐿2
𝑓2𝑥𝑜2 + 2𝐿 1 −
𝐿
𝑓 𝑥𝑜𝑥′𝑜 + 𝐿2 𝑥′𝑜
2
𝑥2 =𝑎
𝑓2+
𝑏
𝑓+ 𝑐
Solve for a,b,c to determine 𝑥𝑜2 , 𝑥𝑜𝑥′𝑜 , 𝑥′𝑜
2
휀 = 𝑥𝑜2 𝑥′𝑜
2− 𝑥𝑜𝑥′𝑜 , 𝛼 = −
𝑥𝑜𝑥′𝑜
휀 , 𝛽 =
𝑥𝑜2
휀 , 𝛾 =
𝑥′𝑜2
휀
“Quad” scan
Transverse emittance
Destructive
Multi Shot
lens , f 1
𝑓= −𝐾𝑙
drift , L
“Screen”
(YAG, OTR,
wire scanner)
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 20
𝜎𝑥12
𝜎𝑥22
……𝜎𝑥𝑛2
=
𝑅11,12 2𝑅11,1𝑅12,1 𝑅12,1
2
………
………
………
𝑅11,𝑛2 2𝑅11,𝑛𝑅12,𝑛 𝑅12,𝑛
2
𝛽𝑜휀−𝛼𝑜휀𝛾𝑜휀
also written Σ = 𝐵𝑂
Solve for O by least square fit
Minimization of 𝜒2 = 1
𝜎𝑥𝑖2 𝜎𝑥𝑖
2 − 𝐵𝑖𝑗𝑗 𝑂𝑗2
𝑖
Error analysis
Calculate covariant matrix 𝑇 = 𝐵 𝑇𝐵 −1
where 𝐵 𝑖𝑗 =𝐵𝑖𝑗
𝜎𝑥𝑖2
Solution is 𝑂 = 𝑇𝐵 𝑇Σ where 𝐵 𝑖𝑗 =𝐵𝑖𝑗
𝜎𝑥𝑖2 and Σ 𝑖 = 𝜎𝑥𝑖
2
Error 𝜎𝑂,𝑖 = 𝑇𝑖𝑖
“Quad” scan
Transverse emittance
Destructive
Multi Shot
Reference ”F.Zimmermann, M.Minty, “ book ref. H.Loos , private communications
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 21
• Choice of quadrupole settings
At each data point , plot lines parametrized in x’i
𝑢
𝑢′= 𝑅
𝜎𝑥𝑖𝑥′𝑖
Optimum location of data points
over-constrain (N points > 3)
at least 3 separated by more than 45 degrees
typically ~ 7 points , covering more than 90 degrees
• Convenient representation in normalized/rotated phase
space
𝑥
𝛽,𝛼𝑥+𝛽𝑥′
𝛽 where 𝛼, 𝛽 Twiss design parameters
“Quad” scan
Transverse emittance
Destructive
Multi Shot
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 22
• Low energy or high density
strong space charge,
R to include space charge defocusing term (beam size dependent)
Use iterative methods
“Quad” scan
Transverse emittance
Destructive
Multi Shot
C.K. Allen “Theory and Technique of Beam Envelope Simulation”, LANL, LA-UR-02-4979 August 2002
C.Limborg, “A Modified Quad Scan technique for space charge dominated beams”, PAC03 ,
http://accelconf.web.cern.ch/AccelConf/p03/PAPERS/WPPG033.PDF
Rsc (Ds)=
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 23
Slice emittance
Slice emittance
Destructive
Multi Shot
e-
sz
sy Transverse
deflector
Projects time
into space
e-
sz
sy Quadrupole
x-focusing
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013
Slice emittance
Slice emittance
Destructive
Multi Shot
TAIL
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 25
• Thermal emittance measurement from slice emittance as a function of laser spot size (at
low charge ~20pC)
• LCLS gun : copper (robustness, long lifetime)
• 0.9 mm-mrad per mm rms from slice emittance measurement
Thermal emittance
Transverse emittance
Destructive
Multi Shot
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 26
• Thermal emittance measurement from photoinjector
Thermal emittance
Transverse emittance
Destructive
Multi Shot
Courtesy F.LePimpec, R.Ganter
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 27
Thermal emittance
C.P Hauri , PRL 104, 234802 (2010)
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 28
휀𝑛 = 𝜎𝑥𝜎𝑝𝑥
𝑚𝑐 for e-source
휀𝑛 = 𝜎𝑥𝑘𝑏𝑇
𝑚𝑐2 transverse velocities expressed in terms of temperature
Typical numbers for photo-injectors (metallic or semi-conductor):
휀𝑛 = 0.9 𝑚𝑚 −𝑚𝑟𝑎𝑑 𝑝𝑒𝑟 𝑚𝑚 𝑟𝑚𝑠
T = 4809 K , 𝑘𝑏𝑇 = 0.41 𝑒𝑉
FELs, linear colliders : small beam size collimated beam
“geometric emittance” 휀 =휀𝑛
𝛾 small at high g and small 휀𝑛
For electron diffraction community, coherence length
𝐿𝑐 =𝜆
2𝜋𝜎𝜃 =
ℏ
𝑚𝑐 𝜎𝑥
𝜀𝑛,𝑥 Lc needs to be many lattice spacing
example: 휀𝑛 = 0.02 𝑚𝑚 −𝑚𝑟𝑎𝑑
𝜎𝑥 = 0.2 𝑚𝑚
Quality of source measured in 𝐶⊥ =𝐿⊥
𝜎𝑥
Emittance , Temperature , Coherence Length
Lc = 4 nm
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 29
Cold Electron source
Courtesy O.J.Luiten
N ~ 108 Rb atoms
R = 1mm
T = 230 mK
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 30
Cold Electron source
Courtesy O.J.Luiten
20K
휀𝑛 = 𝜎𝑥𝑘𝑏𝑇
𝑚𝑐2
𝑇 ≡𝜎𝑝2
𝑚𝑘𝑏
T = 5000 K for 0.9 mm-mrad per rms mm
T = 1500 K for 0.5 mm-mmrad per rms mm
Conventional photo and field
emission fields
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 31
Solenoid scan
Engelen et.al Nature Communications “High-coherence electron bunches produced by femtosecond”
Engelen et al “Effective temperature of an ultracold electron source based on near-threshold Photoionization”
Solenoid scan
for extremely small emittance
Courtesy O.J.Luiten
𝜎𝑒𝑙~20 𝜇𝑚 controlled by ionization laser
Energy measured with Time of Flight from ionization laser (photodiode) to screen
0.4 fC measured on Faraday Cup (~ 3000 particles)
MCP-phosphor screen (photo-multiplication) for enhancing signal for single
electron detection
Pinhole for resolution determination ~100mm
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 32
Solenoid scan
for an extremely small emittance
Transverse emittance , low energy
Destructive
Multi Shot
Courtesy O.J.Luiten
Engelen et.al Nature Communications “High-coherence electron bunches produced by femtosecond”
Engelen et al “Effective temperature of an ultracold electron source based on near-threshold Photoionization” Ultramicroscopy
휀 = 1.4𝑛𝑚 for Q =0.5 fC ( ~3000
particles)
Equivalent to 70 nm-rad per mm rms
~ 10 times smaller than RF photoinjectors
So 100 times larger brightness
Main conclusion
fs-ionization still allows to reach 20K thermal
emittance
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 33
Spatial projection : choice of “screens”
Very good physics description of physics E.Bravin in
http://cds.cern.ch/record/1071486/files/cern-2009-005.pdf
Screens
ZnS phosphor screens
small dynamic range , easily saturated
grain size ~ 20mm
response time
YAG screens :
good yield
thickness
response time
Scintillator properties : http://scintillator.lbl.gov/
YAG combined with MCP for low electron density
OTR screen
Wire scanner
Ultimate wire
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013
• Emitted when a relativistic electron passes boundary between
materials of different electrical properties
• OTR emission from a single electron
• Travelling with relativistic velocity 𝛽 ≈ 1 −1
2𝛾2
• Hitting a foil with reflectivity 𝑅 𝜔 foil
• Typically at 45 degrees w.r.t to beam direction
•𝑑2𝑁
𝑑𝜔𝑑Ω=
𝛼
4𝜋2𝑅 𝜔
𝜔
𝛽2𝑠𝑖𝑛2 𝜃
1−𝛽𝑐𝑜𝑠 𝜃2
34
OTR (Optical Transition Radiation)
ψ = 45°
e-beam
foil
θ
𝜃 > 150 𝑚𝑟𝑎𝑑 , 60% 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 35
OTR far-field imaging
Simulations P.Piot , 38 MeV
resolution 𝑥′~ 0.15
𝛾
(too poor for high brightness beams)
but accurate energy measurement
Deconvolution of e-beam divergence
with single e angular distribution
OTR interferometry
Back TR from 1st foil
Distance between 2 foils > 𝜆𝛾2
R.Fiorito OTR-ODR interferometry 𝑥′~ 0.02
𝛾
resolution 𝑥′~ 0.075
𝛾
Can we do far-field imaging and obtain the e-beam divergence ?
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013
• Calculate Nphotons
• Spectral reflectivity of foil (Al,Ti, Be,Si)
• Spectral sensitivity of imaging system (lens, CCD)
• 𝑆 𝜆𝑖 , 𝜆𝑓 = 𝑅 𝜔
𝜔𝑆 𝜔 𝑑𝜔
𝜔𝑓
𝜔𝑖
𝑅 𝜔
𝜔𝑑𝜔 =
𝜔𝑓
𝜔𝑖log𝜔
𝜆𝑖=400𝑛𝑚
𝜆𝑓=700𝑛𝑚 = 0.56
36
OTR (Optical Transition Radiation)
Quantum Efficiency
from Sony ICX445
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013
Beam size : “point-to-point imaging”
Point Spread Function (PSF) : single e emission (Green’s) through imaging system
𝑃𝑆𝐹 ∗ 𝜌 𝑥, 𝑦 (for incoherent emission)
Example:
50 mm, 1:1 imaging ,100pC , 70 MeV
Collection angle = 100mrad
BW=0.7, QE = 0.5
Nelectrons ~2.106
Disk with 1.5 rms contains 70% of particles
With pixel size (3.75 mm)2 , ~ 1000 e per pixel
NB: full well capacity 30000,
With 8 bits above noise => noise level at 100e
~ 10 pC
37
Imaging using OTR light
Tight
Alignment
tolerances
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013
• PSF “Point Spread Function”: response of imaging system to a point source
• Incoherent: 𝐼𝑚𝑎𝑔𝑒 𝑂1 + 𝑂2 = 𝐼𝑚𝑎𝑔𝑒 𝑂1 + 𝐼𝑚𝑎𝑔𝑒 𝑂2
𝑃𝑆𝐹 ∗ 𝜌 𝑥, 𝑦 => 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 ∝ 𝑁𝑒
• Coherent: image formation linear in complex field
In short 𝐹𝑇−1 𝐸𝑠 𝑘𝑥 , 𝑘𝑦 × 𝜌 𝑘𝑥 , 𝑘𝑦
𝑬 𝒓 =𝑞
𝜋𝑣
𝒓
𝑟𝛼𝐾1 𝛼𝑟 electric field at the transition radiation source with 𝛼 =
𝑘
𝛽𝛾
𝐸𝑆,𝑁 𝑟 = 𝑒−𝑗𝑘𝑧𝑗 𝐸𝑠𝑗 𝑟 − 𝑟𝑗
𝑬𝑆,𝑁 𝒓2= 𝑁 𝑑2 𝑟′ 𝑑𝑧 𝜌 𝒓′, 𝑧 𝑬𝑆,𝑁 𝒓 − 𝒓′
2
+ 𝑁2 𝑑2 𝑟′𝑑𝑧 𝑒−𝑖𝑘𝑧 𝜌 𝒓′, 𝑧 𝑬𝑆,𝑁 𝒓 − 𝒓′2
• Microbunching generates phase relations for particles along bunch making the N2 component
large and dominant
38
OTR (Optical Transition Radiation)
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013
Coherent emission:
OTR image show square of gradient of shape
thus the “doughnut” shape
Spoils measurement of rms beam size (under estimate)
Starts from shot noise => present in continuous spectrum
39
Coherent OTR (COTR)
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013
COTR suppression:
Smearing out microbunching
Spectral separation: imaging for 𝜆 < 𝜆𝑐 (ie extreme UV, in vacuum)
Spatial separation: Use scintillator screen , tilted to avoid COTR
Temporal separation: (scintillator response ~ 70 ns) with expensive
ICCD
Use Phase retrieval algorithm (A.Marinelli) on far-field COTR
40
OTR for beam size measurement
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 41
Beam size measurement despite COTR
Far Field
COTR
|B (kx,ky) | Phase{B (kx,ky) }
A,Marinelli et al .
PRL 110, 094802 (2013)
No-microbunching
Direct OTR imaging
Reconstructed image
(beam is micro-bunched)
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 42
Small wire intercepts beam
Bremsstrahlung radiation and scattered electrons detected on fast ion chambers with PMTs
(PMT = Photo-Multiplying tubes)
detecting Cerenkov from secondary electrons
light from plastic scintillator fibers along chamber
Positioned at low background location
Material
W more signal but burn more easily ~ 20-40 mm
C less signal , but more robust can go down to few mm
for a 4 mm rms beam sizes down to 1 mm can be measured
Major issues
break (high rep. rate and high Ipeak) 2nC in wire of 1 mm
vibrations
beam jitter (from magnet power supplies stability)
Wire scanner Non-destructive beam size
Multi Shot
H.Loos , MOIANB01 Proceedings of BIW10, Santa Fe, New Mexico, US
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 43
Wire scanner Non-destructive beam size
Multi Shot
H.Loos , MOIANB01 Proceedings of BIW10, Santa Fe, New Mexico, US
• Vibrations are a limitation
resonance studies : speed tests
optical measurements
SLAC PUB-6015 McCormick, M.Ross
Mechanical improvements to reduce further
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 44
Compton scattering process
Collision photons with relativistic electrons
Scattered photons
• Direction : in cone with opening angle in 1/𝛾𝑜
• Frequency : Doppler shifted
ℎ𝜈𝑠𝑐 = ℎ𝜈𝑜𝛾𝑜𝐸𝑜 1−𝛽𝑜𝑐𝑜𝑠 𝜓
𝛾𝑜𝐸𝑜 1−𝛽𝑜𝑐𝑜𝑠 𝜓 +ℎ𝜈𝑜 1−𝑐𝑜𝑠 𝜓−𝜃≅ 2𝛾𝑜
2ℎ𝜈𝑜 for 𝜓 ≈𝜋
2
• Intensity :
𝑁𝑠𝑐 ≈ 𝜎𝑐 𝑛𝑜 𝑁𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠𝐷 𝑤𝑖𝑡ℎ 𝑛𝑜 =1
ℎ𝜈𝑜 𝑐
𝑃
𝑆
(𝑃, 𝑆) ∶ ( 𝑝𝑜𝑤𝑒𝑟, 𝑠𝑝𝑜𝑡 𝑠𝑖𝑧𝑒 ) 𝑜𝑓 𝑙𝑎𝑠𝑒𝑟 𝐷 ∶ 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑎𝑐𝑡𝑖𝑜𝑛
𝜎𝑐 ∶ 𝐶𝑜𝑚𝑝𝑡𝑜𝑛 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 ≈ 6.6 10−29𝑚2
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 45
• measure e-beam sizes > 200nm,
• high current beams
(“non-degradable” wire )
• detection of X-Ray (or g-rays)
or recoil energy (for very high Ee-beam)
• scan either laser or e-beam position
• detection requires bending magnet
• challenges
synchronization
focus
scan
Laser wire scanner
Non-destructive
Non-degradable
Multi Shot
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 46
• Measurements SLC
(pioneering experiment)
E = 45 GeV,
Nphotons at waist ~ 8000
Bunch size measured ~ 1mm
Laser wire scanner
Non-destructive
Non-degradable
Multi Shot
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 47
• Focus:
Diffraction limit of a laser beam 𝜎𝑓 =𝜆 𝑓
4𝜋𝜎𝑙𝑎𝑠𝑒𝑟,𝑖𝑛𝑖
Rayleigh length 𝑧𝑟 =4𝜋𝜎𝑓
2
𝜆
Example: 𝜎𝑓 ~125nm , 𝑧𝑟 ~ 625 nm for 𝜆 = 300nm
Beam size measurements limited to ~ 200nm
Applications : ERL, linear colliders
Other application: bunch length measurement
Laser wire scanner
Non-destructive
Non-degradable
Multi Shot
,
References:
Shintake, Tennenbaum , Annu. Rev. Nucl. Part. Sci. 1999. 49:125–62
Lefebvre https://cds.cern.ch/record/535808/files/open-2002-010.pdf
A.Murohk, IPAC10 “A 10 MHZ Pulsed Laser Wire scanner for energy recovery linacs”
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 48
Beam size from
laser interferometer
Non-destructive
Non-degradable
Multi Shot
• measure e-beam sizes < 200nm, by beating the diffraction limit using interferences
• 𝑁𝛾 = 𝐴 + 𝐵 𝑐𝑜𝑠 2𝑘𝐿𝑥 + 𝜓
• 𝑁𝛾 𝑦𝑜 =𝑁𝑜
21 + 𝑐𝑜𝑠 2𝑘𝐿𝑦𝑜 𝑐𝑜𝑠 𝜃 exp
−2 𝑘𝑦𝜎𝑦2
• 𝑁± =𝑁𝑜
21 ± 𝑐𝑜𝑠 𝜃 exp
−2 𝑘𝑦𝜎𝑦2
• 𝑀 = 𝑁+−𝑁−
𝑁++𝑁−
• 𝜎𝑦 =𝑑
2𝜋2𝑙𝑛
𝑐𝑜𝑠𝜃
𝑀
With 𝜃 = 174° , 𝜎𝑦 down to 38 nm can be measured
with a 1mm laser
“Shintake-monitor”
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 49
Beam size from
laser interferometer
Non-destructive
Non-degradable
Multi Shot
Courtesy Jacqueline Yan,KEK
• Systematics
• Imbalance power between 2 arms
• Variation in e-beam angle
• Longitudinal extent of diffraction
pattern
• Spherical wavefront error
• Coherence of laser (transverse +
longitudinal)
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 50
Beam size from
laser interferometer
Non-destructive
Non-degradable
Multi Shot
• Shintake pioneering measurement SLAC (1994)
• KEK measurements
Courtesy Jacqueline Yan,KEK,
1.3 GeV, 𝜃 = 174° Very reproducible over 20 minutes
M 〜 0.306 ie σy 〜 65 nm
Best measurement σy 〜 58 nm
Goal = 37 nm
E = 46.6 GeV σy 〜 77 nm
T.Shintake, P.Tenenbaum, Annu. Rev. Nucl. Part. Sci. 1999. 49:125–62
http://www.jlab.org/accel/beam_diag/DOCS/annurev.nucl.49.1.125.pdf
1.6nC
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 51
Optical Diffraction Radiation
Interferometry (ODRI) Non-destructive
For single shot x,x’
A.Cianchi Journal of Physics: Conference Series 357 (2012) 012019
http://prst-ab.aps.org/pdf/PRSTAB/v14/i10/e102803
• 0.4nC * 20 bunches at 5Hz ~ 80nC enough to damage OTR
• 2 apertures at d < 𝜆𝛾2 (“formation length”) but with different aperture size
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 52
Optical Diffraction Radiation
Interferometry (ODRI) Non-destructive
For single shot x,x’
A.Cianchi Journal of Physics: Conference Series 357 (2012) 012019
http://prst-ab.aps.org/pdf/PRSTAB/v14/i10/e102803
• Calculation Measurements
𝜎𝑦 = 81𝜇𝑚, 𝜎𝑦′ = 203 𝜇𝑟𝑎𝑑
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 53
“single point” emittance
measurement Destructive or non-destructive
Single Point
𝑥 = 1 −
𝐿
𝑓𝑥𝑜 + 𝐿𝑥𝑜
𝑥′ = −𝑥𝑜
𝑓+ 𝑥′𝑜
𝑥2 = 1 −𝐿
𝑓
2𝑥𝑜2 + 2𝐿 1 −
𝐿
𝑓 𝑥𝑜𝑥′𝑜 + 𝐿2 𝑥′𝑜
2
𝑥𝑥′ = −1
𝑓1 −
𝐿
𝑓𝑥𝑜2 + 1 −
2𝐿
𝑓 𝑥𝑜𝑥′𝑜 + 𝐿 𝑥′𝑜
2
Find magnet setting f* such that 𝜕 𝑥2
𝜕𝑓= 0
then correlation term 𝑥𝑥′ =𝑥2
𝐿
at f* , measure 𝑥2 , and deduce 𝑥𝑥′
measure 𝑥′2
emittance at single point
(with 2 images : one near-field, one far-field)
e-beam f
L screen
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 54
BUNCH LENGTHS
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 55
Electro-Optic methods Bunch length
Non-destructive
𝐸𝑟 component of Lorentz contracted Coulomb field
Birefringence induced by 𝐸𝑟 , 𝑃 = 휀𝑜 𝜒𝑒(0) 𝐸 + 𝜒𝑒
(1) 𝐸2 +⋯
Pockels Kerr
Changes polarization and introduces phase retardation
As an E-field pulse mixer, casually referred to as an “ultrafast Pockels cell”
2
𝛾
𝐸𝑟 𝐸𝑟
500 MeV (g = 1000)
r = 5mm
L = 10 mm = 33 fs
r
L
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 56
Electro-Optic Sampling
Bunch length
Non-destructive
Multi Shot
1. Laser pulse much shorter than e-beam pulse used as probe
• Samples small part of e-beam field
2. Analyzer (polarizer) to transmit polarization change to photo-diode
3. Scan delay to trace out e-beam profile
Limitation as multi-shot method:
• Shot-to-shot timing jitter bad for profiling
• (Still useful time of arrival monitor)
from Bernd Steffen,
DESY
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 57
Electro-Optic spectral decoding
Bunch length
Non-destructive
Single Shot
1. Laser pulsed stretched: long chirped laser with linear λ-t correlation
2. Interaction with 𝐸𝑟 from e-beam in EO induces t-dep. change in polarization
3. Analyzer/spectrometer measures change in polarization as function of λ
4. Map λ back to t to deduce e-beam profile
Limitation from non-linear optical mixing:
• Resolution tres worsens with increasing chirp duration “window” Tc as
Typ. temporal resolution > 200fs
from Bernd Steffen,
DESY
cpres TTt
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 58
Electro-Optic temporal decoding
Bunch length
Non-destructive
Single Shot
• Similar to before but pulse is decoded in
time-domain
• Decoding setup similar to fast, optical
cross-correlator
Limitations: again, gate width
thickness of BBO
spatial resolution
from Bernd Steffen,
DESY
𝐼𝑆𝐻𝐺 𝑥 = 𝐼𝑝𝑟𝑜𝑏𝑒 𝑡 + 𝜏 + 𝐼𝑔𝑎𝑡𝑒 𝑡 𝑑𝑡
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 59
Electro-Optic temporal decoding
Bunch length
Non-destructive
Single Shot
Temporal resolution achieved ~ 60 fs
Benchmarked with transverse deflector measurements
G.Berden , PRL , 99, 164801 (2007)
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 60
Electro-Optic spatially resolved Bunch length
Single Shot
A.L Cavalieri PRL 94, 114801 (2005)
Resolution ~ 115fs rms
B.Steffen PhD manuscript,
C.Casalbuoni , PRST-AB, 11, 072802 (2008)
T.Maxwell http://www.niu.edu/physics/_pdf/academic/grad/theses/Maxwell_2012.pdf
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 61
Electro-Optic limits Bunch length
Single Shot
C.Casalbuoni , PRST-AB, 11, 072802 (2008)
Maximize signal but minimize crystal size given all the broadening contributions
TO : Transverse Optical phonons limit bandwidth
GVM: Group Velocity Mismatch
(signal and probe slip through each other)
GVD : Group Velocity Dispersion
(signal and probe broaden)
H.Tomizawa, BIW 2012
Organic crystal DAST, compared to ZnTe
Both crystals are 2mm from beam , and 280 pC
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 62
3D –monitor Tomizawa
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 63
3D Monitor Tomizawa
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 64
Transverse deflector (TCAV)
Bunch length
Destructive
Single Shot
Resolution :
𝜎𝑦2 = 휀𝛽𝑂𝑇𝑅 + 𝛽𝑂𝑇𝑅𝛽𝑇𝐶𝐴𝑉𝜎𝑧
2𝑘𝑟𝑓𝑒𝑉𝑜
𝐸𝑠𝑖𝑛Δ𝜓
2
𝜎𝑧 >
휀
𝛽𝑇𝐶𝐴𝑉
𝜆𝑟𝑓𝐸
2𝜋𝑒𝑉𝑜
Δ𝑦 = 𝛽𝑂𝑇𝑅𝛽𝑇𝐶𝐴𝑉 sin𝜓𝑇𝑐𝑎𝑣→𝑂𝑇𝑅 𝑒𝑉𝑜𝑠𝑖𝑛 𝑘𝑟𝑓𝑧 + 𝜑𝑟𝑓
𝑝𝑐
Δ𝑦′ 𝑧 =𝑒𝑉𝑜𝑝𝑐
𝑠𝑖𝑛(𝑘𝑟𝑓𝑧 + 𝜑𝑟𝑓)
TM11 mode
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 65
Transverse deflector (TCAV)
Bunch length
Destructive
Single Shot
𝜑𝑅𝐹[°] 80 90 100
Be
am
po
sitio
n (
pix
el)
1- calibration at zero crossing : 1° 𝑅𝐹 𝑡𝑜 𝑝𝑖𝑥𝑒𝑙
1° 𝑅𝐹 𝑆 − 𝐵𝑎𝑛𝑑 = 1𝑝𝑠 1° 𝑅𝐹 𝑋 − 𝐵𝑎𝑛𝑑 = 250 𝑓𝑠
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 66
Transverse deflector (TCAV)
Bunch length
Destructive
Single Shot
Deconvolve beam size contribution
𝜑𝑅𝐹 = −90°
𝜑𝑅𝐹 = +90°
𝑛𝑜 𝑓𝑖𝑒𝑙𝑑
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 67
LCLS bunch length measurements
14 GeV
‘Max’ Compression
0.89 ps
14 GeV
135 MeV
1.10 mm rms
14 GeV
BC1 Design Compression
10.3 ps
135 MeV
97 A 950 A 520 A
1.7 ps
14 GeV
PR55 OTR2 135 MeV
14 GeV
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 68
Transverse deflector (TCAV)
Bunch length
Destructive (*)
Single Shot
Resolution : 𝜎𝑧 >𝛾𝜀𝑛
𝛽𝑇𝐶𝐴𝑉 𝜆𝑟𝑓
𝑒𝑉𝑜 𝑚𝑜𝑐
2
2𝜋
(*) pulse stealing on LCLS (1Hz for a 120Hz operation)
Resolution Tech P[MW]
V[MV]
L[m] E[MeV] e [mm-
mrad]/b [m]
Loc.
250 fs S-Band (1) 0.5/0.7 0.4 135 0.3/5 LCLS inj.
11 fs (3) S-Band ?/15 2.44 5000 0.5/60 LCLS main
33 fs X-Band (2) 1/? 0.13 100 1/11 XTA
1 fs X-Band 40/? 2.0 4300 LCLS dump
3 fs X-Band 40 /? 2.0 14000 LCLS dump
(1) S-Band is 2.856 GHz (2) X-Band is 11.424 GHz (3) Measured on wire scanner
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 69
Transverse deflector (TCAV)
Bunch length
Destructive
Single Shot
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 70
Longitudinal Phase space Destructive (but “stealing mode” )
Single Shot
e-
sz
2×1 m RF ‘streak’
Dipole
X-band RF deflector
ener
gy
Undulator
D 90°
bd bs
XTCAV streaks horizontally;
Dipole bends vertically.
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 71
Longitiudinal Phase space
Bunch length
Destructive
Single Shot
Data taken on June 4th, 2013.
Beam energy 3.5GeV, 150pC.
Temporal resolution is about 1.7fs
rms in this test.
Preliminary results.
Lasing
suppressed
Full lasing
Initial Measurement of e-beam and X-ray temporal profiles at LCLS using X-Band
transverse deflector
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 72
Longitudinal Phase space end LCLS injector
Z.Huang, Phys. Rev. ST Accel. Beams 13, 020703 (2010)
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 73
Acknowledgments
C.Pellegrini, D.Xiang, T.Raubenheimer
H.Loos, T.Maxwell, M.Ross, D.McCormick, G.White,
A.Marinelli, Y.Ding, P.Emma, P.Krejcik, J.Wu
J.O.Luiten, J.Yan, F.LePimpec, R.Gantry, F.Zimmermann,
M.Minty , S.Anderson, C.Hauri, A.Anghel, B.Steffen,
B.Schmidt, A.Cianchi, A.Cavalieri, R.Li, W.Engelen,
R.Fiorito, K.Rezaie, A.Nause, T.Shintake, P. Tenenbaum,
D.Dowell, G.Berden, C.Casalbuoni, H.Tomizawa,
…
and all the students
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 74
Topics of interest
• Tomography
• Optical Replica
• Synchronization
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 75
Electro-Optic Sampling
T.Maxwell
http://accelconf.web.cern.ch/accelconf/IPAC2011/papers/tup
c169.pdf
http://www.niu.edu/physics/_pdf/academic/grad/theses/Max
well_2012.pdf
B.Steffen
http://fla.desy.de/projects/eo/index_eng.html
http://www-library.desy.de/cgi-bin/showprep.pl?thesis07-020
Casalbuoni
http://prst-ab.aps.org/pdf/PRSTAB/v11/i7/e072802
Bunch length
Non-destructive
Single Shot
C.Limborg-Deprey, SLAC, SSSEPB July 24th 2013 76
Synchronization (AOS-based)
Cavalieri
http://prl.aps.org/abstract/PRL/v94/i11/e114801
Non-destructive
Single Shot