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Lasers For e Beam
Diagnostics
Triveni Rao, USPAS 2013, Duke
University
Advantages of using
Laser
Short pulse duration
Large Bandwidth
Large EM field
Accurate phase
information
Methods:
Generated photons
FEL
Compton Scattering
Modify laser profile
Electro-optic effect
Triveni Rao, USPAS 2013, Duke
University
Invasive Techniques
Triveni Rao, USPAS 2013, Duke
University
Source of radiation and use of radiation for
electron diagnostics
Courtesy: E. Saldin et al. Proc. Of PAC 07, P. 965
Use standard optical technique to measure beam parameters
Slice emittance, longitudinal distribution of short (100 fs) electron
bunch can not be measured by standard techniques generate
optical replica of the electron beam
Triveni Rao, USPAS 2013,
Durham
Laser wire scan
Triveni Rao, USPAS 2013, Duke
University
Courtesy:
http://www.hep.ph.rhul.ac.uk/~kamps/lbbd/welcome.html#ScientificCase
Non-invasive Techniques
Triveni Rao, USPAS 2013, Duke
University
Electro optic effect as e- beam
diagnostics What is electro-optic effect?
Triveni Rao, USPAS 2013, Duke
University
+ -
+ -
+ -
+ -
Field + -
+ -
+ -
+ -
The electric polarization P can be written as
ε0 is vacuum permittivity, (n) nth order tensor electric susceptibility, I,j, and k
are Cartesian indices, Ei, Ej can have different frequencies
Triveni Rao, USPAS 2013, Duke
University
The first term P = ε0 (1) : E applies to all linear optics and
leads to optical index of refraction and dielectric constant .
For a linear material, terms with higher order vanish and
2
3 3 r r
The second term ∑ ∑ ijk E j Ek
gives rise to optical mixing ε 0 χ (ω1+ω2 and ω1-ω2)j =a1 ndk =1second harmonic generation (ω1=ω2).
When one of the fields varies very slowly compared to the other (ω1>>ω2), then it is Pockel’s effect where the input and output
frequencies are the same and the index of refraction varies linearly with the applied slowly varying field.
Triveni Rao, USPAS 2013, Duke
University
Triveni Rao, USPAS 2013, Duke
University
Triveni Rao, USPAS 2013, Duke
University
Index Ellipsoid: Uniaxial crystal
Triveni Rao, USPAS 2013, Duke
University
Triveni Rao, USPAS 2013, Duke
University
d E
= (/40) (y) dy/r2 r
The field decays rapidly along the y
direction, past the extent of the beam
-0.0006 -0.0004 -0.0002 0.0002 0.0004 0.0006
1´ 106
2´ 106
3´ 106
4´ 106
5´ 106
dE(x,t) = (/40) (y,t) dy/r2
dE(z,t)=(/40) (y,t) dy/r2 d
= (/40) (y) dy/r2
450
4.5
45 y
Triveni Rao, USPAS 2013, Duke
University
1)(2)(2)(2)()()(65432
3
12
22
2
12
12
1
12 jjjjjjjjjjjj ErxyErxzEryzErn
zErn
yErn
x
Triveni Rao, USPAS 2013, Duke
University
2sin)22(sin 22
oII
For Lithium Niobate
Triveni Rao, USPAS 2013, Duke
University
Direction of propagation of Laser
Dir
ectio
n o
f p
rop
agatio
n o
f
Ch
arge B
un
ch
x y z
x
zy
y
EE
E1212
121
101.21104.3016.0
104.36tan
2
1~
~ 0
~ 0
y
~ 0
z
x
E
E12
121
101.21016.0
104.36tan
2
1~
~ 4
z
y
y
E
E
12
12
1
104.3016.0
104.36tan
2
1~
y
x
E
E12
121
104.3016.0
104.36tan
2
1~
y
x
E
E1tan2
1~
Rotation of Principal axes
Is independent of field for 4 cases, dependent on field along
one direction in 1 case
Triveni Rao, USPAS 2013, Duke
University
Direction of propagation of Laser
Dir
ecti
on
of
pro
pa
ga
tio
n o
f c
ha
rge
bu
nch
x y z
x
...dxEE
dxEdxE
dxEdxE
L
L
zy
L
z
L
y
L
y
L
z
0
14
0
213
0
212
00
6
)1067.1(
)1095.1()1097.2(
)0003.0()0014.0(
)1019.1(
...dyE
dyEEdyE
dyEdyE
L
L
y
L
zy
L
z
L
y
L
z
0
215
0
14
0
213
00
6
)1069.3(
)1067.1()1095.1(
)0003.0()0014.0(
)1019.1(
... dzE
dzEE
dzEE
dzEδ
L
y
L
zy
L
zy
L
y
0
325
0
224
0
14
0
)1013.9(
)1051.3(
)1069.6(
)0011.0(
y
.)1051.2(
)1095.1(
)0014.0(
)1019.1(
0
323
0
213
0
6
...dxE
dxE
dxE
L
L
z
L
z
L
z
...dyEdyE
dyE
L
L
z
L
x
L
z
0
213
0
212
0
6
)1095.1()1096.2(
)0014.0(
)1019.1(
... dzE
dzEE
dzEE
dzEδ
L
x
L
zx
L
zx
L
x
0
325
0
224
0
14
0
)1014.1(
)1076.1(
)1034.3(
)0005.0(
z
.)1071.5(
)1097.2(
)0003.0(
)1019.1(
0
322
0
212
0
6
...dxE
dxE
dxE
L
L
y
L
y
L
y
...dyE
dyEEdyE
dyEdyE
L
L
y
L
xy
L
x
L
y
L
z
0
215
0
12
0
212
00
6
)1069.3(
)1092.5()1096.2(
)0003.0()0014.0(
)1019.1(
... dzE
dzE
E
dzEδ
L
x
L
x
y
L
x
0
325
0
2
0
)1014.1(
)0007.0(
)0005.0(
Total Retardation experienced by the laser beam for 3 possible directions of the
laser and electron beams
Two specific cases
Triveni Rao, USPAS 2013, Duke
University
e along y axis, laser along x axis
=
.)1051.2(
)1095.1(
)0014.0(
)1019.1(
0
323
0
213
0
6
...dxE
dxE
dxE
L
L
z
L
z
L
z
e along z axis, laser along x axis
=
.)1071.5(
)1097.2(
)0003.0(
)1019.1(
0
322
0
212
0
6
...dxE
dxE
dxE
L
L
y
L
y
L
y
No cross filed terms, Large Static term, Large coefficient for case 1
Need to compensate for the static term
Triveni Rao, USPAS 2013, Duke
University
We showed that
If laser polarization is set at 45˚ to field free optical axis (θ =45˚
I(t) = I0 + sin2(b+ (t))
where is the intensity extinction
coefficient of the optical arrangement
(fraction of the transmitted intensity in
the absence of the crystal), b is the
static retardation and (t) is the time
dependent component of the
retardation.
0
0.2
0.4
0.6
0.8
1
1.2
-40 -20 0 20 40 60 80 100
T(Deg)
Tra
nsm
itte
d I
nte
nsit
y (
arb
)
Preset operation in linear regime
Triveni Rao, USPAS 2013, Duke
University
For Measurements
Triveni Rao, USPAS 2013, Duke
University
Measurement of Pulse duration in a single shot using CW laser
and fast detector
Triveni Rao, USPAS 2013, Duke
University
Using 7 GHz Oscilloscope:
Resolution limited by the bandwidth
of scope
Using Streak Camera, 3 single shot
traces superimposed
Triveni Rao, USPAS 2013, Duke
University
Measurement of pulse duration in multiple shots using
ultrafast laser (12 fs) and photodiode
NIM A 475 (2001) 504-508
Triveni Rao, USPAS 2013, Duke
University
Converting temporal information to Spatial information:
Information on pulse duration shape, distribution and timing
Triveni Rao, USPAS 2013, Duke
University
Cross correlation between unchirped and chirped pulse-single
shot, information on pulse duration, shape and timing
Replace CCD by spectrometer for spectral encoding of the e beam on chirped pulse
Triveni Rao, USPAS 2013, Duke
University
Spectral encoding of electron beam on chirped pulse Single shot
Limitations
Crystal absorption and dispersion beyond
10 THz (100 fs) regime
Short distance between e beam and
crystal
Edge effects in low relativistic regime
Triveni Rao, USPAS 2013, Duke
University