lasers for e beam diagnostics - u.s. particle …...triveni rao, uspas 2013, duke university the...

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


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Invasive Techniques


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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


University

Courtesy:

http://www.hep.ph.rhul.ac.uk/~kamps/lbbd/welcome.html#ScientificCase

Non-invasive Techniques


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Electro optic effect as e- beam

diagnostics What is electro-optic effect?


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


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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.


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Index Ellipsoid: Uniaxial crystal


University


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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


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1)(2)(2)(2)()()(65432

3

12

22

2

12

12

1

12 jjjjjjjjjjjj ErxyErxzEryzErn

zErn

yErn

x


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2sin)22(sin 22

oII

For Lithium Niobate


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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


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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


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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


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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


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For Measurements


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Measurement of Pulse duration in a single shot using CW laser

and fast detector


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Using 7 GHz Oscilloscope:

Resolution limited by the bandwidth

of scope

Using Streak Camera, 3 single shot

traces superimposed


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Measurement of pulse duration in multiple shots using

ultrafast laser (12 fs) and photodiode

NIM A 475 (2001) 504-508


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Converting temporal information to Spatial information:

Information on pulse duration shape, distribution and timing


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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


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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


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lasers for e beam diagnostics - u.s. particle …...triveni rao, uspas 2013, duke university the...

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