Ellipsoidal bunches by 2D laser shaping

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Nov 29, 2013 (3 years and 9 months ago)

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Ellipsoidal bunches by 2D laser shaping

Bas van der Geer, Jom Luiten

Eindhoven University of Technology

DESY Zeuthen

30 November 2006

2) Experimental progress

1) Why pancakes do not work with 1nC and 40

60 MV/m

Jom Luiten

Bas van der Geer

work as good

as 3D ellipsoids

Waterbags


Transverse phase
-
space


No space
-
charge induced emittance degradation


No ‘slice’ dependence


O.J. Luiten, S.B. van der Geer et al, PRL 094802, (2004).


Confirmed by J. Rosenzweig and C. Limborg in NIM
-
A 557 (2006)



Longitudinal phase
-
space


Ideal for linear compression


Manipulation possible at low energy


Energy spread can be recovered


S.B. van der Geer
et al
,

PRST
-
AB, 9, 044203 (2006)

Transverse (5
-
D) brightness:

Brightness

kT
J
mc
I
B
p
y
n
x
n
p




2
,
,
2
)
2
(



E
z
n
y
n
x
n
B
mc
Q






2
,
,
,
3
)
2
(






B
2
mc Q
B
k T A
 


Source brightness

Options (at fixed Q):


Lower Temperature
T

Ultra Cold Plasma cathode


B.J. Claessens et al., PRL 95, (2005) 164801



Reduce Surface area
A

Carbon Nanotubes



Needle cathodes







Reduce Pulse duration
τ

Pancake regime

Longitudinal phase space density


Long pulse

Pancake


3 ps

30 fs


1 nC

100 pC


~100 A/mm
2

~
1 kA/mm
2


(Both with
A
=
π

mm
2
)

z

Energy

Pancake

Long pulse

Thermal

spread

Longitudinal phase
-
space

at cathode

kT
J
mc
I
B
p
y
n
x
n
p




2
,
,
2
)
2
(



The problem is not the high

space charge
density

...

Gaussian bunch

Brightness degradation

Brightness degradation

p
x

x

Gaussian bunch

Space charge forces:



Non
-
linear



Slice
-
dependent

... the real problem is the

space charge density
distribution
.

p
x

x

Gaussian bunch

1989
-

2003

Fighting the symptoms:



Emittance compensation (B. Carlsten)



Optimized transverse profile (L. Serafini)



Uniform temporal & radial profile (DESY, ...)



...

Gaussian bunch

Waterbag bunch

p
x

x

Space charge forces:



Non
-
linear



Slice
-
dependent

Space charge forces:



Linear



Slice
-
independent

Thermal
-
emittance
-
limited beam!

2004: Fundamental solution

History of uniformly charged ellipsoids

1929

Have linear fields in all three coordinates



O. D. Kellogg,
Foundations of Potential Theory

(Springer
-
Verlag,
1929
).

1965

Ellipsoids with uniform mass collapse into a disk
(astrophysics)



C.C. Lin et al., Astrophys. J. 142, 1431 (
1965
).



Decades of use as idealized beams





1997

Pancakes evolve into approximate waterbags



L. Serafini, AIP Conf. Proc. 413, 321 (
1997
)


2004

Fundamental solution and practical recipe



O.J. Luiten, S.B. van der Geer

et al, PRL
094802, (
2004
).



O.J. Luiten, S.B. van der Geer

et al, EPAC (
2004
).

History of uniformly charged ellipsoids

1929

Have linear fields in all three coordinates



O. D. Kellogg,
Foundations of Potential Theory

(Springer
-
Verlag,
1929
).

1965

Ellipsoids with uniform mass collapse into a disk
(astrophysics)



C.C. Lin et al., Astrophys. J. 142, 1431 (
1965
).



Decades of use as idealized beams





1997

Pancakes evolve into approximate waterbags



L. Serafini, AIP Conf. Proc. 413, 321 (
1997
)


2004

Fundamental solution and practical recipe



O.J. Luiten, S.B. van der Geer

et al, PRL
094802, (
2004
).



O.J. Luiten, S.B. van der Geer

et al, EPAC (
2004
).


2006

Well received in the accelerator community


J.B. Rosenzweig et al., NIM
-
A 557 (
2006
),
Emittance compensation …


C. Limborg et al., NIM
-
A 557 (
2006
),
Optimum electron distributions …


S.B. van der Geer et al, PRST
-
AB, 9, 044203 (2006),
Longitudinal …


...

2D Waterbag bunch recipe

Femtosecond

photoexcitation of pancake bunch


Half
-
sphere transverse laser intensity profile


Temporal laser profile is irrelevant

Automatic evolution into 3D, uniform ellipsoid

fs laser

Ellipsoid creation

How to Realize Uniform Three
-
Dimensional Ellipsoidal Electron Bunches

O.J. Luiten, S.B. van der Geer et al, PRL 094802, (
2004
).

1.5 cell, 3 GHz rf
-
photogun + focusing solenoid


E
acc

= 92 MV/m


Q = 100 pC

Waterbag bunch in a realistic field

z
c

= 0.9 m, E = 4.5 MeV

-0.4
-0.2
0.0
0.2
0.4
GPT
z-zc [mm]
-2
-1
0
1
2
x [mm]
O.J. Luiten, S.B. van der Geer et al, EPAC (
2004
).

Waterbag bunch in a realistic field


Confirmed at higher energies


Compatible with SPARC emittance compensation,
85 MeV


J. Rosenzweig et al., NIM
-
A 557 (
2006
), p. 87.


50% improvement on transverse emitance for LCLS,
63 MeV


C. Limborg et al., NIM
-
A 557 (
2006
), p. 106.

0
0.2
0.4
0.6
0.8
1
0
200
400
600
800
1000
z [mm]
RMS emittance [μm]
Thermal emittance!

O.J. Luiten, S.B. van der Geer et al, EPAC (
2004
).

4 MeV

-0.4
-0.2
0.0
0.2
0.4
GPT
z-zc [mm]
4.1
4.2
4.3
4.4
4.5
4.6
4.7
Energy [MeV]
0
0.2
0.4
0.6
0.8
1
0
200
400
600
800
1000
z [mm]
RMS emittance [μm]
Thermal emittance!

10 fs

-0.4
-0.2
0.0
0.2
0.4
GPT
z-zc [mm]
-2
-1
0
1
2
x [mm]
First waterbag bunch in a realistic field

O.J. Luiten, S.B. van der Geer et al, EPAC (
2004
).

I=50 A

Longitudinal compression

~0.4 m

Laser

rf

φ

S.B. van der Geer et al, PRST
-
AB, 9, 044203 (2006),

3.5 MeV

0.7



2.0 kA


30



100 fs

0.7



1.5
μ
m

2D shaping @ PITZ

Limitations of 2D ‘pancake’ shaping:


Laser
-
pulse duration

<< Asymptotic bunch length


Fields of image charges

<< Acceleration field


PITZ: 1 nC, 50 MV/m, R=1 mm:


Pulse duration: 30 fs

<< 25 ps


OK


Image charges: 36 MV/m

<< 50 MV/m

Questionable

2D shaping @ PITZ

Settings:


50 MV/m uniform, 1 nC, R=1 mm, 2D shaping of 30 fs ‘pancake’

0.1

0.2

0.5

1

GPT

Charge [nC]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

RMS Emittance [micron]

Pancake

3D shaping @ PITZ

Settings:


50 MV/m uniform, 1 nC, R=1 mm, 3D shaping of 3 ps ellipsoid

Pancake

3D

0.1

0.2

0.5

1

GPT

Charge [nC]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

RMS Emittance [micron]

Emission:

3D shaping

2D shaping











Highly non
-
linear fields!

Highly non
-
linear fields!





Lower charge density

Maintain short bunch




Long pulse length

High acceleration field


3D versus 2D shaping

1.5 ps: 10
μ
m

15 fs: 1 nm

3D shaping @ PITZ

Settings:


50 MV/m uniform, 1 nC, R=1 mm, 3D shaping of 10 ps ellipsoid

Pancake

3D: 3 ps

3D: 10 ps

0.1

0.2

0.5

1

GPT

Charge [nC]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

RMS Emittance [micron]

3D shaping @ PITZ

Settings:


50 MV/m uniform, 1 nC, R=1 mm, 3D shaping of 10 ps ellipsoid

Pancake

3D: 3 ps

3D: 10 ps

0.1

0.2

0.5

1

GPT

Charge [nC]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

RMS Emittance [micron]

Pancake

100 MV/m

Next

Experimental progress at

Eindhoven University of Technology


Jom Luiten


2D ‘pancake’ shaping

Ingredients:


Ti:Sapphire 30 fs laser


Transverse shaping
only

Ti:Saphire

30 fs laser

Colinear THG

800nm → 266 nm

Spatial filtering:

800 nm gaussian

π

shaper:

Gauss

half
-
sphere

UV

Sphere

Gauss

800 nm after spatial filtering

ideal

π

Shaper

Laser intensity

radius

0

1 mm

π

shaper

Input:

Gaussian beam

Output:

Half
-
sphere laser intensity profile (without losses)


0.15
mm
BBO SHG

2.5 mm BBO Delay

Zero order retardation plate

0.04 mm BBO THG

R

R+B

R+B

R+B

R+B+UV

Incident beam:

1 kHz, 30 fs pulse @ 800 nm,
1 mJ/pulse

UV beam:

1 kHz, 30 fs pulse @ 266 nm
Conversion efficiency
~
10%

Colinear 3
rd

harmonic generation

Cooling channel

bucking magnet

Tube for

thermoheater

Stainless steel vacuum vessel

1.5 cell S
-
band cavity: Clamped design

f
0
=2.9918 GHz

f
0
=2.9980 GHz

Absorption
> 96 %

Q = 7600

0
-
mode


-
mode

1.5 cell cavity: measured resonances

Lorentzian fits

0.0
0.2
0.4
0.6
0.8
1.0
0
20
40
60
80
100
z (mm)
E/Emax
1.5 cell cavity: field profile
π
-
mode

Superfish



measured

Design and machining precision better than 5
μ
m

Cavity training

First results (November 2006)


15 hours @ 2 Hz, 10
5

rf pulses


65 MV/m

END