Ellipsoidal Geometry and Conformal Mapping - Danish GPS Center
Ellipsoidal bunches by 2D laser shaping
description
Transcript of Ellipsoidal bunches by 2D laser shaping
Ellipsoidal bunches by 2D laser shapingEllipsoidal bunches by 2D laser shaping
Bas van der Geer, Jom LuitenEindhoven University of Technology
DESY Zeuthen30 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
kTJmcI
B p
ynxn
p
2
,,2)2(
Eznynxn
Bmc
Q 2,,,
3)2(
B
2mc QBk T A
Source brightness
Options (at fixed Q):
• Lower Temperature T Ultra Cold Plasma cathodeB.J. Claessens et al., PRL 95, (2005)
164801
• Reduce Surface area A Carbon NanotubesNeedle cathodes…
• Reduce Pulse duration τ Pancake regime
Longitudinal phase space density
Long pulse Pancake3 ps 30 fs1 nC 100 pC~100 A/mm2 ~1 kA/mm2
(Both with A=π mm2)z
Energy
Pancake
Long pulse
Thermalspread
Longitudinal phase-spaceat cathode
kTJmcI
B p
ynxn
p
2
,,2)2(
The problem is not the highspace charge density ...
Gaussian bunch
Brightness degradation
Brightness degradation
px
x
Gaussian bunch
Space charge forces:• Non-linear• Slice-dependent
... the real problem is the space charge density distribution.
px
x
Gaussian bunch
1989 - 2003
Fighting the symptoms:• Emittance compensation (B. Carlsten)• Optimized transverse profile (L. Serafini)• Uniform temporal & radial profile (DESY, ...)• ...
Gaussian bunchWaterbag bunch
px
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 coordinatesO. 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 recipeO.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 coordinatesO. 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 recipeO.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 communityJ.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 BunchesO.J. Luiten, S.B. van der Geer et al, PRL 094802, (2004).
1.5 cell, 3 GHz rf-photogun + focusing solenoid• Eacc = 92 MV/m• Q = 100 pC
Waterbag bunch in a realistic field
zc = 0.9 m, E = 4.5 MeV
-0.4 -0.2 0.0 0.2 0.4GPT z-zc [mm]
-2
-1
0
1
2
x [m
m]
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 MeVC. 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]
RM
S e
mitt
ance
[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 0.4GPT z-zc [mm]
4.1
4.2
4.3
4.4
4.5
4.6
4.7
Ene
rgy
[MeV
]
0
0.2
0.4
0.6
0.8
1
0 200 400 600 800 1000
z [mm]
RM
S e
mitt
ance
[μm
]
Thermal emittance!
10 fs
-0.4 -0.2 0.0 0.2 0.4GPT z-zc [mm]
-2
-1
0
1
2
x [m
m]
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 MeV0.7 – 2.0 kA 30 – 100 fs0.7 – 1.5 μm
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 1GPT Charge [nC]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
RM
S E
mitt
ance
[mic
ron]
Pancake
3D shaping @ PITZ
Settings:• 50 MV/m uniform, 1 nC, R=1 mm, 3D shaping of 3 ps ellipsoid
Pancake3D
0.1 0.2 0.5 1GPT Charge [nC]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
RM
S E
mitt
ance
[mic
ron]
Emission: 3D shaping 2D shaping
Highly non-linear fields! Highly non-linear fields!
Lower charge density Maintain short bunch
Long pulse lengthHigh acceleration field
3D versus 2D shaping
1.5 ps: 10 μm 15 fs: 1 nm
3D shaping @ PITZ
Settings:• 50 MV/m uniform, 1 nC, R=1 mm, 3D shaping of 10 ps ellipsoid
Pancake3D: 3 ps
3D: 10 ps
0.1 0.2 0.5 1GPT Charge [nC]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
RM
S E
mitt
ance
[mic
ron]
3D shaping @ PITZ
Settings:• 50 MV/m uniform, 1 nC, R=1 mm, 3D shaping of 10 ps ellipsoid
Pancake3D: 3 ps
3D: 10 ps
0.1 0.2 0.5 1GPT Charge [nC]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
RM
S E
mitt
ance
[mic
ron]
Pancake100 MV/m
Next
Experimental progress atExperimental progress atEindhoven University of TechnologyEindhoven University of Technology
Jom Luiten
2D ‘pancake’ shaping
Ingredients:• Ti:Sapphire 30 fs laser• Transverse shaping only
Ti:Saphire30 fs laser
Colinear THG800nm → 266 nm
Spatial filtering:800 nm gaussian
π shaper:Gauss → half-sphere
UVSphereGauss
800 nm after spatial filtering
ideal
π Shaper
Laser intensity
radius0 1 mm
π shaper
Input: Gaussian beamOutput: 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 3rd harmonic generation
Cooling channelbucking magnet
Tube for thermoheater
Stainless steel vacuum vessel
1.5 cell S-band cavity: Clamped design
f0=2.9918 GHz
f0=2.9980 GHzAbsorption
> 96 %
Q = 7600
0-mode
-mode
1.5 cell cavity: measured resonances
Lorentzian fits
1.5 cell cavity: field profile π-mode
Superfish♦ measured
Design and machining precision better than 5 μm
Cavity training
First results (November 2006)• 15 hours @ 2 Hz, 105 rf pulses• 65 MV/m
END