Laser-Driven Dielectric Accelerators
Advanced Accelerator Research Department
Stanford Linear Accelerator Center
R. Joel England
E. R. Colby, J. Ng, R. Noble, J. E. Spencer, D. Walz
SLAC
R. Byer, C. McGuinness, E. Peralta, K. Soong
Stanford University
Oct 1, 2010
Catalina Workshop 2010
1
Motivation
S-Band RF
X-Band RF
Optical to IR
3D “woodpile”
structure
dielectric
gratings
Oct 1, 2010
smaller RF structures:
• higher gradient
• machining tolerances
• transverse wakefields
• breakdown (Ez ≤ 100 MV/m)
laser-driven microstructures
• lasers offer high rep rates, strong
field gradients ( >0.5 GV/m),
commercial support
• dielectrics: high breakdown
threshold (1-5 GV/m)
PBG Fibers
Catalina Workshop 2010
2
All-Optical FEL?
beam~ as
Q~fC,
N~nm
point-like
e- source
Oct 1, 2010
1-4 µm laser
MHz rep rates
1-10 µm laser
+
+
acceleratoron-a-"chip"
Catalina Workshop 2010
0.5 to 50 keV
xrays
undulatoron-a-"chip"
3
Needle Field-Emitter Source
70 fs pulses; 200 e- per bunch
rep rate up to 1GHz
?
Hommelhoff, et al, PRL 96, 077401 (2006)
Oct 1, 2010
attosec pulses; 2000 e- per bunch
Catalina Workshop 2010
4
Microbunching
Net laser acceleration of 1.2 keV demonstrated
for 400 attosec microbunches using inverse
transition radiation (ITR) at a metal foil.
C.M.S. Sears, et al. “Production and characterization
of attosecond electron bunch trains,” PRST-AB 11,
061301 (2008)].
C.M.S. Sears, et al. “Phase stable net acceleration of
electrons from a two-stage optical accelerator.”
PRST-AB 11, 101301 (2008).
Oct 1, 2010
Catalina Workshop 2010
5
All-Optical FEL?
1-4 µm laser
MHz rep rates
Q~fC,
N~nm
point-like
e- source
Oct 1, 2010
1-10 µm laser
+
+
acceleratoron-a-"chip"
Catalina Workshop 2010
0.5 to 50 keV
xrays
undulatoron-a-chip
6
Testing of Candidate
Accelerator Structures
E163: A facility for testing laser-driven accelerator structures.
Beam energy = 60MeV; t = 1ps to 400 attosec; E = 0.1%
Oct 1, 2010
Catalina Workshop 2010
7
Grating-Based Planar Structure
Parallel planar gratings with
side-coupled laser and flat
beam.
G0 ~ 10 GV/m ; =10fs
G0 ~ 1.2 GV/m ; =1ps
G0/ELASER
G0/ELASER
T. Plettner, et al. PRST-AB 9, 111301 (2006).
Oct 1, 2010
• 1mm2 gratings purchased
• Working on in-house
fabrication via campus
collaboration (E. Peralta, B.
Byer)
Catalina Workshop 2010
8
Woodpile Structure
simulation of accelerating mode
images courtesy of C. McGuinness
max gradient ~ 400 MV/m
9-layer structure built with ~400nm “logs”
Suitable for 4.5 µm drive laser (Ti:Saph
laser + OPA)
Working on bonding of top/bottom halves.
B. Cowan
Oct 1, 2010
Catalina Workshop 2010
9
Dielectric Fiber Accelerator
conductor
e
hollow dielectric-lined waveguide
aperture ~ 0.26  G0~2.5 GV/m
DF ; e / e  1  2
conductor lossy at
optical wavelengths
damage threshold for SiO2 ~ 5GV/m @ 1ps
Rosing & Gai, PRD 42, 1829 (1990)
e1,e2
hollow Bragg waveguide
aperture ~ 0.3  ; G0 ~ 2.5 GV/m
DF ;
1  (2 a /  )2  2.1
Mizrahi & Schachter, PRE 70, 016505 (2004)
PBG fiber with central defect
aperture ~ 0.68  ; G0 ~ 2.5 GV/m
X. E. Lin, PRSTAB 4, 051301 (2001)
G0  E pk / DF
 t c  (1  g )L fiber
 t  1ps
g  0.6
L fiber,max ;  t c / 0.4 ; 1mm
Oct 1, 2010
Catalina Workshop 2010
10
Manufacturability
custom borosilicate fiber recently built through
Incom, Inc. SBIR proposal
 ~ 6.4µm
CUDOS simulation
of supported accelerating mode with
damage factor DF = 2.
B. Noble
images courtesy B. Noble, J. Spencer
Oct 1, 2010
Catalina Workshop 2010
11
Commercial Fibers

a (pitch)
(µm)
lattice
dia. (µm)
cladding
dia. (µm)
(telecom)
2R
(defect)
(µm)
1550
10.9
3.8
70
120
1060
9.7
2.75
50
123
633
5.1
1.77
33.5
101
830
9.2/9.5
2.3
40
135
• fibers manufactured by Crystal-Fibre, Inc.
• 1060 fiber has geometry closest to Lin Fiber
(R/a = 1.44 vs. 1.48 for Lin fiber) simulations
predict acc. mode with G0,max ~ 30 MV/m
Oct 1, 2010
Catalina Workshop 2010
12
Laser Accelerator
Overview and Challenges
Damage Threshold
Structure Type/Manufacture
Efficient Laser Coupling
Gross Positioning
Beam injection/focusing
Optical Microbunching
Proof-of-principle expt’s
periodic focusing
accelerator section
coupler
Future Studies:
Staging & phase stability
Alignment
Periodic Focusing
Temperature/thermal
Micro-sources (needle emitters,
etc)
Oct 1, 2010
light guide
Catalina Workshop 2010
13
Laser Damage Threshold
Laser damage for dielectric materials such as Si and SiO2 is an area of active research
in our group. The maximum accelerating field in a structure is Ez = Epk/DF where
“DF” is a damage factor of order unity and Epk is the peak field corresponding to the
damage fluence of the material.
Damage Fluence (J/cm2)
Silicon ( = 1ps)
0.28 J/cm2 ~ Epk=1.4 GV/m
Fused Silica
benchmark (K. Soong)
measurement (red)
Published
data from
B. C. Stuart
et. al.2
 (nm)
courtesy K. Soong
Oct 1, 2010
2 J/cm2 ~ Epk=5 GV/m
Catalina Workshop 2010
14
High Gradient Focusing
New Halbach PMQ Design
vacuum compatible motors
Full Halbach design - all wedges same size
material: NdFeB + Al keeper
position readback encoders
tooling balls
19mm
tungsten backplate
(radiation shield)
assembly can be inserted/removed from
beam path
titanium rods with brass bearings & dicronite lubrication
Oct 1, 2010
Catalina Workshop 2010
15
High Gradient Focusing
Measured PMQ Field gradients: 420 T/m
Field strength of each magnet was measured directly with the NLCTA electron beam by
moving the magnet relative to a stationary profile monitor.
Although magnet field strength is correctly predicted, the
focus is not fully resolved: YAG bloom?
Actual data (PMQ 3)
(6 µm resolution)
Stage Position (m)
YAG
Oct 1, 2010
Catalina Workshop 2010
16
Emittance Preservation
ELEGANT simulation of NLCTA e-beam transmission through a 10 micron aperture
as a function of energy spread for different normalized emittances
ELEGANT simulation of focal waist
Transmission vs. Normalized Emittance
* = 0.5 mm
10µm dia aperture
* = 0.5 mm
Oct 1, 2010
Catalina Workshop 2010
17
Emittance Preservation
Normalized Emittance Quad Scan Data: Nov 2009 to Feb 2010
Feb-April 2009
Feb-April 2009
Oct 1, 2010
Catalina Workshop 2010
18
Final Focus Spot Size
• YAG profile monitor: res limit ~ 20 µm
• Tantalum knife edge: 1µm surface finish
• Knife Edge thickness = 0.5mm = Xrad/6
• Intercepted electrons filtered by downstream
spectrometer
• Integrated spectrometer signal measured as a
function of knife edge position (~40 nm res).
X: Extracted x = 8.9 µm
Y: Extracted y = 8.9 µm
e-beam profile image
at PMQ focus
1 pixel ~ 2 µm
June 13-19, 2010
Advanced Accelerator Concepts
Workshop
19
Demonstration Experiments
800 nm
Oct 1, 2010
800 nm
Catalina Workshop 2010
20
Experiment Layout
Required Beam Parameters
Beam
9.6
µmCharge
50 pC
Normalized
Emittance
< 5 mm mrad
Energy
60 MeV
Bunch length
1 ps
Energy Spread
0.1 %
PMQs
Fiber Holder
FIBER HOLDER
4 candidate commercial fibers
beam passes through ~1mm of fiber
Oct 1, 2010
Catalina Workshop 2010
Newport MS 260i
Spectrograph
21
All-Optical FEL?
1-4 µm laser
MHz rep rates
Q~fC,
N~nm
point-like
e- source
Oct 1, 2010
1-10 µm laser
+
+
acceleratoron-a-"chip"
Catalina Workshop 2010
0.5 to 50 keV
xrays
undulatoron-a-"chip"
22
Optical Undulator Concept
T. Plettner, R. Byer, PRSTB 11, 30704 (2008)
Oct 1, 2010
excitation via side illumination with pulsed laser
phase synchronous deflection of e-beam
undulator period can be much bigger than optical 
damage factor: DF ~ 3
material: quartz
channel width w ~  /2 (limits max beam size)
Catalina Workshop 2010
23
Strawman All-Optical FEL
unloaded gradient
G0 
ZC P
2
beam loading
; GF 
Cherenkov
Energy gain per unit length
q cg ZC
qcZ H
;
G

H
4 1  g  2
2
dU beam
 qG  q(G0  GF  GH )
dz
loaded gradient
dU
/ dz
qG
beam
4/3
2
8/3
Parameters for Laser-Driven Accelerator:
Undulator
Parameters:
e N  eth2 (qdU
/ q0 )2// 3dz esc2 (q
/
q
)

e
(q
/
q
)
0
rf
0
(1   )P / q c
B  1.6 T  K  0.14
EM
g
g
grating geometry
u  12 mm
m
grating steps per undulator period: M u  50
N = 1 Recycling
nm
Energy
# undulator periods:
N u  2600
=q =cavity
0.5 fC
drive laser wavelength:
laserlosses
 10  m
microbunch charge: q  0.5 fC
R. H. Siemann, PRST-AB 7, 061303 (2004)
norm. emittance: e N  1 nm
microbunch length:   0.022 fs
laser pulse length:  laser  0.3 ps
damage factor: DF  3
damage surface field: E pk  4.5 GV/m
Oct 1, 2010
 g

2067
(>
 min ;516)
w  0.4 laser ; G
 2.3
0.85GV/m
laser
  25Þ
0
 R  0.1 nm E
(h = 11.5 keV)
eBu

pk
Z

19

K
 C BK 0  2/3 sin 2 
u Z p DF
2 mc
 H  133
 2  10 4
0
Z

4c 2
u  2M u  p  = 1 ps 
u
 182 mm
Lu  N u u
4 3
ZC g
effective deflecting force
 r   max  w /L2opt R 4Z
 g (<
) 2Z
L
 (1
22nm
Cbc)g
Short bunch regime
c
g H
u
e
Lg 
   min 
N
Z R  Lu / 4  575 mm e rms
G
qZopt 2 r2  2320 mm
2
(  Lg )
R
/


k)
H
2(cZ
R
Catalina Workshop 2010
24
Strawman All-Optical FEL
T. Plettner, R. Byer, PRSTB 11, 30704 (2008)
~ 1e6 photons per microbunch x 50 bunches per train
At 1 MHz rep rate, this yields ~50e12 photons/sec
Oct 1, 2010
Catalina Workshop 2010
25
Strawman All-Optical FEL
Parameter comparison from 2010 FLS Workshop
Oct 1, 2010
Catalina Workshop 2010
26
Summary
Dielectric Laser-Driven (Table-Top) FEL?
• Recent Progress:
Optical Microbunching: (400 attosec bunches) recently demonstrated
Various candidate accel. structures now being fabricated or in-hand
Advanced coupler design (simulation): 10% to 90% laser coupling
E163/NLCTA facility (SLAC):
order of magnitude improvement in emittance (100s 10 µm)
high-gradient FF completed: <10 µm RMS beam spots
demonstrated
Planned demonstrations: benchtop and e-beam testing of PBG fibers,
followed by gratings and woodpile structure.
• A few-meter optical-scale FEL looks promising. Significant challenges:
- Source development: higher charge, shorter (1/10) bunches
- Drive wavelength of undulator: 10µm @ 1MHz rep rate (?)
- Significant R&D:
integration of source and accelerator with undulator
low-beta acceleration needed (UCLA: MAP)
alignment of multiple chip-based components over meter(s)
Oct 1, 2010
Catalina Workshop 2010
27
Backup Slides
Oct 1, 2010
Catalina Workshop 2010
28
The Roadmap
Groundwork
E163 Beamline
Construction
Optical Microbunching
Advanced Studies
Coupling Efficiency
Laser to Structure
Laser to Beam
Beam Dynamics
Wakefields
Transport & Focusing
Beam-Beam
Novel Sources
Needle Emitters
SEM
Mechanical
Alignment
Stability/Feedback
Woodpile
Gratings
Fibers
MAP
Other?
HEP
Oct 1, 2010
Final Focus (PMQs)
Beam Emittance
Positioning Hardware
Structure Evaluation
Damage Threshold
Prototyping
Assembly
Benchtop
Mode Profile
Spectral/Coupling
Temp/Phase Stability
Laser Coupling
Beam Test
Focusing/Transport
Microbunching
Net Acceleration
Staged Acceleration
Tabletop
Accelerator
Other Apps:
Light Sources, Medical, Security
Catalina Workshop 2010
29
Repository of Greek Letters
             
  
  

             
  
  

Oct 1, 2010
Catalina Workshop 2010
30
Optimized PBG Fiber Geometry
a = 1.3  ; R = 0.68 
X. E. Lin “Photonic bandgap fiber accelerator,” PRSTAB 4, 051301 (2001)
Oct 1, 2010
Catalina Workshop 2010
31
Search for Candidate Accel.
Modes
HC-1060 SEM image
RSoft BandSolve Model
courtesy of B. Noble
toward SOL line
Oct 1, 2010
Catalina Workshop 2010
32
Demonstration Experiments
4 commercial fibers
e-beam
image of mounted fiber
Oct 1, 2010
Catalina Workshop 2010
33
Woodpile: Fab
SiO2
Photo resist
2
SiO2
1
resist
Step 1: SiO2 Deposition
h
• Uniformity = 1-2%
Si Substrate
Silicon Substrate
Step 2: Resist Coat
a
Step 3: Optical Lithography
• Minimum feature size 450nm
• Alignment 3σ=60nm
w
3
4
Step 4: Dry etch SiO2
Poly-si
Step 5: Poly-si Deposition
SiO2
poly-si
5
Oct 1, 2010
Catalina Workshop 2010
Silicon Substrate
34
6
Step 6: Chemical Mechanical
Polish
Frictional Force
Woodpile: Fab
10sec=15nm
Time
SiO2
7
poly-si
Step 7: Repeat process for
remaining layers
Final Step: Oxide Etch
8
Oct 1, 2010
Catalina Workshop 2010
35
PMQs: Changes
Major Design Changes
8-wedge Halbach design instead of hybrid Iron/Permanent Magnet configuration.
Higher grade of permanent magnet used (BH = 38 to BH = 44)
Tighter tolerances on the NdFeB magnetic moments and dimensions.
Vendor pre-sorting of NdFeB blocks + double order for post-sorting.
Titanium rods and brass bearings, instead of Steel and Aluminum.
Titanium threaded rods, instead of steel.
Dicronite lubrication on the rods instead of vacuum grease or Moly-coat.
Higher-quality in-vacuum MDC motors for moving the magnets (old motors prone to failure).
Removable tooling balls to permit CMM alignment.
New wire-EDMed aluminum keepers.
String-potentiometer encoders to measure magnet positions along beam axis.
Slider stage to move the whole assembly in and out of the beam path.
Spring pins to adjust magnetic center and skew.
Octagonal titanium retainer ring to aid in assembly.
Octagonal titanium insert for the center to aid in maintaining block alignment.
Blocks glued in final assembly.
Oct 1, 2010
Catalina Workshop 2010
36
PMQs: Multipoles
Multipole Tolerances
RADIA + Mathematica simulations
reference radius  = 2.77 mm
 = 2.77 mm
Tolerance values from 12/19/2008
2(n+1)
multipole
Tolerance
B(n)[T/mn-1]
Tolerance
Kn[mn-2]
B() [T]
4
quadrupole
3.04
15.196
0.008
6
sextupole
1.1e5
5.45e5
0.420
8
octupole
3.1e8
1.54e9
1.101
10
decapole
1.13e13
5.64e13
27.97
12
dodecapole
1.83e17
9.17e17
252.26
black curve is tolerance
B() [T]
not possible due to saturation of the
magnetic material
General rule of thumb is that B() from the multipoles
should be less than the quadrupole contribution
Oct 1, 2010
Catalina Workshop 2010
37
PMQs: Assembly
Oct 1, 2010
Catalina Workshop 2010
38
PMQs: Skew Simulation
ELEGANT simulations for spot size and emittance at the IP as a function of skew.
Assumed skew configuration is {+1, -1, +1} for {PMQ1, PMQ2, PMQ3}
For adequately small spot size & emittance, need Skew ≤ 0.2 degrees
Oct 1, 2010
Catalina Workshop 2010
39
Advanced Coupler: Benchmark
Poynting Flux check on Extracted Fields in Mathematica Inner Products
perfE
Driven at 30 GHz
rad (ABC)
port
Total power = 1 Watt
Mode
S11
P (Watt)
1
0.0173
0.125
2
0.1085
0.357
3
0.258
0.432
4
0.4669
0.086
C22  E H
z(mm)
0
2
4
6
8
Re(C22)
0.948272
0.948251
0.948271
0.948272
0.948267
Oct 1, 2010
Im(C22)
-0.111002
-0.233625
0.026292
0.085964
0
Abs(C22)
0.954746684
0.976606676
0.948635419
0.952160488
0.948267
Catalina Workshop 2010
Note: the presence of
the radiation
boundary introduces
reflections.
40
Advanced Coupler: Benchmark
User specified
Mode
1
2
3
4
PFWD 
Calculated
FWD Power
0.12500
0.35698
0.43212
0.08585
Calculated
REV Power
3.73549E-05
0.004203454
0.028899705
0.018589013
E H l  El H
4 El H l
Actual
FWD Power
0.125
0.357
0.432
0.086
* 2
PREV 
Calculated from S11
Actual
REV Power
3.74113E-05
0.004202693
0.028755648
0.018747622
E H l  El H
FWD Power
%Error
0.00017%
-0.00593%
0.02850%
-0.17813%
* 2
4 El H l
Excellent Agreement!
Oct 1, 2010
Catalina Workshop 2010
41
Advanced Coupler:
Orthogonality
CUDOS Full 360˚ Overlaps
CUDOS Overlap integrals: Cartesian Grid 200x200
Project:
Bob Noble's CUDOS Simulations from Jan 2010 with 200x200 grid
Design:
V:/ARDB/FiberAccelerator/CUDOSfiles
Date
2/8/10
CPL = (C12 C21)/(C11 C22)
Lin
P1Mode2
P1Mode3
P2Mode1
P8Mode1
Oct 1, 2010
Lin
1
1.28E-07
5.00E-03
1.26E-17
2.60E-25
P1Mode2
1.28E-07
1
3.70E-03
3.43E-23
1.51E-25
P1Mode3
5.00E-03
3.70E-03
1
-4.43E-23
0
P2Mode1
1.26E-17
3.43E-23
-4.43E-23
1
7.04E-25
Catalina Workshop 2010
P8Mode1
2.60E-25
1.51E-25
0
7.04E-25
1
42
Advanced Coupler Design
code: S3P
courtesy of Cho Ng, SLAC
Prior art on advanced couplers:
• simulations in S3P (Cho Ng)
• in/out power couplers
• analogy to RF tw accelerator
• S11 = 0.1: power coupling
can be close to 100%
• however....
requires “artificial” boundary
conditions
ignores coupling into other
modes
in short, even if you get all of the power into the structure, it
isn’t necessarily going into the mode you want...
Oct 1, 2010
Catalina Workshop 2010
43
Advanced Coupler Design
TE mode
Bragg reflector
TM mode
Oct 1, 2010
Catalina Workshop 2010
44
Advanced Coupler Design
Previously found optimal insertion depth of coupler wgL = 11.9µm
Proceeded to optimize coupling by varying the cross-sectional size of the
waveguide coupler and doing a freq sweep at each value.
HFSS 12.0 Simulation using Lin geometry for  = 2 µm
ABC
ABC
e = 2.3 (glass)
wgL
perfH
perfE
e = 5 (Silicon)
Oct 1, 2010
Catalina Workshop 2010
e = 2.3
45
Advanced Coupler Design
Because the PBG structures are highly over-moded, any attempt to couple from
one end of the structure will excite a superposition of many modes. If the
geometry is chosen appropriately, then only the accelerating mode will survive
after many wavelengths. But power lost to the other modes will decrease
coupling efficiency.
total fields:
  E
 E 
 n

    
H
 H  n  
 n
 E
 n
 
 Hn
Oct 1, 2010

 En

  an 

 Hn






  E
  n
  
H

 
 n

ik z
e n

;
En+ : n’th mode (fwd)
En- : n’th mode (rev)
 E
 n
 
 H n

 E*


n
  bn 
*
H


n
Catalina Workshop 2010

 ikn z
e

46
Advanced Coupler Design
With the following choice of inner product
En H m
v
1
*
  (En  H m )gdS  N m mn
2
the forward and reverse power for a particular mode n=l can be obtained

Pl 
E H l  El H
* 2
4 El H l
Technique benchmarked for
cylindrical waveguide.
and the coupling to mode l can be calculated:
Ptw
 1 
Pin
* 2
E H l  El H
Pl

Ptw 4 El H l (1  )Pin

E H l  El H
Pl  Pl  Ptw


Pin Ptw Pin
4 El H l Pin
* 2
 = port reflectance; Pin = input power; Ptw = total power in waveguide; Pl+ = forward power in mode l.
Oct 1, 2010
Catalina Workshop 2010
47
Advanced Coupler Design
Waveguide coupler
149.011 THz, wgL = 11.9 µm
Oct 1, 2010
“Lin” Accelerating Mode
Eigenfrequency = 149.011 THz
Catalina Workshop 2010
48
Advanced Coupler Design
Power coupling to Accelerating Mode
6-fold coupler design
Pl 
Pin
optimal ~ 6%
freq (THz)
Pl 
Pin
reflection from
ABC close to zero
freq (THz)
Oct 1, 2010
Catalina Workshop 2010
49
Free-Space Laser Coupling
Radially polarized gaussian
laser beam incident on fiber.
Power coupling to Accelerating Mode
Pl 
Pin
optimal ~ 15%
freq (THz)
Pl 
Pin
Likely scenario for initial experimental
tests.
Oct 1, 2010
reflection from
ABC close to zero
freq (THz)
Catalina Workshop 2010
50
Emittance Preservation
Measured Emittance Growth in the NLCTA/E163 Beamline: Spring 2009
Oct 1, 2010
Catalina Workshop 2010
51
Emittance Preservation
Changes implemented to improve NLCTA emittance:
1.
Online beam transport modeling and orbit fitting implemented in the
control system.
2.
Beam-based analysis software for optimized steering through beamline
magnets.
3.
Effective use of saved beamline configs, reference orbits, and magnet
standardization routines.
4.
Photocathode laser converted to 90 deg incidence (thereby improving
mode quality).
5.
New lattice configuration with minimal steering and all chicane
quadrupoles turned OFF.
Oct 1, 2010
Catalina Workshop 2010
52
Microbunching
Monte Carlo of Microbunched Beam
Transformation equations for the microbunching
technique:
 f   0   sin(kL z0 ) Dominant washout terms
z f  z0  R56 [ 0   sin(kL z0 )]  T511 x0 2  T533 y0 2
laser
After PMQ Focus

I(z)  I 0 [1  2 bn cos(nkL z)]
n1
Oct 1, 2010
Primary culprits are the T511 and T533 of the PMQs
Catalina Workshop 2010
53
Microbunching
Possible Remedies
Radially Dependent Amplitude
z f  z0  R56 { 0  (x0 , y0 , z0 )sin(kL z0 )}  T511x0 2  T533 y0 2
T511 x0 2  T533 y0 2
(x0 , y0 , z0 )   
R56 sin(kL z0 )
this requires the IFEL modulation to increase quadratically with radial distance
Collimation
NO collimator
Qf = Q 0
Oct 1, 2010
400 µm diameter collimator
Qf = Q0/6
Catalina Workshop 2010
200 µm diameter collimator
Qf = Q0/21.5
54
High Gradient Focusing
Beam envelope simulation for E-163 matching section
PMQ Triplet
X
Y
Electromagnetic Matching Quads
ELEGANT simulation
Focal Beta Function:* = 0.5 mm
Focal Spot Size: X,Y = 3 µm
Final Focus Magnet Strength: 466 T/m (!)
Solution: Permanent Magnet Quadrupoles
Oct 1, 2010
Catalina Workshop 2010
55
High Gradient Focusing
Initial PMQ Triplet Design (built 2005)
Aluminum keeper
NdFeB
1010 Steel
C.M. Sears, “Production, characterization, and acceleration of
optical microbunches,” PhD dissertation, Stanford U. (2008)
possible explanations for discrepancy:
case 1: low magnetization in NdFeB material
case 2: saturation of the iron
Oct 1, 2010
PMQ#
Design (T)
Measured(T)
 B'dz
 B'dz
Meas/Design
1
4.2
2.804 ± 0.013
0.66
2
8.66
4.459 ± 0.017
0.51
3
8.66
4.590 ± 0.014
0.53
Catalina Workshop 2010
56
High Gradient Focusing
CAD reconstruction of block positions
Skew Correction
PMQ 3
Titanium insert to
reinforce block alignment
The skew appears to be due to cumulative effect
of multiple displacements of the blocks.
Suggested correction: insert a permanent
hexagonal pin in the center to enforce the correct
symmetry.
Oct 1, 2010
Catalina Workshop 2010
57
High Gradient Focusing
PMQ Measurement Summary
PMQ
Effective
Length (mm)
Wire scan
Integrated
Field (T)
PMQ Scans
Feb 2010
Measured
Skew (deg)
1
9.37±0.01
-4.04
-4.00±0.21
0.16
2
17.40±0.14
7.09
7.15±0.40
0.26
3
17.26±0.03
-7.45
-7.30±0.15
0.28
Achieved gradients > 400 T/m
Correct order of magnitude needed for periodic focusing in a
linear collider scenario (300 to 4200 T/m).
Oct 1, 2010
Catalina Workshop 2010
58