Development of RF Undulator-Based
Insertion Devices for Storage Rings
and Free Electron lasers
Sami Tantawi, Muhammad Shumail, Jeff Neilson, Gordon Bowden,
Valery Dolgashev, Chao Chang,
NLCTA Group ( In particular Michael Dunning, Erik Hemsing, and
Stephen Weathersby)
Klystron Shop Group (Andrew Haase et. al.)
Outline
• Introduction
• Microwave Undulators
•
•
•
•
•
Straight forward approaches
The HE11 mode in corrugated waveguide
Scaling laws
The design of the undulator ends
Experimental results
• Optical undulators
• Design philosophy
• Prototype production
2
Why RF Undulator?
Many desirable features
• Fast dynamic control of
- Polarization
- Wavelength
- K
• Possibilities for shorter undulator wavelength while maintaining a large
•
•
•
•
apertures (cm vs mm for static undulator)
No issue with permanent magnet damage by radiation
Economic considerations
Potential use as LCLS “After Burner”
Dynamic undulator for storage ring
Available Resource - NLCTA
3 x RF stations
*
• 2 x pulse compressors (240ns - 300MW max),
driven each by 2 x 50MW X-band klystrons
• 1 x pulse compressors (400ns – 300MW
/200ns – 500MW variable), driven by 2 x
50MW X-band klystrons.
1 x Injector: 65MeV, ~0.3 nC / bunch
In the accelerator housing:
–
*
*
2 x 2.5m slots for structures
Shielding Enclosure:
suitable up to 1 GeV
For operation:
–
Can run 24/7 using automated
controls
(Gain = 3.1)
7/14/2016
Page 4
TW RF Undulator in Circular Guide
TE11 Mode at 11.424 GHz for K=1
Research initiated by Claudio Pellegrini* at UCLA
Undulator K parameter of 1 requires > 1 GW
K = 0.5 of some interest
• power level achievable 250 MW
• surface fields (80 MV/m) would limit pulse length to < 200 ns
Substantial enhancement of K parameter can be obtained with resonant structures
*S. Tantawi, V. Dolgashev, C.Nantista, C.Pellegrini,J.Rosenweig, G. Travish,” A Coherent Compton Backscattering
High Gain Fel Using An X-band Microwave Undulator”,Proc. of 27intl FEL Conf, Aug 2005
Effect of Power Losses
Tuning the Undulator Profile Through LLRF System
Because the e-beam and the em wave are traveling in
opposite directions one can tailor the rf pulse to compensate
for errors in the waveguide and also to taper the undulator field
Waveguide Undulator
e-
RF Power
RF
Time
Outline
• Update on the High Gradient
Research
• RF sources research
• High Repetition Rate accelerators
• Applications:
- RF undulator
- Electron Therapy machine development
GARD review, March 11, 2013
8
1
80
72.737
2
100
64.828
3
100 breakdown
60.133
Waveguide High Gradient Studies: Maximum
electric
4
200
53.528
fields for different geometries and materials
5
500
53.066
M2sort 
Low
magnetic field
80
Max. surface electric field [MV/m]
Max. surface electric field [MV/m]
80
60
40
High
magnetic field
20
0
60
6
500
45.742
7
800
45.255
8
1·10 3
38.385
9
1.3·10 3
36.693
10
100
71.313
11
Copper
150
12
300
60.08
13
400
55.656
14
500
54.787
15
700
47.531
K~1
40
Stainless
steel
67.3
Gold
20
0
500
1000
Time [ns]
1500
0
0
500
1000
Time [ns]
Initial Design point K~0.4
1500
HE11 Mode in Corrugated Guide
P ~ λ/2
b –a ≈ λ/4
2a
2b
P
Inspired by our work on a previous LDRD project which involved
corrugated feed horns for CMB applications
Lowest order mode (HE11) is a combination of primarily TE11 and
TM11 modes
Magnetic field is extremely low on waveguide walls – attenuation
can be less than that of smooth wall cylindrical TE01 mode
Field configuration ideal for beam interaction
Comparison BetweenTE1n and HE1n Modes
Frequency = 11.424 GHz, K = 1, Length = 1 m, Material: Copper
For TE1n modes the undulator is a simple circular waveguide
For HE1n modes the undulator is a corrugated circular waveguide with following
parameters:
Slot Depth = 0.335 l
Slot Thickness = l/16
Corrugation Period= 0.45 l
HE11
TE11
HE12
TE12
HE13
TE13
150
Stored Energy Joules
Power Losses MW
150
100
50
0
0.5
1.0
1.5
Undulator Inner Radius in Free Space Wavelength Units
2.0
HE11
TE11
HE12
TE12
HE13
TE13
100
50
0
0.5
1.0
1.5
Undulator Inner Radius in Free Space Wavelength Units
2.0
Hybrid Mode Fields
Radial Field
Electric Field
Axial Field
Magnetic Field
Azimuthal Field
Axial Field
HE1n Modes Scaling Laws
For an undulator made of copper at room temperature :
l
lu 
2
 0.727141a 2 0.0673433Lx 2 
2 2
Power :
P( MW )  K J1 ( x) 


5/2


l
a
l
u
u


71.5a 2 K 2 LJ12 ( x)
Stored Energy :
U ( Jouls ) 
lu2
Quality Factor :
Filling Time :
1.17 108 a 3 L
Q
128 2 a 3  117 Lx 2 lu2
t f ( s) 
1
lu
124208 a 3 L lu
128
2
a 3  117 Lx 2 lu2

1.02 KxJ1 ( x)
a
3.4 KxJ1. ( x)
Peak Surface B Field : Bs (mT ) 
a
x  {2.40483,5.52008,8.65373,11.7915} for HE11 , HE12 , HE13 , HE14  modes
Peak Suface E Field : Es ( MV / m) 
HE1n Modes Scaling Laws
For an undulator made of copper at room temperature :
lu 
l
2
Optimal Radius :
Minimum Power :
a( m)  0.23l 2/3 3 Lx 2/3
P( MW ) 
0.28K 2 L2/3 x 4/3 J12 ( x)
lu7/6
9.22 K 2 L5/3 x 4/3 J1 ( x) 2
Stored Energy :
U ( Jouls) 
Quality Factor :
Q
Filling Time :
t f (  s )  32.8L lu
lu2/3
30867 L
lu
1.02 KxJ1 ( x)
a
3.4 KxJ1. ( x)
Peak Surface B Field : Bs (mT ) 
a
x  {2.40483,5.52008,8.65373,11.7915} for HE11 , HE12 , HE13 , HE14  modes
Peak Suface E Field : Es ( MV / m) 
Undulator Design
Undulator Mechanical Structure
Electric Field Distribution
1.2
Simulated Magnetic Field c B
Relative Amplitude
Simulated Electric Field
1.0
0.8
0.6
0.4
0.2
0
20
40
60
80
Distance Along the Undulator Axes cm
100
120
Undulator Coupler Design
Two coupling ports 90o apart to excite
two polarizations independently
Coupler Field
Configuration
Undulator Mechanical Structure
Electric Field Distribution
Corrugation Period=0.4254 l
Inner Radius=0.75 l
Outer radius 1.01293 l
Corrugation Thickness l/16
Number of periods 98
l=2.6242296 cm
Undulator Wavelength=1.39306 cm
Power required (for linearly polarized, K=1)=48.8 MW
Q0=94,000
Transverse Beam Distribution
Simulated Bunch Drift for K
0.7
2.5
2.0
y mm
1.5
1.0
0.5
at exit 60 MeV
0.0
at exit 120 MeV
0.5
at entrance
1.0
1.0
0.5
0.0
0.5
1.0
x mm
1.5
2.0
2.5
Field Integrals
f(z) and g(z) represent the axial electrical and magnetic field
distribution along the tapered region
Drift in ρ-z
Undulator Structure Tested at NLCTA
Calculations from cold test data @ 20 °C with air:
Resonance Frequency (f0) = 11.419 GHz (11.424 under vacuum @12.1
°C)
Comparison between Simulations and Cold Test Data
Measured Filling Profile the Structure
Undulator Operation
Far Field @ 69 MeV
Electric field
polarization vector
Far Field @ 69 MeV
Electric field
polarization vector
On-axis
coherent
radiation
due to 2nd
harmonic
of 800 nm
seeding
Off-axis
incoherent
radiation
Date of measurements: July 18, 2012 ( The idea of these measurements was initated
by Erik Hemsing)
Far Field @ 74.8 MeV
Without seed
With 800 nm seed
Spectrum shift as a function of K
Fitting the Measured Spectrum
Measurements of the undulator K parameter
Beam Energy 70 MeV
Radiation Wavelength nm
500
480
Calculated from Measured Spectrum Data
460
Calculated from RF Power Measurements
440
420
400
380
360
0.2
0.3
0.4
0.5
0.6
K 0.96 x Value Calculated from RF Measurements
0.7
Beam Shift
Max drift (measured) = 1.52 + 0.03 mm (assuming 0.094 + 0.002 mm/pixel)
Max drift (calculated) = 1.27 mm
K
0.6
69 MeV
1.5
Measured
1.
Sinusoidal Fit
Drift mm
0.5
0.
0.5
1.
1.5
0
45
90
135
180
225
RF Phase degrees
270
315
360
An HE11 Undulator as an After Burner for LCLS
a  7.848cm
l u  5.55169cm
B p =310 mTesla
K  2.48
Vg/c=0.83
Vp=1.12
TotalPower =46MW
FillingTime  7.5427
Stored Energy=346 Jouls
Peak Electric Field at Guide Wall=40 MV/m
Energy Supllied by One 5045 Klystron is 228 Joules
Metallic structure driven by a THz source
•Status of the development:
— A novel concept for using the balanced hybrid mode in corrugated waveguide to create ultra-high filed in the center of
—
—
—
the waveguide with relatively small surface fields have been developed.
The scaling laws for this device have been developed.
The phase conjugate end mirrors have been developed
The single particle dynamics and the end field profile required to minimize both integrated transverse momentum kick
and total transverse displacement have been studied and implemented in the design
— A prototype at designed with 1.4 cm undulator wavelength is under construction to test the concepts. The undulator is expected
to have a K parameter of ~1 with possibility of switching the polarization by controlling the phases of the RF source
— Initial test for this undulator with beams is scheduled on June 18 at NLCTA at SLAC.
— The THz structure is being designed mechanically.
— The THz source at University of Maryland have been tested up to 80 KW recently with a pulse length of 7 uS.
Parameters for 221 micron undulator
(corresponding to the available 680 GHz
source; with pulse compression few MW could
be achieved using this source)
P( MW ) 
DARPA visit
June 27, 2012
0.24 K 2 L2 / 3 900 kW for K=0.03,
l7u / 6
10 MW for K=0.1 (5.5 T)
t filling( s )  32.8 L lu
48 ns filling time
a (m)  0.41lu2 / 3 3 L
1.4 mm diameter aperture
Resonant Ring Configuration
Load
Miter
Bend
Coupler
RF Input
Power
Corrugated
Waveguide
Undulator
Light
RF
Particle Beam
A closed ring with length nλg
Tune by adjusting ring length
Considerable development for relevant components (miter
bend, couplers) has been done (ITER transmission lines)
Corrugated Waveguide Mode Converter
𝑛
Hardware for a ~ 150GHz RF undulator is being
designed:
• Applied RF is the sum of several modes of HE1n
designed such that RF amplitude = 0 at r = 0 in
regions where beam interaction is not wanted.
𝑎𝑛 ∙ 𝐻𝐸1𝑛
vacuum
r
• A mode converter will produce the desired HE11
mode for the RF undulator.
• Beam and RF will interact in the corrugated
waveguide.
38
First 3 HE1n modes combined
𝑛
𝑎𝑛 ∙ 𝐻𝐸1𝑛
Applied RF should be have no power at radius = 0
upstream of the mode converter:
• First three HE1n modes were combined to form
appropriately shaped RF power with reasonable
coefficients.
• An optimization was performed to find coefficients
a0 → a2 while minimizing RF power for a defined
radius.
• The mode converter is being designed using
CASCADE for these coefficients with scaling laws
applied.
Presentation title
39
Superconducting Undulator( 1 % duty cycle)
Undulator wavelength ~ 1cm imply operating frequency of ~16 GHz.
The undulator test done to date was at 11.4 GHz with undulator wave length of
1.393 cm. Reducing it to 1 cm should be straight forward
5.00
50.00
Filling Time seconds
RF Power Watts
1.00
0.50
4.2 K
10.00
5.00
1.00
0.50
1.8 K
1.8 K
0.10
0.05
4.2 K
0.01
0.10
0.05
2
4
6
u cm
8
10
2
4
6
u cm
•One could decrease the filling time by decreasing the external Q
•The peak power would increase, of course.
•At a filling time of 1 ms, the peak power required is 50kW/m
•At CW the peak power required is 500 watts/m
8
10
Device structure
trench
10mm
10mm
0.2mm
laser
6mm
16um gap
Alignment
structure
Stretching the laser wavelength using either dielectric slab or
Bragg guiding structure undulator
•The philosophy of the design is to write down the
profile of the electromagnetic fields required and
then “dress it with materials to guide it”
•There is rather a limited set of fields that
—satisfy Maxwell’s equations,
—have a dipole like field and
— have net deflection as they propagate with the beam
•The field configurations shown in the figures are
theoretically the best possible field profiles; i.e.,
profiles that gives the highest possible deflecting
field with minimum surface field.
•Typically the relative group velocity is related to the
undulator wavelength by:
vg / c 
Bragg guiding structure
Field is minimized at
the boundary of the
guiding structure.
The effective
deflection field is
due to the
difference
between E&H at
the center
Radius in unites of wavelength
Field is maximized at the
boundary
Slab guiding structure
Es 

Ed
2
 lu / l  1 a / l 
2
lu / l
Smaller deflecting
field
lu / l0  1
lu / l0
Radius in unites of wavelength
DARPA visit
June 27, 2012
Design example of a planer undulator with
an undulator wavelength of 100 micrometer
Si
SiO2
Si
Coupling Scheme
Transmission
Reflection
Incident Angle
44
Simplified fabrication flow
Film
deposition
Si wafer
Photo lithography &
Etching
Assembly
15um
1um
0.75um
1.4um
0.75um
1um
Epoxy
Epi Si
Poly Si
SiO2
Si
Refractive index measurement of deposited films
Poly Si film
SiO2 film
Test setup: measure reflection coefficient
Si wafer
Refractive index of films
Curve fitting at 10.5um
SiO2 TE01 at 10.5um, n= 1.87
Si Substrate TE01 at 10.5um, n= 3.30
Poly Si TE01 at 10.5um, n= 2.90
1
1
1
Measure
Measure
Measure
0.9
0.9
Fitting
0.8
Fitting
0.9
Fitting
0.8
0.7
0.6
0.5
R
0.6
R
R
0.8
0.7
0.7
0.4
0.5
0.6
0.3
0.4
0.2
0.3
0.2
10
0.5
0.1
20
30
40
50
60
70
80
90
Angle (degree)
Si wafer (crystal): n=3.30
(n=3.42 from literature)
0
10
20
30
40
50
60
Angle (degree)
70
80
SiO2 Film: n=1.87
(fused silica n=2.25)
90
0.4
10
20
30
40
50
60
Angle (degree)
70
80
Poly Si Film: n=2.90
90
Images of devices
16um gap
Trench with
Thin film
Front side
Multilayer films
SEM image of device
assembly showing
~16um gap
Alignment
structure
Back side
Look at this surface
The Future
More precision measurements at NLCTA
Superconducting undulators
mm-wave undulators
Optical undulators
Projects that might benefit from this technology:
• After burner for LCLS with polarization control
• Short wavelength Undulator at 10mm for ILC
• Short wavelength undulator for NGLS