Plasma Science and Fusion Center Massachusetts Institute of Technology
Evgenya Smirnova
Massachusetts Institute of Technology
UCLA, January 2005
Photonic Band Gap Accelerator Demonstration at MIT
Plasma Science and Fusion Center Massachusetts Institute of Technology
Outline
Motivation: accelerator applications of photonic band gap (PBG) structures.
Photonic band gap structures: definition and examples.
Theory of PBG structures and resonators.
2D PBG resonators testing.
PBG accelerating structure: cold test
PBG accelerator demonstration
Plasma Science and Fusion Center Massachusetts Institute of Technology
Motivation: accelerator applications of PBG structures.
Plasma Science and Fusion Center Massachusetts Institute of Technology
Motivation
Type of accelerator
X- and K-band accelerators and
klystrons
Laser driven accelerators (μm wavelength)
Problem Higher order modes
(Wakefields)
Low breakdown threshold in
metal components
PBG solution PBG resonator suppresses wakefields
Dielectric PBG accelerator can
be built
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X- and K-band accelerators
High efficiency accelerators are needed Energy stored in accelerator structure decreases with
frequency Wakefields increase with frequency as f 3
PBG structure is effective for damping wakefields
Idea and first PBG experiments: D.R. Smith et al., AIP Conf. Proc. 398, 518 (1997).
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Photonic Band Gap (PBG) Structures
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Photonic band gap structures
A photonic bandgap (PBG) structure is a one-, two- or three-dimensional periodic metallic and/or dielectric
system (for example, of rods).
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Band Gaps
1D example: Bragg reflector
PBG structure arrays reflect waves of certain frequencies while allowing waves of other frequencies to pass through.
Band Gaps
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PBG resonators and waveguides2D PBG structures (arrays of rods) are of main interest for
accelerator applications. If a wave of certain frequency cannot propagate through a photonic crystal wall, then a mode can form in a crystal defect. This way we can construct a PBG resonator or PBG
waveguide.
PBG resonator PBG waveguide Higher order mode PBG
resonator
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Theory of PBG Structures
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Maxwell equations in PBG structures
nmie ,TkxTx
0
0
0
H
E
EH
HE
i
i
2D square lattice:,ˆˆ, bnebme yxnm T
m,n - integers
nm,T
ii HE , must satisfy the Floquet theorem
Maxwell equations solved
k
Field in PBG structures satisfies Maxwell’s equations:
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Solving Maxwell’s equations
b
b x
y
h
hxmnmn ,,1
Finite difference method (metals)
Plane wave method (dielectrics)
Periodic boundary conditions:bik
mNmNxe,,1
12
N
bh
Derivatives:
nm
inm
i nmee,
., xGxkx
Fourier series expansion takes into account periodic boundary conditions
.ˆˆ2
, nmb yxnm eeG
nm
inmnm
i nmee,
.,, xGxk Gk
x
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plotted along the Irreducible Brillouin zone boundary
Brillouin zone and Brillouin diagram
nmie ,TkxTx
k
nmie ,Tk
Brillouin zone
Irreducible Brillouin zone
is periodic, only
inside the Brillouin zone matter.
kBrillouin diagram:
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Global Band GapsGlobal band gap: wave cannot propagate in all directions.
Example of band gap diagram: square lattice of metal rods, TM waves
ab
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PBG resonators
PBG resonators can be studied with many commercial and freeware electromagnetic solvers, such as Superfish, HFSS, Mafia, Microwave Studio, MPB etc.
PBG cavity formed by a defect
In the presence of band gaps a defect in a PBG structure may form a resonator:
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2a
Mode selectivity in PBG resonators
Pillbox Cavity, TM01 mode
PBG Cavity, triangular lattice a/b=0.15, TM01 –like mode
•
Operating Point of PBG structure
b
Single mode operation.No higher order dipole modes.
This structure is employed for the MIT PBG accelerator
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HOM in PBG resonators
Only a single mode confined for 0.1a/b 0.2
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2D PBG resonators
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Resonators for the cold test
Cavity 1 Cavity 2
Lattice spacing b
1.06 сm 1.35 cm
Rod radius a 0.16 cm 0.40 cm
a/b 0.15 0.30
Cavity radius 3.81 сm 4.83 сm
Freq. (TM01) 11.00 GHz 11.00 GHz
Freq. (TM11) 15.28 GHz 17.34 GHz
Axial length 0.787 сm 0.787 сm
10 cm
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Cold test results
Dipole TM11mode(confined)
TM01 modeTM01 mode
Propagationband (no modes confined)
Band gap
Confined TM11 modeBad for accelerators
No confined wakefield modes. Good for accelerators
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Brazed PBG resonator
Theoretical QHFSS(TM01) = 5300
Measured Qmeasured (TM01) = 2000
Reason for low Q: poor contact between rods and end plates
How to improve Q ?
Brazing Electroforming
A resonator was brazed at CPI: Qbrazed (TM01) = 5000
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PBG accelerating structure
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Accelerator with PBG cells
Design the structure
● Choose the accelerator parameters ● Tune the cell to 17.137 GHz ● Tune the coupler
Cold test the structure
● Tune the coupler ● Tune the cell to 17.137 GHz
Hot test the PBG accelerator
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HFSS: accelerator design tool
Accuracy driven adaptive solutions
Optimization tools
Powerful post-processor
Macro language control of calculation.
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PBG accelerator parameters
PBG disk-loaded structure
Disk-loaded waveguide
Frequency 17.137 GHz
Qw 4188 5618
rs 98 M /m 139 M /m
[rs/Q] 23.4 k /m 24.7 k /m
Group velocity 0.013c 0.014c
Gradient 25.2 P[MW] MV/m
25.1 P[MW] MV/m
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2 /3 traveling wave cell: L/c = 2 /3
Iris radius scaled to 17 GHz from the SLC design
Dimensions
PBG disk-loaded
structure
Disk-loaded waveguide
Rod radius, a 1.08 mm -------
Lattice vector, b 6.97 mm -------
a/b 0.155 -------
Cavity radius 24.38 mm 6.88 mm
Cavity length, L 5.83 mm
Iris radius 1.94 mm
Frequency 17.137 GHz
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Tolerances
Both: the coupler cell and the TW cell, are sensitive to the rods radii and spacing. Fabrication tolerance of 0.001’’ is a must. Tuning in the cold test is needed.
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Electroformed PBG structurePBG accelerator was electroformed by Custom Microwave, Inc. (www.custommicrowave.com). Rods and plates of each cell were grown as a single crystal without connections. The cells were brazed together.
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Initial coupling measurements Measured coupling curves were 40 MHz high.
Two cells of the structure were 20 MHz lower than other cells.
Tuning was performed via etching.
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Etching
Etching was performed in Material Science and Technology division, Los Alamos National Laboratory.
Acid solution: 100 ml nitric acid, 275 ml phosphoric acid, 125 ml acetic acid.
Masking material: jack-o-lantern candle wax.
Etching time: 1 min per 0.0001’’.
Etching temperature: 45 C.
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Final cold test results
Good agreement between measurement and computation.
Flat field profile in accelerating mode.
Measured field profile (bead pull)
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PBG accelerator experiments
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MIT PBG experiment setup
Beam line PBG Chamber
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Components schematic
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Accelerator laboratory
Load
Coupling waveguide
PBG chamber
Linac
Klystron
Spectrometer
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High power coupling
2 MW 100 ns pulse was coupled into PBG accelerator
Conditioning time ~ 1 week
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Plan of experiment
Align the spectrometer
Measure electron beam acceleration in PBG structure
To be completed in January 2005
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Conclusion
Photonic band gap structures present accelerator physicists with new opportunities.
Theory of PBG structures is well elaborated.
MIT PBG experiments prove the existing theories.
Design and fabrication of a PBG accelerator were successful.
MIT 17 GHz PBG accelerator experiment to be completed soon !
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AcknowledgementMIT:
Chiping ChenAmit Kesar
Ivan MastovskyMichael ShapiroRichard Temkin
LANL:
Lawrence EarleyRandall EdwardsFrank KrawczykWarren PierceJames Potter
SLAC:
Valery Dolgashev
CPI:
Monica BlankPhilipp Borchard
Custom Microwave:
Clency Lee-Yow
IAP RAS:
Mikhail Petelin