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

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Motivation: accelerator applications of PBG structures.

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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