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Fabrication and cold test of photonic band gap resonators and accelerator structures

Evgenya I. Smirnova,

Ivan Mastovsky, Michael A. Shapiro, and Richard J. Temkin

Plasma Science and Fusion Center, Massachusetts Institute of Technology, 167 Albany Street, Cambridge, Massachusetts 02139, USA

Lawrence M. Earley and Randall L. Edwards

Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87544, USA

(Received 24 June 2005; published 20 September 2005)

We present the detailed description of the successful design and cold test of photonic band gap (PBG)

resonators and traveling-wave accelerator structures. Those tests provided the essential basis for later hot

test demonstration of the ﬁrst PBG accelerator structure at 17.140 GHz [E. I. Smirnova, A. S. Kesar, I.

Mastovsky, M. A. Shapiro, and R. J. Temkin, Phys. Rev. Lett., 95, 074801 (2005).]. The advantage of PBG

resonators is that they were built to support only the main, TM

-like, accelerator mode while not

conﬁning the higher-order modes (HOM) or wakeﬁelds. The design of the PBG resonators was based on a

triangular lattice of rods, with a missing rod at the center. Following theoretical analysis, the rod radius

divided by the rod spacing was held to a value of about 0.15 to avoid supporting HOM. For a single-cell

test the PBG structure was fabricated in X-band (11 GHz) and brazed. The mode spectrum and Q factor

(Q  5 000) agreed well with theory. Excellent HOM suppression was evident from the cold test. A six-

cell copper PBG accelerator traveling-wave structure with reduced long-range wakeﬁelds was designed

and was built by electroforming at Ku-band (17.140 GHz). The structure was tuned by etching the rods.

Cold test of the structure yielded excellent agreement with the theoretical design. Successful results of the

hot test of the structure demonstrating the acceleration of the electron beam were published in E. I.

Smirnova, A. S. Kesar, I. Mastovsky, M. A. Shapiro, and R. J. Temkin, Phys. Rev. Lett., 95, 074801 (2005).

DOI: 10.1103/PhysRevSTAB.8.091302 PACS numbers: 29.17.+w, 41.75.Lx, 42.70.Qs, 84.40.2x

I. INTRODUCTION

Two-dimensional (2D) metallic photonic band gap

(PBG) structures [1] have received considerable attention

recently, because of their possible applications in accelera-

tors [2,3]. Future linear accelerator operating frequencies

may increase from S-band to X- and possibly to Ku-band or

higher frequency band, because the higher frequency im-

proves the energy efﬁciency of the accelerator. At high

frequencies, it is crucial to use new accelerating cavities

that suppress wakeﬁelds, because the excitation of wake-

ﬁelds intensiﬁes with frequency and the wakeﬁelds induce

transverse motion of electrons and emittance growth [4,5].

PBG structures may be applied for constructing the accel-

erating cavities with long-range wakeﬁeld suppression,

based on their remarkable properties to reﬂect waves in

certain ranges of frequencies (called ‘‘global band gaps’’)

while allowing other frequencies to propagate. We experi-

mentally demonstrate that the use of PBG structures is a

promising approach to long-range wakeﬁeld suppression.

A PBG structure, or simply photonic crystal, represents

a periodic lattice of macroscopic pieces, metallic, dielec-

tric or both [6]. For accelerator applications, we employ a

two-dimensional metallic photonic band gap structure,

which is formed by a triangular array of copper rods [7].

We form a ‘‘PBG cavity’’ by removing a rod in the periodic

structure (Fig. 1). The mode, which has a frequency in the

band gap, will not be able to propagate out transversely

through the bulk of the PBG structure and will thus be

localized inside the PBG cavity around the defect. First

attempts to study 2D PBG resonators based on arrays of

metal rods were made by the authors of [2,8]. Smith et al.

[8] constructed and tested a metallic 2D PBG resonator.

Mode conﬁnement in this resonator was successfully

proven. However, higher-order mode (HOM) suppression

FIG. 1. The geometry of a PBG resonator formed by removing

a single rod in a triangular array.

Electronic address: [email protected]

PHYSICAL REVIEW SPECIAL TOPICS - ACCELERATORS AND BEAMS 8, 091302 (2005)

in a metallic 2D PBG resonator was not proven in [2,8],

since the complete theory of global band gaps in 2D

metallic PBG structures did not exist at that time. Global

band gap diagrams for 2D metallic PBG structures were

published in [7]. Based on the global band gap diagrams,

we designed and constructed a single-mode 2D PBG reso-

nator. The design and construction of a PBG accelerator

with long-range wakeﬁeld suppression became possible

after the success of a single-mode 2D PBG resonator

demonstration. Finally, the PBG accelerator was success-

fully tested with the electron beam (hot tested) and the ﬁrst

ever demonstration of the acceleration in PBG structures

was completed. The hot test results are published in [9].

The structure was powered with 2 MW of microwaves and

the electron beam was accelerated by 1.4 MeV. The accel-

erating gradient of 35 MV=m was demonstrated.

This paper provides a detailed description of the design,

fabrication, and cold test of a series of photonic band gap

(PBG) test resonators and ﬁnally of a six-cell, 17 GHz PBG

traveling-wave accelerator structure. The paper is organ-

ized as follows. In Sec. II, we derive the conditions for

which a mode with the frequency inside the global band

gap can be selectively conﬁned inside the PBG cavity.

Next, we design a single-mode 2D PBG resonator based

on the global band gap picture from [7] and our computa-

tions using high frequency structure simulator (HFSS)

code [10]. In Sec. III, we describe the construction and

testing of several PBG resonators. We have demonstrated a

high-Q mode-selective PBG resonator at 11 GHz.

Section IV presents the design of a 6-cell 2=3

traveling-wave (TW) PBG accelerator structure at

17.140 GHz. Section V describes the PBG accelerator

structure manufacturing and tuning. The agreement be-

tween the design and ﬁnal cold test results was excellent.

Section VI is the conclusion.

II. MODE CONFINEMENT IN 2D PBG

RESONATORS

We started the design of a single-mode PBG resonator

by studying the global band gaps chart for the triangular

lattice of metal rods, which was published in [7].

Electromagnetic waves with a frequency inside the band

gap cannot propagate through the PBG structure and will

be reﬂected from the array of elements, such as rods, which

can be called the ‘‘PBG wall.’’ However, by perturbing a

single or several lattice sites, we can permit a single mode

or set of closely spaced modes with frequencies inside the

gap. The perturbation in two dimensions can be created by

removing a single rod or replacing it with another one

which has a size or shape different from the original. The

wave with a frequency inside the band gap cannot propa-

gate into the bulk of the PBG structure, so, under certain

conditions, the mode of this frequency can be localized

around the defect. Unlike in a traditional pillbox resonator

only the modes with frequencies inside the band gap can be

conﬁned in a PBG cavity. Other frequencies will leak out

through the PBG wall. Consequently, the spectrum of

eigenmodes in a PBG resonator will be quite rare. The

PBG resonator which can selectively conﬁne an accelerat-

ing (TM

-like) mode is a good candidate for an accelera-

tor cell [2,3].

We choose the simplest possible two-dimensional me-

tallic PBG resonator, which is formed by one removed rod

in a triangular lattice (Fig. 1). The rods are sandwiched

between metal plates, which are so closely spaced that we

do not have longitudinal (along the rods) ﬁeld variation for

the range of frequencies of interest. Analysis of the PBG

resonators was performed using the HFSS code. We found

that the mode with frequency in the band gap was conﬁned

in a PBG structure with only three rows of rods (Fig. 1). For

this geometry, the diffraction Q factor was found to be of

the order of 10

, which is much higher than the computed

Ohmic Q factor of about 5000. Therefore, three rows of

rods in this PBG structure are sufﬁcient for construction of

a PBG resonator.

We computed the eigenmodes of the PBG resonator of

Fig. 1 for different ratios of the PBG structure rod radius, a,

to the spacing between the rods, b. The computed eigen-

frequencies for the TM modes are plotted in Fig. 2. The

same band gap picture as in [7] is shown on the !b=c

versus a=b diagram, where !  2f, f is the wave fre-

quency, c is the speed of light. The solid black curve

represents the boundary of the band gap region. A wave

with a frequency to the right of the solid black curve cannot

propagate through the PBG structure, while a wave with a

frequency to the left of the black curve can propagate.

FIG. 2. The eigenfrequencies of the TM modes in PBG cavity

formed by a single removed rod from the triangular lattice. The

eigenfrequencies are plotted with dots for different ratios of a=b:

Black solid lines show the band gap boundaries. Dashed lines

represent the frequencies of modes of a pillbox cavity with the

radius R  b  a: For the values of a=b inside the shaded region

the PBG resonator only conﬁnes a single, TM

-like mode.

EVGENYA I. SMIRNOVA et al. Phys. Rev. ST Accel. Beams 8, 091302 (2005)

091302-2

Modes with a frequency to the right of the curve are called

‘‘defect modes’’ and are conﬁned in the defect region of the

PBG structure, while modes to the left are not conﬁned.

The frequencies of the defect modes are plotted over the

band gap picture with dots. The dashed lines on the picture

show the eigenfrequencies of the pillbox cavity with a

radius R  b  a: As the radius of the rods increases the

effective radius of the PBG cavity goes down and the

frequencies of the eigenmodes increase.

The ﬁeld pattern of the modes conﬁned inside the PBG

resonators is shown in Fig. 3 [9]. We note from Fig. 2 that

for some values of the radius of the rods (0:1 < a=b < 0:2)

only a single lowest order mode is conﬁned by the PBG

structure. This frequency range is shaded in Fig. 2. The

ﬁeld pattern of the conﬁned mode resembles the pattern of

the TM

mode in a pillbox resonator [Fig. 3(a)], thus we

named it the TM

-like mode. The TM

-like mode can be

employed as an accelerating mode in a PBG accelerator

cell. For this choice of a=b, the dipole mode, which is the

-like mode, is not conﬁned within the central region

or defect region of the cavity. However, the mode can still

exist in the structure if a metal wall is placed at the

periphery, as can be seen in Fig. 3(a). Therefore, for

effective HOM damping, the outside wall should either

be made of absorber or be located relatively far from the

center of the PBG structure. For a=b > 0:2 the PBG struc-

ture conﬁnes the higher-order TM

-like mode [Fig. 3(b)],

and is no longer attractive for accelerators, since the TM

mode is a dangerous wakeﬁeld mode. The electric ﬁeld of

the TM

mode has a transverse component, and thus, the

dipole mode is primarily responsible for kicking the elec-

tron beam off axis. Thus, only PBG structures with 0:1 <

a=b < 0:2 can be applied for the construction of a single-

mode accelerator cavity.

III. 2D PBG RESONATOR CONSTRUCTION

AND TESTING

A. Brass PBG resonator testing

In order to verify experimentally the mode conﬁnement

and higher-order mode suppression in PBG resonators, we

constructed two PBG resonators for cold testing (Fig. 4).

The resonators were fabricated using brass cylinders

closed at each end by brass circular plates. PBG structures

were formed by brass rods ﬁtted into arrays of holes at the

end plates. A single rod was missing from the center of the

PBG structure to form the PBG resonator. Dimensions of

the resonators are summarized in Table I. In cavity 1, with

a=b < 0:2, only the TM

mode was conﬁned by the PBG

FIG. 3. (Color) Modes of PBG resonators with different ratios of

a=b: (a) a=b  0:15, the TM

mode is conﬁned by the PBG

structure, a dipole mode is conﬁned by the outside wall; (b)

a=b  0:30, the TM

and the TM

modes are conﬁned by the

PBG structure [9].

FIG. 4. (Color) PBG resonators built for the cold test.

FABRICATION AND COLD TEST OF PHOTONIC BAND ... Phys. Rev. ST Accel. Beams 8, 091302 (2005)

091302-3

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