Photonic Band Gap Structures for Accelerator
Applications
E.L Smirnova, M.A. Shapiro, C. Chen, RJ. Temkin
Plasma Science and Fusion Center
Massachusetts Institute of Technology
Cambridge, MA 02139 USA
Abstract. We report the results of our theoretical investigation and cold test of a twodimensional (2D) metal photonic band gap (PEG) accelerator cell and propose to construct a
27T/3 linear accelerator structure with reduced wakefields as a stack of PEG cells set between
disks with irises. We developed a computer code, called Photonic Band Gap Structure Simulator
(PBGSS), to calculate the complete dispersion curves for square and triangular arrays of metal
rods [1]. Using the PBGSS code, the global photonic band gaps of the arrays were determined
and employed to design the PBG cavities. The modes of the 2D PBG cavity formed by a defect
(missing rod) in the triangular array of metal rods were studied numerically using the HFSS [2]
code. The cavity was designed with only the fundamental TM0i mode confined and higher order
modes suppressed. The cold test was performed and the results proved the suppression of the
wakefields. Dielectric PBG structures were also studied as applied to microwave devices. A
dielectric PBG resonator with the TM02 mode confined and TM0i and TMn modes absent was
designed. The construction of such a resonator overcomes the problem of mode competition in
overmoded structures and thus will allow the extension of the operating frequency of the devices
to higher frequencies at higher order modes.
INTRODUCTION
In microwave linear accelerators, an intense electron beam interacts with the rf
circuit and excites higher order modes (wakefields). The wakefields are unwanted
modes, because they can affect the propagation of subsequent bunches of electrons. To
obtain high-efficiency acceleration, accelerating cavities must be selective with
respect to the operating mode, and the wakefields must be suppressed. The use of
photonic band gap (PBG) structures [3], and in particular two-dimensional (2D) PBG
structures [4], has been experimentally shown to be a promising approach to the
realization of mode selective circuits [5,6].
In recent years, numerous advances have improved the understanding of the theory
of PBG structures. The PBG structure or simply, photonic crystal, represents a lattice
of macroscopic pieces (for example, rods) of dielectric or metal. Scattering of the
electromagnetic waves at the interfaces can produce many of the same phenomena for
photons (light modes) as the atomic potential does for the electrons. In particular, one
can design and construct photonic crystals with photonic band gaps, preventing light
of certain frequencies from propagating in certain directions. If, for some frequency
CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli
© 2002 American Institute of Physics 0-7354-0102-0/02/$19.00
383
range, a photonic crystal reflects light incident at any angle, we say that the crystal has
a global photonic band gap.
The presence of a global photonic band gap in a photonic crystal allows us to
construct a PEG resonator, which can be formed by the defect (missing rod) in a
periodic lattice. The mode, which has a frequency in a global photonic band gap, will
not be able to propagate through the bulk of the PEG structure and will be localized
around the defect. The advantage of the PEG resonator over the conventional pillbox
cavity is its high mode selectivity: only the modes with frequencies within the global
band gap can be confined.
We aim to solve an important problem of designing and testing the PEG resonator,
which would selectively confine a single mode. There are two aspects, which needed
to be studied for the design of metallic PBG-based mode selective cavities. The first
involves the global band gaps calculation, and the second concerns mode confinement
in a PEG cavity. Global band gaps for two-dimensional (2D) triangular lattice of metal
rods have been recently calculated by these authors and reported in [1]. The analysis
of the mode structure in PEG resonators is accomplished with the HFSS code [2].
METAL PBG STRUCTURES THEORY
We started our theoretical investigation of the bulk properties of 2D PBG structures
by considering the square and triangular lattices of rods shown in Fig. 1 (in the figure
a is the radius of the conducting rod, b is the rod spacing). The square-lattice-based
PBG resonators have been investigated previously by Smith, Schultz, Kroll, etc. [5],
but no rigorous theoretical investigation of the bulk properties of square lattices was
reported in [5]. The triangular lattice attracted our attention because of the better field
symmetry in the modes of the PBG resonator [6].
(a)
FIGURE 1. Scheme of PBG structure representing: (a) square lattice, and (b) triangular lattice of
perfectly conducting cylinders.
The electromagnetic field in a 2D PBG structure can be decomposed into two
independent classes of modes: the transverse electric (TE) mode and the transverse
magnetic (TM) mode. We restrict the discussion to the TM modes, since the TM
modes are of the primary interest in accelerators. The dispersion properties of TE
modes were reported in [1]. All the field components in the TM modes can be
expressed through the axial component of the electric field, which we will further
denote by iff. Since the system is homogeneous along the z-axis, we take the Fourier
384
transform of iff in axial coordinate z and time t. The Helmholtz equation for
^(x_L,£ z ,fij) follows from Maxwell's equations
(i)
The boundary conditions on the surfaces S of the conducting rods are \//\s = 0 for
the TM mode. The discrete translational symmetry of the conductivity profile allows
us to write the fundamental solution of the Helmholtz equation in Bloch form
(2)
where x± = xex + yey is the transverse displacement, T is any of the lattice period
vectors of Tmn defined as
m bex + n be y
(square lattice),
2)
x
+
n b
2
t
y
(triangular lattice),
(3)
m,n are integers, k ± = kxex + A^e^ is an arbitrary transverse wave number.
Eqs. (1) and (2) together with the boundary conditions define the eigenvalue
problem of finding K2 as a function of k ± . The eigenvalue problem is solved
numerically with the PBGSS code [1], which employs the standard coordinate-space
finite-difference method.
12.0
16.0
8.0
4.0
0.0
x
M
FIGURE 2. Seven lowest normalized eigenfrequencies for TM mode. Here a I b = 0.2. The two cases
correspond to (a) square lattice and (b) triangular lattice.
The PBGSS code is designed to calculate the dispersion characteristics (Brillouin
diagrams) and, most importantly, the global photonic band gaps for TE and TM modes
in square and triangular lattices for different ratios alb. Figure 2 shows the Brillouin
diagrams for seven lowest TM modes for a I b = 0.2. In Fig. 3 the TM global band
385
gap boundaries for square and triangular lattices are plotted with solid lines as
functions of the ratio alb. The regions of frequencies to the right of solid curves
correspond to the global band gaps, whereas the frequencies to the left of the curves
lie in the pass band.
20.0
15.0
I10-0
5.0
(a)
.
0.0
0.1
0.2
a/b
0.3
0.4
0.5
FIGURE 3. Plots of global frequency band gaps for TM mode as functions of alb for (a) square lattice,
and (b) triangular lattice.
2D PEG RESONATOR DESIGN
By perturbing a single or several lattice cites in PEG structure we can create a PEG
resonator. For example, in a two-dimensional lattice of rods, the perturbation can be
created by removing a single rod or replacing it with another whose size or shape is
different from the original. The wave with the frequency inside the global band gap
cannot propagate into the bulk of PEG structure and thus under certain conditions the
mode can be confined in the vicinity of the defect.
We study the simplest model of 2D PEG resonator formed by a single rod missing
in a triangular lattice of metal rods. The rods are sandwiched between metal plates,
which are so closely spaced that kz = 0 for the range of frequencies of interest, and
only TM modes can exist in this structure. We had to restrict ourselves to considering
only a three rows of metal rods and surrounded them by the metal wall (see Fig. 4).
The HFSS eigenmode solver [2] was employed for modeling the PEG resonator.
PBG cavity
Metal wall
Metal rods
FIGURE 4. HFSS model of PBG resonator.
386
20.0
20.0
* TM01-like
TM01 - like
15.0
* TM1(| - like
15.0
wb/c
*vn TM
TM
TM
A
ow
*x
n
10.0
xw
n
5.0
5.0
0.0
0.0
0.0
0.0
n
10.0
n
- like
11
21 -like
- like
21
TM02-like
TM02 - like
TM12-like
TM - like
TM12
31 -like
TM31
- like
* *
* *
0.1
0.1
0.2
0.2
0.3
0.3
al
a/b
b
0.4
0.4
0.5
0.5
FIGURE
in triangular
triangular array
array of
of
FIGURE5.5. TM
TM eigenfrequencies
eigenfrequencies of
of PEG
PBG cavity
cavity formed
formed by
by single
single rod
rod missing
missing in
metal
metalrods.
rods.
The
for lattices
lattices with
with
Thefrequencies
frequencies of
of the
the PEG
PBG resonator
resonator eigenmodes
eigenmodes were
were calculated
calculated for
different
ratios
ofa/b.
The
results
are
presented
in
Fig.
5.
The
frequencies
of
the
defect
different ratios of a/b. The results are presented in Fig. 5. The frequencies of the defect
modes
The dashed
dashed lines
lines
modesare
areplotted
plottedover
overthe
theband
band gap
gap picture
picture from
from Fig.
Fig. 3(b)
3(b) with
with dots.
dots. The
ininFig.
5
show
the
eigenfrequencies
of
the
pillbox
cavity
with
the
radius
R=b-a,
which
Fig. 5 show the eigenfrequencies of the pillbox cavity with the radius R=b-a, which
isisabout
alb
aboutthe
theeffective
effectiveradius
radius of
of the
the PEG
PBG cavity.
cavity. One
One can
can see that for small ratios of a/b
<< 0.2
higher ratios
ratios of
of a/b
alb
0.2 only
only aa single
single mode
mode can
can be
be confined
confined below the cutoff. For higher
higher
higherorder
ordermodes
modescan
can also
alsobe
be confined
confined below
below the
the cutoff
cutoff and in the band gaps.
TM01
TM01
(a) a/b = 0.15
(b) alb
a/b = 0.30
(b)
TM11
TM11
11
FIGURE6.6. Modes
Modesof
ofthe
the PEG
PBG resonator
resonator for
for two
two different
different ratios
ratios of
of alb,
a/b.
FIGURE
Thefield
fieldpatterns
patterns of
of two
two modes
modes confined
confined in
in aa 2D
2D PEG
PBG resonator
The
resonator for
for two
two different
different
ratiosof
ofalb
a/b are
are shown
shown in
in Fig.
Fig. 6.
6. The
The field
field pattern
pattern of
of the
the mode
mode confined
ratios
confined below
below the
the
cutofffor
foralb
a/b ==0.15
0.15 closely
closely resembles
resembles those
those of
of the
the pillbox
pillbox cavity
cavity TMoi
TM01 mode.
mode. This
cutoff
This
allows us
us toto name
name itit TM
TM001
-like mode.
mode. Obviously,
Obviously, the
the metal
metal wall
wall of
of the
the cavity
allows
i-like
cavity can
can
confine
higher
order
modes,
which
are
not
confined
by
the
PBG
structure.
confine higher order modes, which are not confined by the PEG structure. One
One of
of
thesehigher
higherorder
ordermodes
modes with
with the
the field
field pattern
pattern resembling
resembling the
the TMn
TM11 mode
mode of
these
of aa pillbox
pillbox
cavityisisshown
shownin
inFig.
Fig. 6.
6. ItIt evolves
evolves into
into the
the TMn-like
TM11-like mode
mode of
of the
the PEG
PBG resonator
cavity
resonator as
as
387
the
the TM
and TMn
TM11 modes
modes
01 and
the ratio
ratio of
of a/b
alb isis increased.
increased. For
For the
the rods
rods with
with a/b
alb =
= 0.30,
0.30, the
TMoi
of
ofthe
thePBG
PEG resonator
resonator are
are shown
shown in
in Fig.
Fig. 6.
6.
The
the PEG
PBG structure
structure
The higher
higher order
order modes
modes confined
confined by
by the
the metal
metal wall
wall surrounding
surrounding the
can
be
suppressed
if
an
absorber
is
placed
at
the
periphery.
This
will
not
affect
the
can be suppressed if an absorber is placed at the periphery. This will not affect the
modes
confined
by
the
lattice.
Thus,
the
resonator
which
confines
selectively
a
single
modes confined by the lattice. Thus, the resonator which confines selectively a single
TM
basis of
of PEG
PBG structure
structure with
with alb
a/b =
=
01-like mode
TMoi-like
mode can
can be
be created,
created, for
for example,
example, on
on aa basis
0.15.
0.15.
COLD
COLD TEST
TEST OF
OF 2D
2D PBG
PBG RESONATORS
RESONATORS
In
we
In order
order to
to verify
verify experimentally
experimentally the
the higher
higher order
order mode
mode suppression,
suppression, we
constructed
two
PBG
resonators
for
cold
testing
(Fig.
7).
The
resonators
were
constructed two PBG resonators for cold testing (Fig. 7). The resonators were
fabricated
brass circular
circular plates.
plates. The
The
fabricated using
using the
the brass
brass cylinders
cylinders closed
closed at
at each
each end
end by
by the
the brass
PBG
structures
were
formed
by
copper
rods
fitted
into
the
array
of
holes
at
the
PBG structures were formed by copper rods fitted into the array of holes at the
endplates.
The
parameters
of
resonators
are
summarized
in
Table
1.
In
Cavity
1,
only
endplates. The parameters of resonators are summarized in Table 1. In Cavity 1, only
the
the Cavity
Cavity 22 PBG
PBG resonator
resonator
the TM
TM010i mode
mode was
was confined
confined by
by the
the PBG
PBG structure
structure and
and in
in the
the
TM
and
TM
modes
were
confined.
Cavities
1
and
2
are
designed
so
that the
the
01 and TMn
11 modes were confined. Cavities 1 and 2 are designed so that
the TMoi
frequencies
of
their
TM
modes
are
the
same.
WR62
waveguides
were
employed
to
frequencies of their TM010i modes are the same. WR62 waveguides were employed to
feed
rf
power
to
the
cavities,
and
the
same
size
waveguides
were
connected
feed rf power to the cavities, and the same size waveguides were connected
symmetrically
symmetricallyto
to the
the opposite
opposite ports.
ports.
FIGURE 7.
7. PBG
PBG resonators
resonators built for the cold test.
FIGURE
TABLE1.1. Parameters
Parametersof
ofPBG
PBGresonators
resonators for
for cold
cold test.
TABLE
Cavity 11
Cavity
0.16cm
Rodradius
radiusaa
Rod
0.16
cm
1.06cm
Latticespacing
spacingbb
Lattice
1.06
cm
alb
0.15
a/b
0.15
Cavityradius
radius
3.81 сm
cm
Cavity
3.81
Axiallength
length
0.787 сm
cm
Axial
0.787
11. 00 GHz
GHz
Freq.(TM
(TMoi)
Freq.
11.00
01)
Freq.(TM
(TM11n))
15.28 GHz
GHz
Freq.
15.28
388
Cavity 2
0.40 cm
1.35cm
1.35
cm
0.30
4.83 cm
сm
0.787 cm
сm
11. 00 GHz
11.00
17.34 GHz
17.34
GHz
0.10
0.08
0.04
0.04
0.02
0.02
0.01
|
)
0.00
000
ii..
1;
10 11 12 13 14 15 16 17 18
10 11 12 13 14 15 16 17
freq., GHz
(a)
freq., GHz
(b)
u.uo
o.os :
0.04
.
0.02
.
10
0.04
fi
0.06.
1
11
12
13
14
freq., GHz
f\
15
16
CO
0.01
n nn
17
i jy
I
0.02
10 11 12 13 14 15 16 17 16
freq., GHz
(c)
(d)
FIGURE 8. 812 curves for PEG resonators: (a) a/b=OJ5, no absorber; (b) a/b=0.30, no absorber; (c)
a/b=0,15, with absorber; (d) a/b=0,30, with absorber.
We measured the 812 elements of the scattering matrix using the HP8510 vector
network analyzer. In a first set of measurements we did not place the absorber at the
metal walls of the cavities and thus the eigenmodes of the PEG resonator as well as
the eigenmodes of the metal wall resonator can be seen in Fig. 8 (a) and (b). Then we
placed the eccosorb at the periphery of the cavities, which reduced by a factor of 10
the Q-factors of the modes not confined by the PEG structure as well as increased the
frequencies of these modes (Fig. 8 (c) and (d)). Only the TMoi mode at 11 GHz
survived in Cavity 1, and the TM0i mode at 11 GHz and the TMn mode at 17 GHz
survived in Cavity 2. These results agree with the cavities design. We also measured
the Sn elements of the scattering matrices and derived from those that the ohmic Qfactors for the TM0i modes in both cavities were about 2000.
271/3 PBG ACCELERATING STRUCTURE DESIGN
The PBG cavity supporting a single TM0i-like mode is a good candidate for an
accelerator cell. In a traditional accelerator cell in addition to the accelerating mode
there exist many unwanted HOM, which can be excited by the beam. The advantage
of the PBG accelerating cavity lies in the efficient suppression of the higherfrequency, HOM wakefields. We propose to build a disk-loaded 2;i/3 accelerator
structure with a stack of PBG cavities set between the disks with the beam holes
inserted on axis. Figure 9 depicts the 3-cells of the 2;i/3 structure. The irises in the
structure are similar to those in a conventional disk-loaded linear accelerator. The iris
dimensions are scaled to 17 GHz from the SLAC 2.856 GHz accelerator design [7].
The axial period L of the PBG structure is chosen so that the electron moving with the
speed of light c is at resonance with the 27i/3mode: 27ri3=ct)Llc.
389
Rod
Rod
Beam
Beam hole
hole
OOuterwall
uter wall
Iris
Front view
view
Front
L
Side
Side view
FIGURE9.9. The
Thetransverse
transverse and
and axial
axial cross-sections
cross-sections of the 2n/3
FIGURE
2π/3 PEG
PBG accelerating
acceleratingstructure.
structure.
TheHFSS
HFSS eigenmode
eigenmode solver
solver [2]
[2] was
was employed
employed to determine the
The
the properties
properties of
of the
the
PEG
accelerator
structure
with
beam
holes.
The
model
included
three
cells
from
PBG accelerator structure with beam
included three cells from the
the
Fig.9.9.The
Theideal
ideal metal
metal EE-wall
boundary conditions were specified
Fig.
wall boundary
specified at
at both
both end
end plates
plates
of
the
structure.
Table
2
summarizes
the
results
of
the
HFSS
simulation.
of the structure. Table 2 summarizes the results of the HFSS simulation. For
For
comparison, the
the accelerating
accelerating characteristics
characteristics of
of aa conventional
disk-loaded
comparison,
conventional 2^/5
2π/3 disk-loaded
acceleratingstructure
structureare
are also
also shown
shown in
in Table
Table 2.
2.
accelerating
TABLE2.2. PBG
PEGstructure
structureversus
versus pillbox
pillbox structure:
structure; comparison
comparison of
TABLE
of accelerator
accelerator characteristics.
characteristics.
Pillbox
PEG
PBG
Pillbox
———
Rodradius,
radius,aa
1.05mm
Rod
1.05
mm
------_______
Lattice
vector,
b
7.02mm
Lattice vector, b
7.02 mm
------_______
a/b
0.15
a/b
0.15
------Cavity radius
23.34mm
6.88mm
Cavity radius
23.34
mm
6.88 mm
Cavity length
5.83mm
Cavity length
5.83 mm
Iris radius
1.94mm
Iris radius
1.94 mm
Frequency
17.14
GHz
Frequency
17.14 GHz
3588
5618
Q
3588
5618
Qww
0.38 MW/cm
0.71 MW/cm
r
s
0.38
MW/cm
0.71
MW/cm
rs
0.13kW/cm
O.llkW/cm
[rJQ]
0.11
kW/cm
0.13
kW/cm
[r
/Q]
Groups velocity
0.012c
0.012c
Group velocity
0.012c
0.012c
Gradient
17A/P [MW] MeV/m
19A/P[MW] MeV/m
Gradient
17√P [MW] MeV/m
19√P[MW] MeV/m
It can be seen from the table, that due to the field enhancement at the rods the QIt can be seen from the table, that due to the field enhancement at the rods the Qfactor of the PEG structure is one and a half times less than the Q-factor of the pillbox
factor of the PBG structure is one and a half times less than the Q-factor of the pillbox
structure. Therefore the shunt impedance is also smaller. Nevertheless the [rlQ] ratio
structure.
Therefore
shunt
is also
smaller.
Nevertheless
the to[r/Q]
ratio
and the gradient
are the
almost
theimpedance
same for both
types
of cavities.
This is due
the fact,
and
the
gradient
are
almost
the
same
for
both
types
of
cavities.
This
is
due
to
the
fact,
that the electric field distribution is almost the same for both PEG and pillbox
that
the
electric
field
distribution
is
almost
the
same
for
both
PBG
and
pillbox
structures and so, the dispersion characteristics (see Fig. 10) and the accelerator
structures
theare
dispersion
characteristics (see Fig. 10) and the accelerator
properties and
of theso,cells
very similar.
properties
of
the
cells
are
very
similar.
Further research is underway at MIT in order to construct and test a PEG
Further research
accelerating
structure.is underway at MIT in order to construct and test a PBG
accelerating structure.
390
17.1
17.0
16.9
16.8
30
60
90
120
150
180
6, degrees
FIGURE 10. The dispersion curves of PEG and pillbox accelerating structures. Straight line
corresponds to CD = 9c IL,
FREQUENCY SELECTIVE RESONATORS BASED ON
DIELECTRIC PBG STRUCTURES
In recent years, dielectric structures have proved to be useful for accelerator
applications [8]. They have shunt impedances comparable to conventional copper
accelerator structures and are easy to construct. The major difference between the
band gap schemes in dielectric PBG structures and in metal PBG structures is the
absence of the cut-off for the TM modes in dielectric. Under certain conditions this
may allow us to exclude the lower-order modes in dielectric PBG resonators, while
confining the higher order operating mode. Creation of such a resonator will overcome
the problem of the mode competition in overmoded structures and thus will allow the
extension of the operating frequency of microwave devices to higher frequencies.
v TM21-like
* TM02-like
0
v
o
°
0.0
0.1
0.2
0.3
0.4
TM31-like
TM12-like
TM32-like
TM13-like
0.5
FIGURE 11. TM eigenfrequencies of PBG cavity formed by 19 rods missing in triangular array of
A12O3 rods.
391
We
the dielectric
dielectric PBG
PEG resonator
resonator formed
formed by
by aa defect
defect in
in aa triangular
triangular
We investigated
investigated the
array
of
A1
O
rods,
8
(A1
O
)
=
9.7.
The
band
gap
scheme
for
the
triangular
arrayofof
2
3
2
3
array of Al2O3 rods, ε (Al2O3) = 9.7. The band gap scheme for the triangular array
aluminum
rods were
were calculated
calculated by
by the
the authors
authors of
of [9].
[9]. For
For our
our PBG
PEG resonator
resonator
aluminum ceramics
ceramics rods
we
with a/b
a/b == 0.39
0.39 and
and create
create the
the defect
defect in
in the
the PBG
PEG structure
structure by
by
we choose
choose the
the rods
rods with
removing
rod and
and two
two rows
rows of
of rods
rods around
around itit (19
(19 rods
rods total).
total). The
The
removing the
the central
central rod
eigenfrequencies
of the
the resonator
resonator were
were calculated
calculated by
by HFSS
HFSS [2]
[2] and
and are
are shown
shown ininFig.
Fig.
eigenfrequencies of
11.
The
TM
2-like
mode
is
confined
in
the
PEG
resonator
(see
Fig.
12),
while
11. The TM002-like mode is confined in the PBG resonator (see Fig. 12), while thethe
TM
TMn
modes are missing.
TM001i and
and TM
11 modes are missing.
The
PEG
accelerating
cell can
can be
be constructed
constructed on
on the
the basis
basis of
of aa dielectric
dielectric resonator
resonator
The PBG accelerating cell
confining
the
TMo2
mode.
Since
the
TMoi
and
TMn
modes
are
absent,
the
accelerator
confining the TM02 mode. Since the TM01 and TM11 modes are absent, the accelerator
cell
of lower
lower order
order wakefields.
wakefields. Additionally,
Additionally, the
the HOM
HOM wakefields
wakefields
cell will
will be
be free
free of
spectrum
will
be
rare.
The
acceleration
parameters
of
the
PEG
resonator
confining
the
spectrum will be rare. The acceleration parameters of the PBG resonator confining the
TM
2 mode
17 GHz
GHz are
are summarized
summarized in
in Table
Table 3.
3.
TM002
mode at
at 17
FIGURE 12. Field
Field pattern
pattern of
of the
the TM
TM0202-like
-like mode
mode inindielectric
dielectricPBG
PEGresonator.
resonator.
TABLE 3. Acceleration parameters of dielectric
dielectric PBG
PEG resonator
resonator with
withTM
TM0202-like
-likemode.
mode.
Permittivity, ee
tan δ8
Lattice spacing b
Rod radius a
a/b
alb
Freq. (TM
Freq.
(TM02
02))
Q
Qww
rrss
[r
[rJQ]
s/Q]
9.7(Al
(A1
9.7
2033))
2O
-4
5-10-4
5·10
0.44сm
cm
0.44
0.17cm
0.17
cm
0.39
0.39
17.14
17.14GHz
GHz
4700
4700
11MW/cm
MW/cm
212
W/cm
212W/cm
CONCLUSION
CONCLUSION
The main
main advantage
The
advantage of
of PBG
PEG cavities
cavities over
over the
the conventional
conventional pillbox
pillbox cavities
cavities lies
lies inin
their high
high mode
mode selectivity.
their
selectivity. Thus,
Thus, if
if applied
applied to
to the
the linear
linear accelerators
accelerators the
the PBG
PEG cavities
cavities
will sufficiently
sufficiently reduce
reduce the
will
the wakefields.
wakefields.
The
PBG
accelerator
The PEG accelerator design
design must
must start
start from
from studying
studying the
the bulk
bulk properties
properties of
of the
the
PBG
structures
and
then
the
PBG
resonators
must
be
investigated.
The
PEG structures and then the PEG resonators must be investigated. The wave
wave
392
propagation in bulk PEG structures was studied with the PBGSS code [1], Brillouin
diagrams and global band gaps were calculated for square and triangular metal lattices.
PEG resonators formed by a single rod missing in a triangular array were studied
using HFSS [2]. Two PEG resonators were constructed and cold tested. We showed
that for sufficiently small ratio of the rod's radius, a, to the distance between the rods,
b, the PEG cavity selectively confines a TM0i-like mode.
Dielectric PEG structures may allow extension of accelerator frequencies to higher
frequencies using HOM without facing the problem of lower order wakefields. Use of
dielectric PEG structures may allow construction of a PEG resonator, which
selectively confines the TMo2-like mode. Dielectric PEG resonators were studied with
HFSS.
Further research is underway at MIT in order to construct and test a 2;i/3 PEG
accelerating structure.
ACKNOWLEDGMENTS
The work was supported by the DOE grant. Authors thank Steve Korbly, Ivan
Mastovsky and Jagadishwar Sirigiri for help in the lab and discussions.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
Smirnova, E.I., Chen, C., Shapiro, M.A., Sirigiri, J. R., and Temkin, R.J., /. Appl. Phys. 91(3), 960-968 (2002).
Ansoft High Frequency Structure Simulator - User's Manual, Ansoft Corp, 1999.
Yablonovitch, E., Phys. Rev. Lett. 58, 2059 (1987).
Joannopoulos, J. D., Meade, R. D., and Winn, J. N., Photonic Crystals: Molding the Flow of Light, Princeton:
Princeton Univ. Press, 1995.
Smith, D.R., Schultz, S., Kroll, N., Sigalas, M., Ho, K. M., and Souloulis, C. M., Appl. Phys. Lett. 65, 645
(1994).
Shapiro, M.A., Brown, W.J., Mastovsky, I., Sirigiri, J.R., and Temkin, R.J., Phys. Rev. Special Topics:
Accelerators and Beams 4, 042001 (2001).
Wilson, P.B., "Application of High-Power Microwave Sources to TeV Linear Colliders" in Applications of
High Power Microwaves, edited by A.V. Gaponov-Grekhov and V.L. Granatstein, London: Artech House,
1994, pp. 229-318.
Gold, S.H., Gai, W., "High Power Testing of 11.424 GHz Dielectric-Loaded Accelerating Structures" in
Proceedings of the 2001 Particle Accelerator Conference, edited by P. Lucas and S. Webber, Chicago, 2001,
pp. 3984-3987.
Johnson, S. J. and Joannopoulos, J. D., Optics Express 8( 3), 173-190 (2001).