A Tunable Dielectric Wakefield
Accelerating Structure
A. Kanareykin, W. Gai*, J. Power*, E. Sheinman**, A. Altmark**
Euclid Concepts LLC, 5900 Harper Rd, Solon, OH 44139, USA
*High Energy Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA
**St. Petersburg Electrical Engineering University, 5 Prof. Popov St., St. Petersburg, 197376, Russia
Abstract. We present a method to vary the resonant frequency of a dielectric loaded structure
(driven either by the wakefield of a beam or an external rf source). It consists of a thin layer of a
ferroelectric material backing a layer of conventional ceramic. A DC bias voltage is used to vary
the permittivity of the ferroelectric layer and thus tune the overall frequency of the accelerating
structure. In this paper, a detailed model is given for this device and an experimental test is
proposed. Employing this scheme would compensate for frequency shifts in the accelerating
structure caused by ceramic waveguide machining tolerances and dielectric constant heterogeneity.
We have identified a suitable material for this application: a BST ferroelectric-oxides compound
with a dielectric constant of 300-500. A tuning range of (2-4)% could be achieved for a (11-13)
GHz dielectric accelerating structure.
INTRODUCTION
The field of advanced accelerators is in search of novel revolutionary
technologies to allow progress in particle accelerators for high energy physics
experiments. Techniques based on the Dielectric Wakefield Accelerator (DWFA)
concept are some of the most promising to date in terms of their potential to provide
high gradient accelerating structures for future generation linear colliders [1,2]. These
structures may be excited by a high current electron beam or an external high
frequency high power RF source and have been under intensive study in recent years
[1-6]. The basic RF structure
FIGURE 1. A Ceramic Waveguide driven by a Bunch-train (two bunches, separated by A,rf, shown).
is very simple— a cylindrical, dielectric loaded waveguide with an axial vacuum
channel is inserted into a conductive sleeve (Fig. 1). A high charge, (typically 20-40
nC), short, (1-4 mm) electron drive beam generates TMoi mode electromagnetic
Cherenkov radiation (wakefields) while propagating down the vacuum channel.
Following at a delay adjusted to catch the accelerating phase of the wakefield is a
second electron witness beam. The witness beam is accelerated to high energy by the
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
565
wakefield produced by the drive beam. [1-6] A series of proof of principle
experiments have been successfully performed at Argonne's Advanced Accelerator
Test Facility [1].
There has been tremendous progress in ceramic structure-based acceleration
research in the past few years [1-6]. One of the most critical issues for the Dielectric
Wakefield Acceleration is the improvement of the transformer ratio available in this
class of device [5,6,11]. The transformer ratio is a parameter that characterizes the
efficiency of the accelerator and it is defined as R = (Maximum energy gain behind
the drive bunch)/(Maximum energy loss inside the drive bunch).
The dielectric wakefield acceleration technique was originally developed
using drive and witness beams passing through the same dielectric device along the
same trajectory but at different phases, where the drive beam is a single symmetric
electron bunch. This class of collinear wakefield devices can achieve very high peak
accelerating fields but are intrinsically limited as to the total energy gain for each
structure. According to the wakefield theorem [8,9], the accelerated beam in these
cases cannot gain more than twice the energy of the drive beam, or in other words, R
is less than 2.
Several schemes have been proposed to obtain R > 2 in collinear wakefield
accelerators. One proposed scheme [9] is to send a single drive bunch with an
asymmetric axial current distribution through a collinear wakefield device.
Simulations show that R can be much greater than 2 for the triangular (ramped) bunch
distribution shown Fig. 2a. Using a similar idea, a second scheme tailors the profile of
a train of individually symmetric drive bunches [10] into a triangular ramp (dotted
line in Fig. 2b) to produce R > 2. In this latter scheme, the individual bunches in the
train are symmetric (e.g. gaussian) separated by a distance d.
zW
V \
(a)
(b)
FIGURE 2. Two schemes that have been proposed to generate R = W^/W » 2. The height of the
shaded area, p(z), represents the total amount of charge in the bunch at location z while the solid, sinelike, line is the amplitude of the wakefield driven by the beam, (a) A single drive bunch with a
triangular axial current distribution moving to the left, (b) A train of gaussian drive bunches with an
overall triangular pattern of the train (see dotted line) moving to the left.
The charge in each bunch is then adjusted such that the first bunch in the train
has the lowest charge and the last bunch the highest with an overall triangular
envelope. The difficulty with the scheme 1) that proposes to use asymmetric axial
current distribution to achieve R > 2, arises from the lack of suitable techniques to
tailor the axial distribution of the single drive beam. In this paper we consider the
latter, here termed the ramped bunch train (RBT) method of transformer ratio
enhancement. Since the AWA facility has already generated a 'flat' bunch train we
plan to develop hardware to generate the RBT, construct a suitable dielectric
structure, and demonstrate dielectric wakefield acceleration with R « 7 — 8. In this
566
paper we show how the waveguide machining tolerances and dielectric constant
paper we show
howthe
thefrequency
waveguidespectrum
machiningof tolerances
and dielectric
heterogeneity
affect
the dielectric
structure constant
for the
heterogeneity
affect
the
frequency
spectrum
of
the
dielectric
for the
transformer ratio enhancement experiment. We propose to use a structure
tunable dielectric
transformer
ratio enhancement
experiment.
Wecaused
propose
a tunable
dielectric
structure
to compensate
for the frequency
shift
by to
theuse
structure
imperfection.
structure
to
compensate
for
the
frequency
shift
caused
by
the
structure
imperfection.
Finally, we describe the tunable waveguide design, show numerical simulations of
Finally, we describe the tunable waveguide design, show numerical simulations of
the wakefields, present the (10-13) GHz structures parameters and discuss future
the wakefields, present the (10-13) GHz structures parameters and discuss future
experiments.
experiments.
WHY TUNABLE STRUCTURES?
WHY TUNABLE STRUCTURES?
WAVEGUIDE
TRAIN
WAVEGUIDE TOLERANCES
TOLERANCES AND
AND BUNCH
BUNCH TRAIN
PARAMETERS
PARAMETERS
In this section we present the parameters of the bunch train for the transformer
In this section we present the parameters of the bunch train for the transformer
ratio enhancement experiment. We have calculated the longitudinal wakefield in a
ratio enhancement experiment. We have calculated the longitudinal wakefield in a
dielectric
in the
the single
single bunch
bunch
dielectric structure
structure excited
excited by
by an
an axial
axial current
current distribution
distribution in
approximation
[11].
The
simulations
show
that
there
is
a
tradeoff
between
R
and
the
approximation [11]. The simulations show that there is a tradeoff between R and the
accelerating
gradient.
Maximum
gradient
is
obtained
by
driving
the
collinear
accelerating gradient. Maximum gradient is obtained by driving the collinear
accelerator
transformer ratio
ratio is
is obtained
obtained
accelerator with
with aa very
very short
short bunch
bunch while
while the
the maximum
maximum transformer
when
4 where
is the
point of
of
whenσ=λ/
<j=k/4
where σeris
the rms
rms length
length of
of the
the individual
individual bunches.
bunches. The
The optimal
optimal point
operation
is
arguably
near
λ
/20,
but
since
for
the
purposes
of
this
experiment
we
are
operation is arguably near 720, but since for the purposes of this experiment we are
interested
in
maximizing
the
transformer
ratio,
we
choose
interested
in
maximizing
the
transformer
ratio,
we
choose
σ<j near
λ/4
(
σ
/
λ
=
0.1−0.3),
so
that
R
is
maximized
and
the
accelerating
gradient
is
near>t /(rf >V=0.1-0.3), so that R is maximized and the accelerating gradient is
still
large.
still large.
Multibunch Wakefield
N=4
=ff
FIGURE
electron bunches
bunches of
of bunch
bunch
FIGURE3.3.The
Theresultant
resultant wakefield
wakefield produced
produced in
in aa DWFA
DWFA by
by aa train
train of
of 44 electron
length
Q33 =
= 63,41nC.
63.41nC.
length1.5
1.5mm
mmand
andcharge
chargeintensities
intensities QQ00 ==10nC,
lOnC, QQj1 == 26.47nC,
26,47nC, Q
Q22 =
= 45.65nC,
45,65nC, and
and Q
The
bunches on
on the
the same
same linac
linac rfrf
TheTransformer
Transformer Ratio
Ratio RR ==7.6.
7.6. For
For clarity
clarity we
we have
have shown
shown the
the electron
electron bunches
cycle;
23 cm
cm (=
(= ^imacrf
λlinac rf )•
).
cycle;ininthe
theactual
actualexperiment
experiment each
each would
would be
be separated
separated by
by an
an additional
additional 23
For
new algorithm
algorithm that
that
For the
the multimode
multimode approximation
approximation we
we have
have invented
invented aa new
allows
the distances
distances between
between bunches.
bunches.
allowsus
us to
to optimize
optimize the
the required
required bunch
bunch charges
charges and
and the
The
based on
on equalizing
equalizing the
the energy
energy loss
loss of
of
The basic
basic physics
physics idea
idea for
for the
the simulation
simulation is
is based
each
eachdrive
drivebunch
bunch in
inthe
the RBT
RBT [11].
[11].
The
drove the
the
The available
available bunch
bunch length
length and
and finite
finite group
group velocity
velocity considerations
considerations drove
choice
at the
the AWA
AWA facility.
facility. The
The
choice of
of structure
structure parameters
parameters for
for the
the DWFA
DWFA experiment
experiment at
upgradedAWA
AWA facility
facility will
will be
be able
able to produce a 40 nC beam with rms
upgraded
rms bunch
bunch length
length
567
of
and
of 1-2
1-2 mm,
mm, with
with aa linac
linac rfrf frequency
frequency of
of 1.3
1.3 GHz.
GHz. Based
Based on
on the
the RBT
RBT algorithm
algorithm and
using
we require
require aa dielectric
dielectric structure
structure with
with
using the
the conservative
conservative number
number of
of 44 mm
mm for
for aσ we
mm
and
f
=13.625
GHz.
λAo
0 == 22.01
TM01
22.01 mm and fTMoi=13.625 GHz.
Using
we construct
bunch train
train according
according to
to the
the
Using the
the above
above DWFA
DWFA structure,
structure, we
construct aa bunch
algorithm
described
above
[11].
The
resultant
wakefield
excited
by
this
RBT
algorithm described above [11]. The resultant wakefield excited by this RBT isis
shown
the train
train of
of 44 bunches
bunches excites
excites the
the
shown in
in Fig.
Fig. 3.
3. A
A close
close examination
examination shows
shows that
that the
peak
accelerating
gradient
of
40
MeV/m
and
an
overall
transformer
ratio
for
this
peak accelerating gradient of 40 MeV/m and an overall transformer ratio for this
experiment
experiment of
of 7.602.
7.602.
13.4
13.5
13.6
a.
a.
13.7
13.8
13.9
f,GHz
13.4
13.5
13.6
13.7
13.8
13.9
f.GHz
b.
b.
FIGURE
by waveguide
waveguide tolerances
tolerances and
and dielectric
dielectric
FIGURE4.4.Transformer
Transformer ratio
ratio vs.
vs. frequency
frequency shift
shift caused
caused by
heterogeneity
d: a)
a) dd =
= 23.3
23.3 cm
cm b)
b) d=23.1cm.
d=23.1cm.
heterogeneity for
for nominal
nominal bunch
bunch separation
separation d:
In
the optimization
optimization of
of the
the distance
distance
In this
this section
section we
we give
give an
an example
example of
of the
variation
the maximum
maximum transformer
transformer ratio
ratio
variation between
between the
the bunches
bunches in
in the
the RBT
RBT to
to ensure
ensure the
taking
heterogeneity and
and the
the tolerance
tolerance of
of the
the
taking into
into account
account the
the dielectric
dielectric constant
constant heterogeneity
dielectric
potentially contribute
contribute to
to frequency
frequency
dielectric inner
inner surface
surface finish,
finish, both
both of
of which
which could
could potentially
deviations
distances between
between bunches
bunches in
in aa
deviations in
in the
the structure.
structure. Optimization
Optimization of
of the
the distances
collinear dielectric
dielectric wake
wake field
field accelerator
accelerator is a key issue for the
collinear
the transformer
transformer ratio
ratio
enhancement experiment.
experiment. We
We present here numerical simulations
simulations for
enhancement
for aa 13.625
13.625 GHz
GHz
structure with
with dielectric
dielectric constant
constant of 9.4. We have calculated the
structure
the interbunch
interbunch
separations ddi,
and transformer
transformer ratio R for a bandwidth of
of [f-Af,
[f-∆f, f+Af]
f+∆f] where
where ff
separations
1, dd2,
2, dds
3 and
13.625 GHz.
GHz. The
The maximum
maximum frequency
frequency excursion Af
== 13.625
∆f is determined
determined by
by the
the
waveguide radius
radius tolerances
tolerances ∆R
AR and maximum dielectric constant
waveguide
constant variation
variation As:
∆ε:
± ∆R,
AR, R
Ro
AR, εsi=9.4
RRinner=0.5cm
=0.678cm ± ∆R,
∆ε, AR=20jLim
∆R=20µm and
and As=0.1.
∆ε=0.1. The
The
uter=0.678cm
inner=0.5cm ±
outer
1=9.4 ± As,
bunch length
length isis σ=0.4
a=0.4 cm,
cm, and
and the
the bunch charges have been chosen
bunch
chosen as
as Q2=3Qi,
Q2=3Q1,
Q44=7Q
=7Qi.
QQs=5Qi,
3=5Q1, Q
1.
The numerical
numerical calculations
calculations show
show that the maximum base frequency
The
frequency shift
shift isis Af
∆f
=
0.313
GHz.
The
nominal
bunch
separation
d
=
A,
ii
rf
+
A,
wakefield
/2
=
23.1
cm.
λ wakefield /2 = 23.1 cm.
= 0.313 GHz. The nominal bunch separation
λ linac
nac rf
We have
have calculated
calculated the
the spacing
spacing which
which optimizes
optimizes the maximal transformer
We
transformer ratio
ratio for
for aa
range
of
frequencies,
for
d=23.1cm
and
d=23.3cm.
Fig.
4.a
shows
the
transformer
range of frequencies, for d=23.1cm
4.a shows the transformer
ratio RR as
as aa function
function of
of the
the frequency
frequency for
for d=23.1cm
d=23.1cm and
ratio
and d=23.3cm.
d=23.3cm. RR isis flat
flat in
in the
the
range
[13.324—13.594]
GHz
for
d=23.1cm,
Fig.
4b.
range [13.32413.594] GHz for d=23.1cm, Fig. 4b.
This isis encouraging
encouraging insofar
insofar as
as the
the dielectric
dielectric constant
constant heterogeneity
This
heterogeneity and
and surface
surface
tolerance
do
not
impact
seriously
on
the
maximum
transformer
ratio,
and
tolerance do not impact seriously on the maximum transformer ratio, and ff in
in the
the
[13.5—13.7]
GHz
range
still
gives
R
in
the
range
of
(6.8-7.0).
Fig.4a
corresponds
[13.513.7] GHz range still gives R in the range of (6.8-7.0). Fig.4a corresponds to
to dd
23.3cm
cm (λ
(A,wakefield
= 13.5
13.5 GHz).
GHz). In
In this
this case
case the
wakefieid =
==23.3
the frequency
frequency shift
shift does
does not
not allow
allow high
high
568
R as result of the dielectric structure imperfection. R(f) is not flat for f>13.625 GHz,
and for high frequencies the transformer ratio is decreasing rapidly.
TUNABLE ACCELERATING STRUCTURE: BASIC CONCEPTS:
HOW TO VARY THE PERMITTIVITY.
A tunable structure is a possible solution for the adjustment of the frequency
shift caused by the ceramic waveguide tolerances and beam position dispersion,
provided one can find an appropriate way to control and vary the basic frequency of
the ceramic waveguide. The dielectric accelerating structure, unlike the conventional
one, admits a unique possibility for implementing a tunable device by using a
nonlinear material as part of the dielectric loading of the guiding structure. The basic
frequency of the conventional metal accelerating structure is defined just by the
waveguide or the cavity geometry. Dielectric structures have another important
parameter that determines the frequency spectrum; the dielectric constant of the
loading material. There are 2 basic group of materials that can be tunable, in other
words, that can be controlled by external fields applied, ferrites and ferroelectrics,
controlled by magnetic fields and by DC electric fields, respectively. Ferrite material
does not appear to be an appropriate solution because of its extremely high loss factor
and magnetic field required in presence of the high charged electron beam. In this
paper we propose a new scheme that will allow control of the dielectric constant (and
consequently the frequency spectrum) for the dielectric waveguides by incorporating
ferroelectric layers [12]. The use of ferroelectrics would be a most evident solution
for tunability purposes, but ferroelectric materials' high dielectric losses make them a
poor bulk material for the high (more than 10 GHz) frequency range. The typical loss
factor for BxSri_xTiO3 (BST) ferroelectric, commonly used at room temperature, is (13)*10~2 for the 10 GHz frequency range [13,14], while the corresponding parameter
for a good linear microwave ceramic is (5-0.5)* 10"4 [7]. We propose to use a
combination of ferroelectric and ceramic layers to permit tunability for the composite
ceramic-ferroelectric waveguide while keeping the effective material loss factor = (45)*10"4. It will be shown that loss factor mentioned above corresponds to the average
dielectric loss of any kind of dielectric accelerators that have been experimentally
tested recently [6,11,12]. These devices most commonly consist of a single dielectric
cylinder inserted into a conductive copper jacket. The permittivity Si of the ceramic
material is determined by the type of the structure, typically in the range of 4 - 36 [7].
The main idea of the proposed device is a substitution of loading by a single
ceramic by a composite of 2 layers as shown in Fig. 5. The inner layer is ceramic and
is covered by an outer film made of BST ferroelectric placed between the ceramic
layer and the copper sleeve.
569
metal
metal
ferroelectric
ferroelectric
dielectric
vacuum
metal
metal
ferroelectric
ferroelectric
dielectric
beam
vacuum
FIGURE 5.
5. Basic
Basic designs
FIGURE
designs of
of tunable
tunable dielectric
dielectric accelerating
acceleratingstructures.
structures.
a), cylindrical
cylindrical geometry,
a).
geometry, outer
outer layer
layer is
is ferroelectric,
ferroelectric,inner
innerlayer
layerisis ceramic.
ceramic.
The thickness
thickness of
of the
the ferroelectric
The
ferroelectric layer
layer is
is 1/10
1/10 of
of the
theceramic
ceramicone.
one.b)b)Planar
Planargeometry.
geometry.
The waveguide
waveguide tuning
of the
the
The
tuning can
can be
be carried
carried out
out by
by varying
varyingthe
thepermittivity
permittivity82
ε2 of
ferroelectric
film
by
applying
an
external
DC
electric
field
across
the
ferroelectric.
ferroelectric film by applying an external DC electric field across the ferroelectric.
This allows
allows us
us to
to adjust
adjust slightly
slightly the
This
the effective
effective dielectric
dielectric constant
constant of
of the
thewhole
wholesystem
system
and
therefore
we
obtain
fast
and
programmable
control
of
the
structure
tuning
and therefore we obtain fast and programmable control of the structure tuningduring
during
operation. The
The basic
basic design
design of
operation.
of both
both planar
planar and
and cylindrical
cylindrical geometries
geometries are
are shown
showninin
Fig.5. The
The relative
relative depths
depths of
of the
Fig.5.
the layers
layers in
in this
this figure
figure are
are not
not to
to scale;
scale; the
the ferroelectric
ferroelectric
layer
is
actually
10
times
thinner
than
the
ceramic
layer.
The
typical
thickness
layer is actually 10 times thinner than the ceramic layer. The typical thicknessisis(2-3)
(2-3)
mm
for
the
ceramic
layer
and
(200-300)
jum
for
ferroelectric
film.
It
should
mm for the ceramic layer and (200-300) µm for ferroelectric film. It shouldbebe
mentioned that
that this
this geometrical
geometrical factor
mentioned
factor of
of 10
10 plays
plays an
an important
important role
role for
forthis
thisstructure
structure
design.
The
dielectric
constant
of
the
BST
ferroelectric
is
typically
within
design. The dielectric constant of the BST ferroelectric is typically within1000-2000,
1000-2000,
and we plan to reduce this by using a composition of BST and oxides to (300-500) to
and we plan to reduce this by using a composition of BST and oxides to (300-500) to
avoid any extra magnetic loss at the conducting walls. A DC field can vary this
avoid any extra magnetic loss at the conducting walls. A DC field can vary this
dielectric constant in the range of (20-30)% or about 100 units. Thus the primary
dielectric constant in the range of (20-30)% or about 100 units. Thus the primary
ceramic layer with the dielectric constant of (4-20) and (2-3) mm in thickness will be
ceramic layer with the dielectric constant of (4-20) and (2-3) mm in thickness will be
still tuned by the comparatively thin (200-300) jum ferroelectric layer. The loss factor
still tuned by the comparatively thin (200-300) µm ferroelectric layer. The loss factor
of the whole accelerating structure will be about the same as the ceramic due to the
of the whole accelerating structure will be about the same as the ceramic due to the
geometric factor, since the volume of high loss ferroelectric material is much less
geometric factor, since the volume of high loss ferroelectric material is much less
than the basic ceramic loading.
than the basic ceramic loading.
The design shown in Fig.5 is not the only one possible; the positions of the
The be
design
shownand
in Fig.5
is not the only
positions
the
layers can
swapped,
the ferroelectric
film one
willpossible;
form thethe
inner
layer. ofThe
layers can be swapped, and the ferroelectric film will form the inner layer. The
570
advantages of this design would be the reduction of the magnetic loss in the
advantages copper
of this walls.
designAtwould
be thetime,
reduction
of the material
magnetic surface
loss in will
the
conducting
the same
ferroelectric
conductinghigh
copper
walls.
the and
same
time, ferroelectric
experience
gradient
RFAt
fields
scattered
electrons, andmaterial
heating surface
and the will
DC
experience
high gradient
RF fields and
electrons,
and heating
and thelayer
DC
bias
field supply
are problematic.
Thescattered
design with
the inner
ferroelectric
bias
field
supply
are
problematic.
The
design
with
the
inner
ferroelectric
layer
position described above would be really fortunate for studies of nonlinear effects
position
above
would
be really
fortunate forfilm
studies
of nonlinear
effects
since
bothdescribed
RF and DC
fields
influence
the ferroelectric
with gradients
exceeding
since
both
RF
and
DC
fields
influence
the
ferroelectric
film
with
gradients
exceeding
10MV/m.
lOMV/m.
FERROELECTRIC TUNING: MICROSTRIP CONFIGURATION
FERROELECTRIC TUNING: MICROSTRIP CONFIGURATION
Fig.5 shows the dielectric accelerating structure with ferroelectric layer tuned
Fig.5 shows
theDC
dielectric
accelerating
structure
ferroelectric
layer tuned
by an external
electric
field. One
has to supply
this with
DC field
to the ferroelectric
by
an
external
electric
DC
field.
One
has
to
supply
this
DC
field
to
the
ferroelectric
film placed between the ceramic layer and the copper cylinder. Here we will use the
film placed between the ceramic layer and the copper cylinder. Here we will use the
well-developed technology based on lithography and microstrip contact deposition.
well-developed technology based on lithography and microstrip contact deposition.
This technology has been widely used in the field of high frequency phase-shifters
This technology has been widely used in the field of high frequency phase-shifters
and tunable filters design based on thin ferroelectric films [13-15]. The main
and tunable filters design based on thin ferroelectric films [13-15]. The main
problems to be addressed in order to apply this technology for our particular design
problems to be addressed in order to apply this technology for our particular design
are:
are:
• The configuration has to match the desired set of guiding modes
• The configuration has to match the desired set of guiding modes
• DC field penetration into the ferroelectric layer with the field magnitude for
• DC field penetration into the ferroelectric layer with the field magnitude for
the maximum tuning range (10 V/µm for the material to be used)
the maximum tuning range (10 V/jum for the material to be used)
• satisfy conditions of minimum insertion losses.
• satisfy conditions of minimum insertion losses.
Fig.
Fig.66shows
showsthe
thepreferable
preferable design
design for
for the
the configuration
configuration of
of the
the microstrips
microstrips for
for
the
ferroelectric-ceramic
tunable
accelerating
structure.
the ferroelectric-ceramic tunable accelerating structure.
We
just the
We have
have chosen
chosen toto align
align the
the microstrips
microstrips axially
axially to
to support
support just
the
longitudinal
electric
RF
field
modes.
It
will
allow
us
to
use
the
microstrips
marked
longitudinal electric RF field modes. It will allow us to use the microstrips marked on
on
the
theferroelectric
ferroelectricsurface
surfacenot
notonly
onlyas
asaaDC
DC field
field contacts
contacts but
but also
also as
as part
part of
of aa deflecting
deflecting
(transverse)
(transverse)modes
modessuppressor.
suppressor.The
The basic
basic idea
idea was
was initially
initially published
published in
in [16]
[16] and
and the
the
simulation
and
the
first
experimental
testing
has
been
done
in
[17].
It
was
shown
simulation and the first experimental testing has been done in [17]. It was shown that
that
the
the hybrid
hybrid modes
modes for
for the
the dielectric
dielectric waveguides
waveguides require
require both
both azimuthal
azimuthal and
and axial
axial
surface
current.
surface current.
3d
d
dd ==60
60 µm
jum
a).
a).
b).
b).
FIGURE
FIGURE6.6.Design
Designofofthe
themicrostrip
microstripconfiguration
configuration for
for the
the ferroelectric-ceramic
ferroelectric-ceramic
tunable
tunableaccelerating
acceleratingstructure.
structure.
571
IfIf the
current (this
(this evidently
evidently corresponds
corresponds to
to
the outer
outer conductor
conductor allows
allows only
only axial
axial surface
surface current
our
configuration
in
Fig.6a),
the
deflecting
modes
will
radiate
beyond
the
outer
walls
our configuration in Fig.6a), the deflecting modes will radiate beyond the outer walls
to
modes. The
The numerical
numerical simulations
simulations
to decay
decay in
in the
the form
form of
of surface
surface waves
waves and
and trapped
trapped modes.
and
experimental
testing
show
[17]
that
the
accelerating
fields
are
unaffected
by the
the
and experimental testing show [17] that the accelerating fields are unaffected by
lined
wire
boundary
(Fig.6a)
and,
at
the
same
time,
the
transverse
fields
could
be
lined wire boundary (Fig.6a) and, at the same time, the transverse fields could be
damped
in
a
few
cycles
by
placing
a
shell
of
microwave
absorber
around
the
damped in a few cycles by placing a shell of microwave absorber around the
structure.
structure.
Fig.6b
microstrips structure
structure for
for (10-13)
(10-13)
Fig.6b shows
shows the
the particular
particular dimensions
dimensions of
of the
the microstrips
GHz
accelerating
waveguide.
We
have
to
find
an
appropriate
microstrip
width
for the
the
GHz accelerating waveguide. We have to find an appropriate microstrip width for
particular
layer.
Our
simulations
showed
that
for
the
(180-220)
jum
layer
that
particular layer. Our simulations showed that for the (180-220) µm layer that
corresponds
GHz average
frequency the
the optimal
optimal ratio
ratio is
is h=3*d,
h=3*d, where
where hh isis the
the
corresponds to
to 11
11GHz
average frequency
layer
thickness
and
d
is
the
strip
width.
The
microstrip
separation
is
approximately
layer thickness and d is the strip width. The microstrip separation is approximately dd
as
=(50-60) µm.
jum. A
A DC
DC bias
bias of
of (0.5-1)
(0.5-1)
as well.
well. For
For the
the (10-13)
(10-13) GHz
GHz frequency
frequency range
range dd =(50-60)
KV
is
applied
across
this
gap
to
provide
the
10
V/jum
tuning
field.
KV is applied across this gap to provide the 10 V/µm tuning field.
NUMERICAL
NUMERICAL SIMULATIONS
SIMULATIONS
Fig.7
the electric
electric field
field components
components for
for the
the
Fig.7 shows
shows the
the radial
radial dependence
dependence of
of the
11.42
the ferroelectric
ferroelectric layer
layer of
of 200
200 µm
jumand
and
11.42 GHz
GHz dielectric
dielectric loaded
loaded waveguide
waveguide with
with the
dielectric
beam of
of 100
100 nC,
nC, σazz==22 mm.
mm. The
The
dielectric constant
constant of
of 500
500 excited
excited by
by the
the high
high current
current beam
accelerating
inside the
the vacuum
vacuum channel
channel and
and decays
decays
accelerating gradient
gradient of
of 30 MV/m is flat inside
rapidly
tunability isis
rapidly inside
inside the
the ceramic
ceramic layer.
layer. The important question of ferroelectric tunability
the
DC field
field inside
inside the
the
the ratio
ratio between
between the
the DC
DC and RF axial field magnitudes. The DC
ferroelectric
lOV/jum. Our simulations show
show that
that the
the maximum
maximum
ferroelectric layer
layer does
does not
not exceed 10V/µm.
longitudinal
is
longitudinal RF
RF field
field inside
inside the
the ferroelectric
ferroelectric layer for the parameters mention above is
EEzz== 0.23
0.23 MV/m
MV/m and
and therefore
therefore
Ezvacuum/Ezferro=166, EDC/Ezferro=43.5.
> 2 107
0.5
||
aa
0.6
| ||b|
|b|
R,cm
R,
cm
FIGURE7.
7. Longitudinal
Longitudinal and transverse fields vs. radius of the double-layer
FIGURE
double-layer dielectric
dielectric loaded
loaded
waveguide of
of 11.42GHz,
11.42GHz, Si=16,
ε1=16, eε22=500
=500 ,, ferroelectric
ferroelectric thickness
thickness d=
waveguide
d= 200µ,
200ja, q=100nC,
q=100nC, σazz=0.2cm.
=0.2cm.
Ceramic layer, |b| - ferroelectric layer.
|| aa | -- Ceramic
The ferroelectric
ferroelectric layer
layer remains
remains tunable;
tunable; the
the effect
The
effect of
of the
the beam
beam and
and RF
RF field
field isis
negligible in
in comparison
comparison with
with the
the DC
DC field
field between
between the
negligible
the microstrip
microstrip contacts.
contacts. ItIt should
should
bementioned
mentioned that
that transverse
transverse field
field magnitude
magnitude is
is much
be
much less
less than
than the
the longitudinal
longitudinal inside
inside
ferro
ferro
the ferroelectric
ferroelectric as
as well,
well, E
Ezzferro
>>E
One can
can see
r
the
»Erferro
.. One
see in
in Fig.
Fig. 88 the
the wakefields
wakefields of
of the
the
100 nC
nC beam
beam inside
inside the
the 11.42
accelerating structure.
We have
100
11.42 accelerating
structure. We
have studied
studied the
the wakefields
wakefields
modification due
due to
to the
the ferroelectric
ferroelectric tuning
tuning of
of (20-30)%
modification
(20-30)% with
with an
an unbiased
unbiased dielectric
dielectric
572
constant of
of 500.
500. The
The wakefield
wakefield structure
structure in
in Fig.
Fig. 88 experiences
experiences the
the dramatic
dramatic phase
phase
constant
changes as
as aa result
result of
of (2-3)%
(2-3)% basic
basic frequency
frequency shift.
shift.
changes
.10 7
44 -10
Ez, V/m
.10 7
22 -10
a
>
0
.10 7
-22 -10
.10 7
-44 -10
0
5
10
10
15
15
z,cm
z,cm
20
20
25
25
30
30
FIGURE 8.
8. Longitudinal
Longitudinal wakefields
wakefields of
of q=100nC,
q=100nC, aσzz=0.2cm
=0.2cm electron
electron beam
beam inside
inside the
the double-layer
double-layer
FIGURE
dielectric loaded
loaded waveguide
waveguide (11.42GHz,
(11.42GHz, Si=16,
ε1=16, eε22=500
=500 ,, ferroelectric
ferroelectric layer
layer thickness
thickness 200jam).
200µm).
dielectric
FERROELECTRIC MATERIALS.
MATERIALS. LOSS
LOSS FACTOR
FACTOR
FERROELECTRIC
We discussed
discussed in
in the
the previous
previous sections
sections the
the possibility
possibility of
of adjusting
adjusting the
the Af=
∆f= 200
200
We
MHz frequency
frequency shift
shift caused
caused by
by the
the ceramic
ceramic tolerances
tolerances and
and dielectric
dielectric constant
constant
MHz
heterogeneity by
by the
the tunable
tunable ferroelectric
ferroelectric layer.
layer. We
We require
require an
an accelerating
accelerating structure
structure
heterogeneity
design for
for the
the frequency
frequency range
range f=(10-13)
f=(10-13) GHz
GHz with
with the
the tunability
tunability of
of (2-3)%
(2-3)% or
or 200
200
design
MHz. Fig.
Fig. 99shows
MHz.
shows the
the frequency
frequency dependence
dependence on
on the
the BST
BST dielectric
dielectric constant
constant for
for the
the
waveguide with
with the
the vacuum
vacuum channel
channel and
and the
the ceramic
ceramic layer
layer radii
radii of
of 0.5
0.5 and
and 0.7
0.7 cm
cm
waveguide
respectively for
for the
the dielectric
dielectric constant
constant of
of 5,
5, 77 and
and 9.
9. The
The ferroelectric
ferroelectric layer
layer thickness
thickness
respectively
has
been
adjusted
to
obtain
the
TM01
frequency
of
11.42GHz.
has been adjusted to obtain the TM01 frequency of 11.42GHz.
Tunable ferroelectric
ferroelectric devices
devices are
are generally
generally used
used above
above the
the Curie
Curie temperature
temperature
Tunable
in
the
paraelectric
regime,
where
there
is
a
significant
dependence
of
the
permittivity
in the paraelectric regime, where there is a significant dependence of the permittivity
on
the
applied
DC
field
[13,14].
For
room
temperature
applications
the
Sr1-xxTiO3
TiO3
on the applied DC field [13,14]. For room temperature applications the BBxxSri_
(BST)
ferroelectric
is
typically
made
with
x
<
0.7.
Normally
BST
thin
films
for
(BST) ferroelectric is typically made with x < 0.7. Normally BST thin films forhigh
high
frequency applications
applications have
have Ba:Sr
Ba:Sr ratio
ratio of
of 50:50
50:50 or
or 60:40.[14].
60:40.[14].
frequency
f, GHz
/;GH
Z
1
2
3
ε2
FIGURE 9.
9. Wakefield
Wakefield frequency
frequency vs
vs ferroelectric
ferroelectric dielectric
dielectric constant
constant £ε22-.
FIGURE
1). Si
ε1 == 5,
5, hh =
= 0.132
0.132 mm;
mm; 2).
2). Si
ε1== 7,
7, hh =
= 0.168
0.168 mm;
mm; 33 ).). Siε1== 9,
9, hh== 0.183
0.183 mm.
mm.
1).
573
A typical loss factor for thin (Iju) ferroelectric film is ~10~2 for the 10 GHz
band. Some encouraging results published recently showed the same parameter as
6*10"3 for a dielectric constant of 1800 and DC field variation from 4 MV/m to zero
[15].
11.42GHz
Base frequency f, GHz
1 .Parameters of the Rc=0.5cm
waveguide
with Rd=0.633cm
Rw=0.656cm
ferroelectric layer
21.0GHz
Rc=0.5cm
Rd=0.561cm
Rw=0.574cm
33.0GHz
Rc=0.5cm
Rd=0.534cm
Rw=0.542cm
8i=16
8i=16
8i=16
s2-250
tan5i=0.0005
s2-250
tan5i=0.0005
s2-250
tan8i=0.0005
2.
Equivalent
parameters of typical
dielectric waveguide
Rc=0.5cm
RWjd=0.665cm
Rc=0.5cm
Rw,d=0.665cm
Rc=0.5cm
Rw,d=0.545cm
8i=16
8i=16
8i=16
3.
Thickness
of
ferroelectric layer, jam
4. Loss tangent of
ferroelectric, tan52
5. Ferr. losses, %
230|Li
130n
80|Li
0.005
0.008
0.01
15.4
20.2
19.12
6. Metal losses, %
7. Loss ratio
8.5f/f,%,(e 2 ±0.3e 2 )
73.8
1.8
2.219
74.0
2.045
2.711
76.9
2.023
2.445
TABLE 1. The waveguide parameters and loss factor for the 11.42, 21.0 and 33.0 GHz accelerating
structures. Highlighted the ferroelectric layer thickness and the frequency tunability factor.
We plan to use a composite material made of high quality BST bulk ceramic
with addition of oxides to reduce the dielectric constant of BST from 1500 to 300
range with a tunability of K=1.3 (30%) increasing the DC tuning field maximum to
10 MV/m. The expected loss factor for the BST-oxides composition is (4-5)* 10"3 for
the 11 GHz frequency range. Table 1 shows the basic waveguide parameters of the
accelerating structures made of double-layer ceramic-ferroelectric composite for 11,
21 and 33 GHz respectively.
We have chosen the tunability of the structure not to exceed 3% to allow us to
adjust for a maximum 200 MHz frequency shift. One can see that the ferroelectric
layer thickness decreases for the high frequency from 230jum for 11 GHz to SOjum for
33 GHz. Magnetic losses in the copper sleeve are much higher than ferroelectric loss
due to the high dielectric constant of the outer layer. But the total ratio of losses in the
tunable structure to the same frequency structure made of regular ceramic is in the
range of (1.7-1.8), Wdiei/Wferr <2. (line 7 of the table, "Loss ratio"). It means that our
price for tunability is the increase of energy loss by (1.5-2.0) dB for the double layer
3% tunable accelerating structure in comparison with a (non-tunable) dielectric
loaded waveguide. It should be mentioned here that the temperature of the
ferroelectric layer has to be stabilized in the range of AT= (10-15)°C.
574
SUMMARY
A new scheme of the tuning accelerating structures has been proposed. The
basic idea is to use a double layer of dielectric. The upper layer, made of ferroelectric
material with permittivity controlled by an applied DC field, will tune the whole
accelerating structure to the desired frequency. One can apply this technology to
compensate for the frequency shift caused by ceramic waveguide tolerances and
dielectric constant heterogeneity of the structure. The (11-13) GHz structure will be
3% tunable with the ferroelectric layer about 200 jum thick with a dielectric constant
of 250-400, tunability of 20% and loss tangent of 5*10"3, and peak applied DC bias
field of lOV/jum. This tuning effect is fast and programmable in real time during
operation of the accelerator.
The proposed scheme will allow us to implement tunability in any dielectric
accelerating structure for almost any kind of experimental or practical application.
Unlike conventional metal-vacuum structures dielectric loaded devices have one
important parameter that can be used for the tuning - dielectric constant of the
ceramic loading. The proposed approach also uses the well known feature of the
dielectric structure that the maximum accelerating field is in the axial center of the
waveguide and falls off close to the copper layer.
The multi-layer tunable technology can also be extended to many different
aspects of high frequency, high power accelerating and generating types of devices
such as switches and pulse compressors [18]. Beyond this an open avenue for future
research is studies of nonlinear effects in structures [19] where the high frequency
wakefields generated by an electron beam in the dielectric loaded guiding system
interact with the ferroelectric layers. The possibilities of shock wave solutions [18],
self-focusing and many other nonlinear phenomena may be studied.
ACKNOWLEDGMENTS
This research was supported by the Department of Energy, High Energy
Physics Division.
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