21-GHz Ceramic RF Power Extractor
David Yu, David Newsham, and Alexei Smirnov
DULYResearch Inc., Rancho Palos Verdes, CA 90275
Abstract. We report progress on the development of a dielectric based rf power source suitable
for two-beam acceleration schemes for future linear colliders and compact accelerators. We first
derived from basic principles the formulas for rf power generation of a bunched beam through a
ceramic tube, and calculated the properties of the power extractor using analytical numerical
simulations. In preparation for a proof-of-principle, high power demonstration we designed and
constructed a 21-GHz ceramic power extractor and power coupler.
INTRODUCTION
The dielectric based rf power source promises superior performance and lower cost
compared with conventional devices. Novel material and simple design characterize
the compact rf power source. In this power extractor, a "train" of high-charge electron
bunches travels down the axis of a dielectric lined, circular metallic waveguide. In the
wake of the electron bunches, rf Cherenkov radiation is produced in the dielectric
layer. This radiation is then extracted from the dielectric for coupling to an output
waveguide for subsequent use.
High-energy electron/positron linear colliders are needed by the high energy
physics community for experimentation and exploration of the fundamental nature of
the universe. To reach a center-of-mass energy above 1 TeV, the two beam
accelerator (TEA) has been proposed as an efficient acceleration scheme for future
linear colliders [1]. If successfully demonstrated, the ceramic device may well be the
simplest and the best way to extract rf power in a TEA, surpassing earlier relativistic
klystron and free electron laser concepts, and the power extraction and transfer
structures presently in use at CERN.
The two beam accelerator [1] uses a conventionally accelerated, high-current,
relativistic, drive electron beam which is transformed into a high power rf source that
drives a high energy, electron or positron linear accelerator. In the TEA scheme, a
device must first extract rf power from the kinetic energy of a high-charge, lowvoltage, pulsed electron beam, deliver it to a second, low-current beam, and accelerate
it to high energy. Such a voltage transformer can be utilized to efficiently accelerate
electron and positrons in future linear colliders. The use of a ceramic tube for power
extraction, together with a matched power coupler, provides a simple method to
generate and deliver high rf power from the primary electron beam to a linear collider
for electron and positron acceleration. A recent version of the TEA [2], now adopted
by CERN and being considered by SLAC for future colliders, makes use of a beam
bunch stacking scheme to achieve high frequency operation. The concept uses a lowCP647, 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
484
frequency (L or S-band), long pulse length, electron beam, and transforms that energy
into a higher-frequency, short pulse length, high rf power by means of electron bunch
combiner rings and a power extracting device. High frequency operation is achieved
with short bunch spacing, which is obtained by the combiner rings [3]. The electron
bunches are then decelerated in a low impedance structure that extracts the beam
energy as rf energy at the desired (designed) frequency. In the case of TEA, this
power is delivered to a high-impedance structure where it will accelerate a low-current
beam to high energies. Alternately, this power could be delivered to any device,
similar to the output of any rf power supply. Because of the low-loss propagation of
the hybrid electromagnetic (HEM) waves [4] in a dielectric loaded waveguide, the
proposed power extractor will efficiently transport the wakefield to an rf coupling
device for delivery to the second stage of the accelerator.
Unlike classical Cherenkov devices, the ceramic based rf power source has no
medium (i.e. gas) filling the beam interaction region or material in contact with the
electron beam itself. Thus, the wakefield excitation is a volume waveguide mode
rather than a surface wave, and does not decay exponentially with distance from the
surface. This allows significantly increased electron current and relaxed beam quality
requirement. Unlike free-electron-laser (FEL) devices that radiate through selfmodulation and self-oscillation stages, the dielectric power source only uses the
waveguide as a radiator for a beam that has been previously bunched. This provides
the ability to avoid the excitation of parasitic modes, increases efficiency, and reduces
the required interaction length. The pre-bunched electron beam must be produced at a
subharmonic of the desired radiation frequency. An additional advantage of the
ceramic based power extractor as an rf power source is the possibility of multi-staging
by alternating rf power extraction sections with beam energy recovery linac sections
along the same electron beam line. This feature is also ideally suited for future linear
colliders, and is complementary to the aforementioned TEA version.
The most striking feature of the proposed dielectric power source is simplicity of
construction. The typical geometry of the cylindrical^ symmetric device is shown in
Figure 1. The structure is a simple ceramic tube, of inner radius a, and outer radius b,
inserted into a conducting copper sleeve. A power coupling device is attached to the
end of the dielectric lined structure to transfer the rf power from the dielectric medium
into a circular copper waveguide. Using this bunched-train driven, dielectric-based
technology for rf power extraction directly from an intense, relativistic electron beam
has significant advantages since the radiation characteristics (frequency, power,
bandwidth, etc.) depend on the beam properties (bunch spacing, current, voltage,
energy spread), the device geometry, and the material properties of the dielectric.
Recent advances in dielectric materials for microwave applications have made very
low loss (tanS ~ 10-4) and high Q materials commercially available. In particular, the
dielectric Cordierite [5] has a relatively low permittivity (e ~ 4.6) and low losses
(Q ~ 5000, tanS ~ 0.0005) that are suitable for the proposed power source.
485
- Dielectric Material
2b
Conductor •
2a
-cTh-
-cTh-
>$S$$$^$$^^$^^
FIGURE 1. Dielectric loaded structure. qb is the charge per bunch, cTb is the bunch spacing, L is the
structure length, a is the inner radius and b is the outer radius.
THEORY
The field and power radiated by and electron beam propagating in a closed, high
group velocity, ceramic lined waveguide with linear dispersion was calculated in the
time-domain for synchronous Cherenkov wakefield modes that are produces. This
analysis includes the calculation of the attenuation, field amplitudes, form and loss
factors for both a single bunch and multi-bunch train. The main assumptions that are
included in the analysis are:
1. The relative group velocity, p g , of the radiated wave can be comparable to
the velocity of the particle, P , but that they are not so close that their
difference fails to be much greater that the inverse of the Q factor of the
cavity.
2. Any tapering of the waveguide and bunch parameters is sufficiently
adiabatic to maintain a constant Cherenkov resonant frequency.
3. The transverse motion of the electron beam is slow and there is no
transverse current.
4. There are no reflections from transitions and there is no diffusion of the
group front.
The derivation of the relevant parameters begins with the Fourier
transformation of the bunch current r|(z) into the frequency domain. This density is
then applied to the generalized fields induced in the waveguide through the interaction
integrals with the induced fields in the frequency domain with the eigenmode fields
[6]. Finally, integrating over the frequency domain including the residuals performs
the inverse Fourier transformation.
486
Resonant Wake-Fields in Slow-Wave Structure
Single-Bunch Fields
We assume here that the waveguide is matched for the resonant frequency. We
neglect dispersion of group velocity 8vgrs / dh and velocity spread in the bunch. The
bunch velocity v(zq ) = dzq I dt , its transverse position pL(zq), linear charge density
?7(z,z'), group velocity v grj (z) and shunt impedance rs(z) are assumed slowly
varying functions of the longitudinal coordinate z in the scale of corresponding
wavelength of radiation:
— ln{v(z), T/(Z,Z'), rs(z), vgrs(z)]« h's, where hfs=2?r/As
is radiation wave
number for the waveguide eigenmode s.
For infinitely long matched structure having finite length L of radiator we can
L
represent the current density of the bunch as that having finite lifetime
TQ
= (dzlv
0
passing through the structure:
7(r,0 = v5^(r ± -p J .)i7(z,z')(n(0-n(/-T 0 )),
(1)
where II(f) is the Heaviside function, 8 (f± ) = 8 (x)8 ( y) = 8 (r) / 2^r is the 2D
delta-function.
In the frequency domain we apply a general approach developed by Condon [7],
Vainshtein and Solntsev [6]. This approach is based on the field expansion in series of
eigen-modes:
,° exp(±/V) dz
_ -^ "
Q
E _S exp(+/V) \dz \dSj,(r,ai)E«a exp(±iA,z)
-oo
where
E±s = J E° s (z,F L )exp(±/A s z)
Ns =— \dS\EsxH_s-E_sxHs]
4;r *_
are
1
the
forward
and
backward
waves;
is normalization factor. For an ideal loss-less
waveguide this factor is proportional to the power Ps:
4\PS \ sgn(&>) —^^0 >~NS .
Note, the normalization factor Ns is constant in tapered waveguide by this definition
h=- [hdz = h' + ih" ,h'>0,
?J
(±)= sgn h"s , and
hs = hs (co)
is the
complex
wavenumber.
The Fourier-transform of the current j(r,t)from (1) is the following:
. co + co
487
,.
-(z-z)
where Sr > 0, v(z) = z \dz'lv(z'} is the averaged particle velocity, and /(z) is the
/ o
bunch length.
We substitute the Fourier-transform jz(r,a>) into the equations of waveguide
excitation given above. The inverse Fourier transformation with residuals gives the
following expression for electric field of the given mode s:
E.<?,t) = -2«R,F,(z./)
where F,(z,0 = ®,(^Zi)exp(i(^-vO)[n(/ 1 )-n(/ 1 - *0 )Jl(vf - z)/(v - v ^ ) ; U(x)
is symmetric step-function: 11(0) = 1/2; ~hs=h's-ih"vgrs /(v- v^ s );
z-v ,W
z-v
(z>
f
z, =————-————;t,
=———-———;and
l-iV,(z)/v(z)
v(z)-v^(z)
1
^ ~ ~( ^ ^
O (z,zj = - fdz'77(z 1? z')exp - ^ z'^^- is the generalized bunch formfactor.
v z
0/d)
I
( i)J
Let us express the longitudinal field using the standard longitudinal shunt
impedance per unit length rs(x9y,z) = E"z(z,r^}2/\dPs Idz\ = QSU2 /coWL (see,
e.g., P. Wilson [8]):
where Qs is the waveguide Q-factor for the mode s, Wand £7are the power stored and
voltage respectively.
Important to note, that the fundamental theorem of single bunch beam loading in
(2,3) is a natural consequence of the Jordan lemma that results in
Ezs(z = vf) = jEzs(z = v/ - 0). This theorem can be read as follows: the decelerating
field Ed induced by the bunch and acting on itself is half of the decelerating field Ev
acting on the witness bunch following close to the primary bunch. This theorem can be
derived also from energy conservation principle:
F - \r & w - \r & j ? j - \r ® & r T 2 _ r & _ 9 / 7
v =
\~Q~L loss=\Q~L d q=\Q~L~*~Q q = ~Q~2q = d
The modal loss factor kqs = Wloss /q2 in tapered waveguide follows directly from
(3):
To find the power generated by a single bunch Plb = Wloss IT^ =q2 kqs/T1 let us
determine the pulse length Tv. From (2) we have: T V — L vgrs (L) - v (L)\.
488
So the average power generated in non-tapered structure by a single bunch during
the pulse 7] is:
_ q
*\b ~
K
qs _
^
2^_^
~" # ~7T7"
The formfactor can be calculated as <D5 = sin(£// 2/7) /(£/ 72/7) for rectangular
bunch shape (length /) and O5 = exp(-(fa?z /ft)2 12) for Gaussian distribution with
characteristic length 8Z .
The peak power generated by a single bunch in non-tapered structure can be
estimated as:
Let us calculate the peak power for the TEA experiment done earlier [9]. For the
stage I Cherenkov radiator we have a=6mm, b=11.15mm, e=4.6, L=30cm,
8Z I c = IQps, and #=20nC. From GdfidL [10] simulations we found r/<g«6.6kOhm/m
and j3gr=Q.23. It gives us Plbpeak = 3.82MJF , whereas the measured peak power is 4
MW. Calculated maximum pulse length is 3ns, and measured effective pulse length is
2.5ns.
Note, there is neither singularity at vgr=0 nor at vgr=c in (2,3). In the particular case
1 - Pgrs « 1, y » 1 we deal with a pipe loaded by thin dielectric or small periodic
corrugations [11] that both have similar properties [12]. One can see, that the value
( r s / Q s ) / ( l - f t g r s ) remains finite [11] at ftgrs^>\. With the exception the case of
perfect (low-loss) structure the resonant wake-field becomes short due to high
'dynamic' attenuation lmhs (see (2,3)). In this specific case non-resonant and resistive
wake-fields can be dominant.
Multiple Bunch Train
To recall the simple formulae for beam-induced fields when the group velocity is
substantial we assume {v, O, Tb , q] = const, pL =Q = r±, and a constant impedance
waveguide without detuning: Tb =K-27r/a>l, where K is an integer number of beam
subharmonic with respect to the resonant frequency. The field amplitude EAs is
defined here as:
Ez(r,t) = ReEAs(z,t)exp (i(h'sz - coj}} .
The field in the transient regime can be obtained using the principle of
N-l _
superposition E^ (r , 0 = X ^'t~nTb) applied to (3):
«=o
A, =-Irs3>s(l-exp((o';(z/v-t)/(l-vgrs/v)))n(t-z/v\
489
(5)
where
I = q/Tb
t<z/v
grs>
In
v
tf
the
grs>^
is
the
beam
average
current,
t<Llv + (L-z)l\vgrs,ifvgrs<^.
steady-state
regime,
when
t>z/vi grs>
t> L/v + (L- z)/\vgrs L // vgrs < 0 expression (3) and superposition principle give
exactly the same result known from the standard formulation [8,14]:
1-exp
(6)
Hence, the average output power generated by the steady-state beam loading at
high group velocity satisfies the same formula known from the conventional approach
[8,14]:
E.
P,,=
2
2h"r
1
4a
grs
h"L
4a
i
grs
•(7)
h"L «1
Evidently, the expressions (5-7) and the power (7) are valid only if the drain time
I exceeds much the bunch separation IV In the specific case when Tv = Tb we have:
[
Ibpeak '
STRUCTURE DESIGN
The first and foremost issue regarding the design of the rf power extractor was a
careful calculation of the steady state rf power produced by an electron bunch train
passing through the device. This power is given in Equation (7), and a complete
derivation based on combining the fields produced by a train of individual bunches as
discussed in the previous section.
In addition to simulations using GdfidL [10], we developed an analytical matched
field model in MathCad to calculate the fundamental parameters of the TMoi in the
dielectric loaded waveguide, including resonant frequency, g, r/Q, and group velocity.
A survey of several sets of parameters was performed to benchmark the analytic
model, GdfidL simulation and experimental results [9,13,15] as shown in Table 1.
The results are reasonably similar for all but Q. This discrepancy can be attributed to
the documented inaccuracy of the Q calculation when GdfidL is run with periodic
boundary conditions.
490
TABLE 1. A survey of parameters for a dielectric loaded waveguide as determined from the
analytic matched field model, GdfidL numerical calculation (in ()) and experimental
measurement (in [] ).
/GHz
r/Q, k^/m
(a, b) mm, 8, tan8*104
0Br
Q
(3, 4.56), 20, 1
11.47(11.7)
8.866(9.16)
0.055 (0.053)
10860(4775)
[11.424]
[8.96]
[0.057]
[9509]
(6, 11.15), 4.6, 2
7.801 (7.5)
5.89 (6.6)
0.23 (0.23)
6100 (15000)
[6.12]
[7.8]
[0.25]
7534(11354)
(7.0, 9.992), 4.98, 2
11.31(11.395)
5.064 (5.23)
0.271 (0.27)
7261 (10624)
(5, 7.38), 4.5, 2
15.01 (15.18)
7.11(7.7)
0.28 (0.277)
0.345 (0.352)
(5, 6.42), 4.98, 2
21.04(21.5)
6.28 (6.38)
9242 (8936)
6.234 (6.02)
(5, 6.507), 4.5, 2
21.0(21.15)
0.362 (0.367)
9195 (9357
29.93 (30.4)
(4, 5), 4.5, 2
7.07 (7.76)
0.41 (0.415)
10360(8530)
(10, 10.3585), 20, 2
30.03 (29.983) 0.576 (0.657)
0.7604 (0.788)
50760(10677)
(5, 5.85), 4.98, 2
30.01 (30.27)
4.48 (4.53)
0.502 (0.509)
14060 (9015)
Table 2 shows the steady state power generated by an electron bunch train using the
numbers calculated with both the analytic model and GdfidL. The power calculation
depends on r/Q and not Q itself. For these calculations, a dielectric constant of 4.5
was used.
TABLE 2. Steady state power generated by a train of Gaussian (rectangular) bunches with
8Z = 1 mm (2 mm), Tb = 0.33 ns in a dielectric pipe with s = 4.5, q = 10 nC and L = 30 cm.
f,GHz
GdfidL
Analytic
b, mm a, mm
Power
Power
Tf, 7i ns
r/Q
r/Q
GdfidL Analytic
MW
MW
kQ/m
kQ/m
142 (152)
7.68 158 (168)
15.0
15.2
7.38
5
3.57,2.57
7.11
124 (141)
6.02 118(134)
21.0
21.15
6.507
5
2.76,1.7
6.234
30.4
29.93
5
4
2.44,1.44
7.07144(186)
7.7
155 (201)
Figure 2 shows design curves for varying the internal radius of the dielectric tube.
The process of design and manufacture of the power extractor begins with the
dielectric tube. After the material was chosen, a ballpark value of the dielectric
constant is known. The material used, Cordierite, has a nominal range of dielectric
constants of 4.5-4.9. It is clear from Figure 2 that a smaller tube radius would result in
larger produced power while requiring thicker material. To obtain a desired power of
over 100 MW, with the beam size limitation in CTF2 where a 21 GHz test is planned,
the inner radius was fixed at 5 mm.
491
FIGURE
FIGURE 2.
2. Dependence
Dependence of
of the
the design
design parameters on the internal radius of the ceramic tube for a
dielectric
dielectric constant
constant of
of 4.5.
4.5.
After
After manufacture,
manufacture, lot
lot samples
samples of
of dielectric
dielectric material
material from
from which
which the
the ceramic
ceramic tubes
tubes
were
were made
made were
were measured
measured to
to have
have aa dielectric
dielectric constant
constant of
of 4.72
4.72 ±
± 0.03.
0.03. Based
Based on
on this
this
value
value of
of the
the dielectric
dielectric constant,
constant, the
the target
target outer
outer radius
radius is
is 6.4675
6.4675 mm.
mm. Table
Table 33 and
and
Figure
Figure 33 show
show the
the sensitivity
sensitivity of
of the
the power
power extractor
extractor to
to variations
variations in
in the
the outer
outer radius
radius
and
and dielectric
dielectric constant
constant of
of the
the ceramic
ceramic tube.
tube. From
From the
the slopes
slopes in
in Figure
Figure 3,
3, aa ±100
±100 MHz
MHz
tolerance
tolerance on
on the
the resonant
resonant frequency
frequency requires
requires aa tolerance
tolerance on
on the
the outer
outer diameter
diameter of
of
±±0.01
0.01 mm,
mm, which
which is
is within
within grinding
grinding tolerances
tolerances of
of the
the ceramic
ceramic material.
material. The
The
measured
MHz window
window in
in
measured tolerance
tolerance ±± 0.03
0.03 in
in the
the dielectric
dielectric constant
constant leads
leads to
to aa ±55
±55 MHz
frequency.
frequency. Table
Table 44 gives
gives the
the final
final parameters
parameters and
and expected
expected performance
performance of
of the
the
21
21 GHz
GHz structure
structure
TABLE
TABLE 3.
3. Sensitivity
Sensitivity of
of outer
outer radius
radius and
and resonant
resonant frequency
frequency to
to variations
variations in
in dielectric
dielectric
constant.
constant.
Dielectric
radius, b (mm)
frequency, f GHz
forb=6.471
for
for
b=6.471 mm
for f=20.99
^20.99 GHz
GHz
permitivity εs
4.6
6.4891
21.173
4.6
6.4891
21.173
4.7
6 All
4.7
6.471
20.9893
6.4604
20.882
4.76
6.4604
20.882
4.76
6.4534
4.8
4.8
6.4534
20.811
492
Dieieolrfc Constant
4.9
4.6
4,7
Nominal Parameters
Inner Radius « 5*0 mm
Outer Radius * 6.467 mm
Dtetectric Consist« 4,72
20.990 OHz
2175
21.50
8s
8f
e.500
H3T 21.2
-1.8 GHz
= -10 GHz/mm
6,475 .2
20.75
$.450
1
Q
8e
= -.17 mm
20.50
20.25
20.00
8.400
Frequency vs Outer Radius
Fresiutrssy v$ Dtefec&te Oonste^it
« Oyfer Radius vs C^edrks Coolant
6,425
6.450
8.475
6,500
6,425
6400
6J525
$.580
Outer Radius (b, mm)
FIGURE 3. Sensitivities to manufacturing and material variations.
TABLE 4. Parameters of the 21 GHz structure and its predicted performance.
Frequency/0 (GHz)__________________20.99_______________
Charge per bunch qb (nC)
10
1
RMS Gaussian Bunch length az (mm)
Bunch spacing Tb (ps)
333
Structure length L (cm)
27 (36)
Inner radius a (mm)
5
Outer radius b (mm)
6.467
4.72
Dielectric constant s
0.0005
Loss tangent tan(8,)
0.35
Group velocity Pg
Attenuation of the structure (dB)
0.38 (0.5)
100(176)
Power generated (A///0 = .04 ) (MW)
Peak deceleration field (MV/m)___
28.0(37.1)
CERAMIC TAPER
To reduce reflections and achieve the best power coupling, the ceramic must be
tapered. The structure was modeled in 3D using a full trial version of a commercial
electromagnetic simulation software CST MicroWave Studio [16]. Figure 4 shows the
root-mean-square energy density stored in the electric (left) and magnetic (right)
493
fields. In the dielectric loaded section of the tube, the bulk of the energy is stored in
the dielectric as expected. The electric field energy is concentrated at the dielectricvacuum interface while the magnetic field energy is at the dielectric-wall interface.
The conversion of the electric field into the unloaded pipe mode occurs quite rapidly
at the beginning of the taper, whereas the transfer of the magnetic energy is spread out
along the taper section. It is clear that in the taper section, magnitude of the electric
field increases greatly as the power is transferred from the dielectric loaded structure
to the unloaded circular pipe. The length of the taper is 15 mm, which corresponds to
a taper half-angle of 5.6°. Figure 5 shows the Sn and 821 parameters for a TMoi mode
launched in the ceramic loaded section, as well as the Sn parameter for several taper
lengths, indicating that 15 mm is close to the optimal taper length.
494
Electric
Electric Field
Field Energy
Energy Density
Density
Type
Monitor
Plane at x
Frequency
=
=
=
=
Electric Energy Density (rms)
eden [1,11
0
Z0-99
Magnetic Field
Field Energy
Energy Density
Density
Magnetic
-7e-005 J/nT3
Type
Monitor
Plane at x
Frequency
=
=
=
=
M a g n e t i c Energy Density (rms)
hden [1,11
0
Z8-99
FIGURE 4.
4. (Top)
(Top) Electric
FIGURE
Electricfield
field energy
energydensity
densityfor
forthe
the21
21GHz
GHzceramic
ceramictaper
taper
showing
the
quick
transfer
of
energy
from
the
ceramic
lining
to
the
showing the quick transfer of energy from the ceramic lining to the circular
circular
waveguide. (Bottom)
(Bottom) magnetic
magnetic field
field energy
waveguide.
energy density
density showing
showing aa slower
slower transition
transitionof
of
power.
Note
that
the
color
scales
are
different.
power. Note that the color scales are different.
495
S-Parameters in dB
H Taper:: 18 m
j^ Taper = 1 / m
f Taper =16 m
f Taper-15m
Q Taper =14 m
^ Taper = 13 m
Taper = 12 rn
S-Parameter Magnitude in dB
Frequency/GHz
the ceramic
ceramic taper
taper with
with varying
varying taper
FIGURE 5.
5. S
11 for
FIGURE
Sn
for the
taper lengths
lengths (Top).
(Top). S-parameters
S-parameters for
for aa 21
21 GHz
GHz
ceramic taper
taper section
with aa taper
ceramic
section with
taper length
length of
of 15
15 mm
mm (Bottom).
(Bottom).
496
POWER COUPLER
Power produced in the power extractor must be coupled to the waveguide for
delivery to an accelerator or other device. The problem with coupling the power from
the extractor to the waveguide is fundamentally the same as the problem of coupling
that power back into an accelerating structure. For this reason, CERN has been
actively pursuing mode launcher designs for operation at 30 GHz [17]. The 21 GHz
coupler is based on a mode launcher. The coupler employs a choke to prevent the
TM0i mode from propagating downstream and two identical rectangular waveguides
with a step to provide the necessary matching. The coupler has been optimized to
provide over 99% transmission efficiency.
Based on a 30 GHz 2-port mode launcher developed by Igor Syratchev [17] at
CERN, DULY Research designed a copper power coupler for operation at 20.99 GHz.
Figure 6 shows the 3D model of the dual-waveguide power coupler along with
S-parameters that correspond to the modes of interest in the waveguide. The radius of
the input beam pipe was 6.25 mm. This value was chosen to be smaller than the outer
radius of the ceramic power extractor. This difference in radii requires a reducing
taper that will serve the function of a mechanical stop to the dielectric tube. The two
main features of this coupler are the stepped waveguide output ports and a
downstream choke. The outer (wider) portion of the output corresponds to a WR42
waveguide, and the section between the WR42 and the beam tube has the same height
(b) as WR42, but the width of the waveguide has been reduced. The purpose of the
choke is to reflect the rf power at 20.99 GHz, and the dimensions of the choke were
optimized to minimize the 841 parameter (with port 1 the input port, ports 2 & 3 are
the rectangular waveguide outputs, and port 4 is the downstream beam pipe). A
critical distance involved in the coupling of the TMoi mode in the pipe to the
rectangular waveguide mode is the distance between the waveguide sections and the
choke. The choke effectively sets up a standing wave pattern. The efficiency of the
coupling depends on how close the waveguide opening is to a node or an antinode of
the standing wave pattern. This is the reason that the Sn curve takes a sharp dip near
20.5 GHz.
The data presented was produced using a Vi-model, for which the TEn mode is not
supported based on the symmetry of the model. After optimizing, a !/2-model was run
for comparison, no difference in the values of the S-matrix presented was seen, and
the S-parameters associated with the TEn mode were on the order of-150 dB.
497
S1.1 (1.1)
4 sz.i (i,i)
S4.1 (1.1)
0_
FIGURE 6.
FIGURE
6. 21
21 GHz
GHz power
power coupler
coupler model
model (Top)
(Top) and
and S-parameters
S-parameters (Bottom).
(Bottom).
498
Figure 7 shows the energy density stored in the electric and magnetic fields. There
Figure 7 shows the energy density stored in the electric and magnetic fields. There
is a region of large field magnitude between the rectangular waveguides and the
is a region of large field magnitude between the rectangular waveguides and the
choke, where there is an antinode of the standing wave pattern set up by the choke.
choke, where there is an antinode of the standing wave pattern set up by the choke.
The region between the choke and the waveguides has a large stored field and may
The region between the choke and the waveguides has a large stored field and may
require external cooling.
require external cooling.
Electric
ElectricField
FieldEnergy
Energy Density
Density
Magnetic
Density
Magnetic Field
Field Energy
Energy Density
FIGURE
FIGURE7.7. (left)
(left)Electric
Electricfield
fieldenergy
energydensity
density and
and (right)
(right) magnetic
magnetic field
field energy
energy density
density for
for the
the 2-port
2-port
2121GHz
GHzpower
powercoupler.
coupler.
THREE-PORT
THREE-PORT POWER
POWER COMBINER
COMBINER
The
Theequipment
equipment available
available for
for testing
testing the
the 21
21 GHz
GHz power
power extractor
extractor includes only a
single
singlehigh
highpower
powerload.
load. Short
Short of
of building
building an
an additional
additional high
high power
power load, this leaves
two
options:
1)
design
a
new
coupler
that
had
only
a
single
waveguide
two options: 1) design a new coupler that had only a single waveguide output; or 2)
design
designaapower
powercombiner
combinerthat
thatwill
willdeliver
deliverthe
the output
output from
from the
the two
two waveguides
waveguides into the
single
singleload.
load.The
Thefirst
firstoption
optionisis an
an acceptable
acceptable solution,
solution, and
and the
the design of such a device
would
would be
be useful
useful toto reduce
reduce the
the cost
cost of
of any
any future
future testing
testing of the ceramic power
extractor/generator
extractor/generator atat any
any frequency,
frequency, not
not to
to mention
mention the
the simplicity of one extractorone
one accelerator-one
accelerator-one waveguide
waveguide in
in aa two
two beam
beam acceleration
acceleration scheme. If the second
option
optioncan
canbe
beachieved
achievedwith
with simplicity
simplicity of
of both
both design
design and
and construction, it will be an
expedient
expedient solution
solution given
given the
the time
time constraints
constraints due
due to
to the
the imminent
imminent CTF2
decommissioning
decommissioningschedule.
schedule.
Figure
Figure88 shows
shows the
the model
model of
of aa 21
21 GHz,
GHz, 3-port
3-port combiner
combiner and associated
S-parameters. This
Thismodel
model isis scaled
scaled from
from aa 30
30 GHz
GHz variant,
variant, which
which was produced at
S-parameters.
CERN and
and served
served as
as the
the design
design model
model for
for this
this application.
application. The
The only significant
CERN
499
difference
differencebetween
betweenthis
thisdesign
design and
andthe
the CERN
CERN design
design isis the
the size
size of
of the
the waveguide
waveguide (and
operating
operatingfrequency).
frequency).
S-Parameter Magnitude in dB
FIGURE8.8. 21
21GHz
GHz3-port
3-portpower
powercombiner
combiner(Top)
(Top) and
and S-parameters
S-parameters (Bottom).
(Bottom).
FIGURE
500
INTEGRATED EXTRACTOR/COUPLER SIMULATION
INTEGRATED EXTRACTOR/COUPLER SIMULATION
Figure 9 shows the model and the S-parameters for the integrated
Figure 9 shows the model and the S-parameters for the integrated
extractor/2-waveguide coupler. The ceramic tube in this model is much shorter than
extractor/2-waveguide coupler. The ceramic tube in this model is much shorter than
the actual tube, in order to conserve computation time. For manufacturing reasons, the
the actual tube, in order to conserve computation time. For manufacturing reasons, the
length
of each ceramic section that could be reliably constructed is limited to 9 cm
length of each ceramic section that could be reliably constructed is limited to 9 cm
long.
But
100 MW,
MW, the
the ceramic
ceramic tube
tube should
should be
be long
longenough
enough
long. But in
in order
order to
to generate
generate over
over 100
toto accommodate
a
sufficient
number
of
electron
bunches
inside
the
tube
at
any
given
accommodate a sufficient number of electron bunches inside the tube at any given
time.
Based
on
these
considerations,
the
length
of
the
active
section
of
the
power
time. Based on these considerations, the length of the active section of the power
extractor
As ceramic
ceramic pieces
pieces are
are not
not brazed
brazedinto
intoplace,
place,
extractor will
will be
be 36
36 cm
cm long
long (4
(4 pieces).
pieces). As
an
alternative
method
to
mechanically
secure
the
ceramic
pieces
inside
the
copper
tube
an alternative method to mechanically secure the ceramic pieces inside the copper tube
was
developed.
This
method
secures
the
dielectric
by
reducing
the
inner
radius
of
the
was developed. This method secures the dielectric by reducing the inner radius of the
copper
tube
to
less
than
that
of
the
dielectric;
thus
preventing
the
dielectric
from
copper tube to less than that of the dielectric; thus preventing the dielectric from
sliding
sleeve holds
holds the
the dielectric
dielectric atatthe
theupstream
upstreamside.
side.InIn
sliding past
past the
the reduction.
reduction. A
A copper
copper sleeve
order
from the
the reduced
reduced size
size copper
copper tube,
tube, aa slight
slight taper
taper was
was
order to
to prevent
prevent reflections
reflections from
introduced.
10 shows
shows the
the electric
electric and
and magnetic
magnetic field
field energy
energy densities.
densities. The
The
introduced. Figure
Figure 10
slight
in place
place can
can be
be seen
seen in
in Figure
Figure10,
10,just
justtotothe
theright
right
slight taper
taper that
that holds
holds the
the dielectric
dielectric in
of
the
taper
in
the
ceramic.
of the taper in the ceramic.
FIGURE 9.
9. Integrated
Integrated 21
21 GHz
FIGURE
GHz extractor
extractor and
and coupler
couplermodel
modeland
andS-parameters.
S-parameters.
501
Electric
ElectricField
FieldEnergy
EnergyDensity
Density
Magnetic
MagneticField
FieldEnergy
EnergyDensity
Density
FIGURE
FIGURE10.
10. (left)
(left)Electric
Electricfield
fieldenergy
energydensity
densityand
and(right)
(right)magnetic
magneticfield
fieldenergy
energydensity
densityfor
forthe
the2121
GHz
GHzintegrated
integratedextractor/coupler.
extractor/coupler.
CONCLUSION
CONCLUSION
Figure
Figure11
11 shows
shows aa 3-D
3-D model
model ofofthe
the ceramic
ceramicbased
basedpower
powerextractor
extractornear
nearthe
thefinal
final
stages
of
construction.
Figure
12
shows
a
cut-model
of
the
same
device.
stages of construction. Figure 12 shows a cut-model of the same device. Once
Once
completed
completed the
the structure
structure will
will be
be tested
tested on
onCTF2
CTF2atatCERN
CERNand
andisisexpected
expectedtotoproduce
produce
over
100
MW
of
rf
power
at
20.99
GHz.
over 100 MW of rf power at 20.99 GHz.
.
502
FIGURE 11.
3-D model
model of
of the
the 21-GHz
21-GHz ceramic
ceramic based
based power
power extractor.
FIGURE
11. 3-D
extractor.
503
FIGURE 12.
12. Cut
Cut section
section of
of the
the 3-D
3-D model
model shown
shown in
in Figure
Figure 11.
FIGURE
11.
ACKNOWLEDGMENTS
ACKNOWLEDGMENTS
The authors would like to thank W. Gai, W. Liu, R. Konecny, I. Syratchev and L.
The
authors would like to thank W. Gai, W. Liu, R. Konecny, I. Syratchev and L.
Throndahl, for useful discussions, comments and technical assistance. This work is
Throndahl, for useful discussions, comments and technical assistance. This work is
supported by DOE SBIR Grant No. DE-FG03-01ER83232.
supported by DOE SBIR Grant No. DE-FG03-01ER83232.
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