JAERI-Conf 95-021

PA17
RF CHARACTERISTICS OF THE BULLET-SHAPE SiC ABSORBER
FORKEKB
Yasunao TAKEUCHI
KEK, National Laboratory for High Energy Physics, 1-1 Oho, Tsukuba, lbaraki, 305 JAPAN
Abstract
Sixteen bullet-shape sintered SiC (silicon carbide)
ceramics were used as the HOM absorbers for a
prototype of KEK B-factory (KEKB) normal conducting
cavity[l]. RF simulations show that the reflection ratefrom the SiC absorber increases abruptly when thefrequency decreases under 1GHz. This behavior can be
explained as the attenuation property of a cylindricaldielectric waveguide. The RF characteristics of the SiC
absorber are discussed by analyzing properties of thecylindrical dielectric waveguide.

absorber. The permittivity of the SiC material is 22.26.10j at 0.75GHz and 20.7-4.58j at 1.5GHz. The designof the SiC absorber is based on the S-band waveguideload for the 2.5-GeV electron linac in KEK[3].
Closed circles (a=20mm) in figure 2 show thefrequency response of the reflection (S 11 ) from the HOM
absorbers in the test cavity, which is simulated withhfss[4]. The TEM mode in the coaxial waveguide isassumed in this simulation. When the frequency
decreases under 1GHz, the reflection increases rapidly.
This poor absorpti?n properties under 1GHz should be
improved because some HOM's exist at 0.7-0.8GHz.

1. Introduction

2. Frequency response of the HOM absorber

A prototype of normal conducting cavity for KEKB
was designed and built [2]. This prototype cavity isloaded with a coaxial waveguide for damping higher
order modes (HOM's). The waveguide is equipped with anotch filter. Figure 1 shows a schematic drawing of thiscavity with the SiC absorber. For HOM absorption,
sixteen bullet-shape sintered SiC ceramics are inserted
from the end of the coaxial waveguide.· The absorberdimensions are 40 mm in diameter, and 400 mm in total
effective length including a 100-mm nosecone section.
Each SiC absorber has a cooling water channel boredinside and is directly cooled. The HOM power (atfrequencies above 0.7 GHz) to be handled will be on theorder of -10 kW per cavity, corresponding to -1 kW per

Several solutions, which improve the frequency
response at 0.7-l.OGHz, were obtained throughnumerical simulations with hfss. It was found that
effective parameters are the radius of the absorber (=a)
and the real part of the permittivity (=e'). Figures 2 and 3
show the effects of these parameters. Larger values of aand e' improve the absorption at lower frequencies. But
the length of the absorber is not so effective as a and e'.
Figure 4 shows the effect of the nosecone section at thetip of SiC. A SiC absorber without the nosecone section
has a similar frequency response at 0.7-l.OGHz. The
taper improves the absorbing properties above 1GHz.
The frequency responses shown Figures 2 and 3
resemble the cutoff response of a metal waveguide filledwith a dielectric material. This suggests· that the RF
propagation properties in the SiC absorber, which isconsidered a kind of waveguide, are essential in its

0.6::

SiC AbsorberCl)

0.4%~.5~~~~1.e5~~2~~2.~5~=13
L=400 mm

Frequency(GHz).. j

Figure 1: A schematic drawing of the test cavity with the SiCabsorber.

Figure 2: S 11 frequency response curves for the -HOMabsorbers with a=15, 20, and 25 mm. Closed circle for the SiC
absorber (a=20) employed in the test cavity.

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4. Analysis using waveguide theory. ...;;...""'· ·t··--------·;---------·

0.8~...,;;,..;;....;;;;;;.

~=20mm, (=400mm i,o.s ....
~~~~"'"'j""'"""l""""'"f"""""'f""""":

0.4 -----~.-- :.........

:::!........... j...........j ........ ..

0.2 ..........
' ;!il.. ..... :!........... :!...........:!........ ..

:: \i"''l!l::!

!
1.6

1.21Frequency (GHz)

Figure 3: S 11 frequency response of the SiC absorbers withdifferent petmittivities.
_....with 1OOmm-nosecone_.....without nosecone····------... -----------.-----------,.'.' ---------··---------..

0.8.

'(J)tj £ '= 22.2, loss tangent=0.274;___ .. ___ ·: .•:-20m"'!' _L:-_400rnf' ... ____ , _! _________ _0.6::.. : T"' 0.40.2

Here we will analyze the attenuation properties ofthe cylindrical dielectric waveguide which is regarded asa simplified model of the bullet-shape SiC absorber.
Attenuation in a dielectric circular rod was studied by
Elsasser and Chandler in detail[5][6]. The analyticalsolutions of the propagating modes are described inmany textbooks. We shall follow the notation in thetextbook by Kawakami [7]. We will choose a cylindricalcoordinate system r, (), z with the z axis lying along theguide axis. The radius of the rod will be a; dielectric
constants inside and outside the rod will be t:1 and t:2(which are assumed real numbers). The longitudinalcomponents of the field vector are, inside the rod,E.= An lifltr) cos (n()+on) e'jOX'Hz= Bn liflt r) sin (n()+On) e .
r..2 1/22.
w1th fit= ( m t:1)10 - p )iland outside the rod,·ox
Ez = Cn KnCatr) cos (n()+on) e'·ox

1.5

22.5

Hz= Dn Kn( CXr r) sin (n()+on) e'

3Frequency(GH z)

Figure 4: The effect of the nosecone on the S11 frequency
response.

frequency response.

with at = ({i - m2ezJlo / 12
where J n is a Bessel function; Kn is a modified
Bessel function. Kn decreases exponentially for large
values of r.
The continuity of the tangential components of thefield at the boundary r=a gives the following relation.
2In order to identify the propagating mode clearly, asimplified 2-dimension al lossless model without acooling water channel was simulated in a parallel platetransmission line. Figures 5-(a) and 5-(b) show theelectric field of the propagating mode obtained by thehfss simulation. The electromagnetic wave (HE 11 -likemode) is mainly propagating inside the SiC at 1.5GHz.
On the other hand, the electromagnetic wave tends topropagate outside the SiC at 0.7GHz.

--~.

~

Magnetic short....

Magnetic short_.... _,__'------...1-----. ........L•• j

Magnetic short(a) f= 1.5 GHz

Magnetic short(b) f = 0.7GHz

Figure 5: Electric field of the propagating mode in the 2dimensionallossless model. (a=20mm, e'=22)

222(1]]+1J 2 )(t:1 1]j+t:2 1}2 )=n ((1/u )+(1/w ))((t:/u )+2(4-1)(t:jw ))
w=a ta, 1}1=.Jn'(u)!(uliu )),with u = flta,

3. Propagating mode in the SiC absorber

1Jz=Kn'(w )l(wKn(w))

In addition u and w are related by the equation
2222(4-2)v
u + w = m (t:rt:2)Jlaa
From the equation (4-1) the values of u and w of the· HE 11 mode (n = 1) are obtained by numericalcalculations. These are shown in figure 6. On the other
hand, the equation (4-2) expresses a circle on the u-w
12coordinate. The radius of the circle is ma((ere2)f.l0/ =v. Numerical solutions are obtained by the intersectionsof the circle (expressed by (4-2)) with the curves in Fig.
6. No matter how small v becomes, even at v=O, there isalways an intersection. This means that this mode has nocutoff frequency.
In order to evaluate the field outside the rod, we will
pay attention to the value of w (=ap). When w is large
enough, Kj(wr/a) decreases rapidly as r increases, thenthe outside field of the propagating mode is confinednear the rod surface. Figure 6 shows that w increases
abruptly above the some value of u, especially when t:1 islarge. Above this value of u the solution of w becomeslarge with extreme rapidity with small increase of the-71-2=

JAERI-Conf 95-021

00.5

1.5

u2

2.5

0~~~~~~--~--~~~.
0.6
0.8
1
1.2
1.4
1.6

3

Frequency(GHz)

Figure 6: The values of u and w of the HEu mode (n=:l) a~f
obtained by numelical calculations. A quarter of the cucle 1s
given by equation (4-2).

circle radius (=v) of (4-2). Let us define this criticalvalue of v as vt" When v is smaller than vt the field isspread out and only small amount of the field exists
inside the rod. On the other hand, when v is larger than vt
the field concentrates inside the rod and near the rod
surface. If the dielectric waveguide is lossy, theattenuation change abruptly at v=vt' Since vis a functionof ro, a and E 1 indicated in (4-2), the attenuation
properties strongly depend on these three parameters. It
should be noted here again that the absorption propertiesof the SiC depend on the parameters. Figure 7 showswla( =ar) as a function of frequency for three radii of therod. The values of wla(=ar) are plotted in figure 8 as afunction of frequency for three dielectric constants of therod.
The critical frequencies indicated by arrows infigures 7 and 8, which correspond to vt, show good
agreement with the those of the SiC absorber shown infigures 2 and 3.
5. Conclusion
The frequency response of the bullet-shape SiC
absorber can be explained as the attenuation properties of
the cylindrical dielectric waveguide in which the HE 11
mode propagates. The electric field pattern of the50 f:==;:;~-=;!<~rrr-'l-.-a=15 mm

40_....a=20 mm-e~a=25 mm. Figure 8: Values of wla(=a1) as a function of frequency forthree permittivities.

propagating mode dominates the frequency response of
the SiC absorber mainly. This dielectric waveguidemodel gave us much information to design the bulletshape and similar type absorber. The result of thisanalysis suggests that a thicker SiC absorber than thepresent design would be better. Furthermore, a shorter
absorber design would be possible because the length of
the absorber is not so effective to the frequency response.
The design of a new SiC absorber is being under way.
6. Acknowledgment
The author would like to thank T.Kageyama forvaluable discussions.
7. References[1] Y.Takeuchi et al., "HOM Absorber for the KEKB

Normal Conducting Cavity", KEK Preprint 95-69.
[2] T.Kageyama et al., "Development of a HOMDamped Cavity for the KEK B-Factory (KEKB)",KEK Preprint 95-52 ..
[3] H.Matsumoto et al., "Application of SiC Ceramics for
Microwave Absorber", Proc. 9th Linear Accelerator
Meeting in Japan, Kyoto, 1984, pp. 124-126.
[4] "High-frequency structure simulator" supplied byHewlett Packard Ltd ..
[5] W. M. Elsasser, "Attenuation in a dielectric circularrod", J. Appl. Phys., vol.20, pp.l193-1196, Dec.
1949.
[6] C. H. Chandler, "Investigation of dielectric rod aswaveguide", J. Appl. Phys., vol.20,pp.1188-1192,
Dec. 1949.
[7] S. Kawakami, "Koudouharo", Asakura-syoten,
Tokyo, 1980.

0,._~~-.--~~1~=-~1~.5~--~2Frequency(GHz)

Figure 7: Values of wla(=a1) as a function of frequency forthree radii.

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