JAERI-Research99-018
JP9950180
AN RF INPUT COUPLER FORA SUPERCONDUCTING SINGLE CELL CAVITY
March 1999
Benjamin FECHNER, Nobuo OUCHI, Frank KRAWCZYK*,Joichi KUSANO, Motoharu MIZUMOTO and Ken MUKUGI
B * W 1- ti ffi % P/fJapan Atomic Energy Research Institute
(T319-1195
- ( T 3 1 9 - 1 1 9 5
iotfi) it.
This report is issued irregularly.
Inquiries about availability of the reports should be addressed to Research Information
Division, Department of Intellectual Resources, Japan Atomic Energy Research Institute,
Tokai-mura, Naka-gun, Ibaraki-ken, 319-1195, Japan.
© J a p a n Alomic Energy Research Institute, 1999
JAERI-Research 99-018
An RF Input Coupler for a Superconducting Single Cell Cavity
Benjamin FECHNER*,Nobuo OUCHI, Frank KRAWCZYK*.
Joichi KUSANO, Motoharu MIZUMOTO and Ken MUKUGI
Center for Neutron Science
Tokai Research Establishment
Japan Atomic Energy Research Institute
Tokai-mura, Naka-gun, Ibaraki-ken
(Received February 3, 1999)
Japan Atomic Energy Research Institute proposes a high intensity proton accelerator for the
Neutron Science Project. A superconducting linac is a main option for the high energy part of the
accelerator. Design and development work for the superconducting accelerating cavities (resonant
frequency of 600MHz) is in progress. Superconducting cavities have an advantage of very high
accelerating efficiency because RF wall loss is very small and much of the RF power fed to the cavity
is consumed for the beam acceleration. On the other hand, an RF input coupler for the superconducting
cavity has to be matched to the beam loading. Therefore, estimation of coupling coefficient or external
quality factor (Qext) of the RF input coupler is important for the design of the couplers.
In this work, Qext's were calculated by the electromagnetic analysis code (MAFIA) and were
compared with those by the measurements. A j3 (ratio of the particle velocity to the light velocity)=0.5
single-cell cavity with either axial coupler or side coupler was used in this work. In the experiments,
a model cavity made by copper is applied. Both 2- and 3-dimensional calculations were performed in
the axial coupler geometry and the results were compared. The agreements between calculated and
measured values are good and this method for calculation of Qext is confirmed to be proper for the
design of the RF input couplers.
Keywords: Neutron Science Project, High Intensity Proton Linac, Superconducting Cavity,
RF Input Coupler, External Quality Factor, Time Domain RF Analysis
* STA Research Fellow* Los Alamos National Laboratory
JAERI-Research 99-018
Benjamin FECHNER* • Aft falz • Frank KRAWCZYK*
(Qext)
- KMAF
ial coupler)
It*.
LTft
=0.5
(side coupler)
2 - 4
•)K S T A ' J t - f 7 x D -
JAERI-Research 99-018
Contents
1. Introduction 1
2. Two Dimensional Model of the Single Cell Cavity 2
2.1 Introduction to the Two Dimensional Model of the Single Cell Cavity 2
2.2 Determination of External Q of the Axial Coupler to the Cavity 3
2.3 Optimised Method for the Evaluation of Qext 6
3. Calculations Concerning a Single Cell Cavity using Mafia T3 Time Domain
Solver in Three Dimensions 8
3.1 Introduction to the Model of the Normal Conducting Cavity 8
3.2 Model of the Lossless Cavity in Three Dimensions 8
4. Measurements on a Cavity with an Axial Coupler 15
4.1 Measurements on an Axi-symmetric Normal Conducting Cavity 15
4.2 Comparison of Calculations and Measurements 22
5. The Superconducting Cavity with a Side Coupler 23
5.1 Introduction to the Superconducting Cavity with a Side Coupler 23
5.2 Measurements to Determine the Side Coupler's External Q 24
5.3 Calculation of the Side Coupler's External Quality Factor 27
5.4 Comparison of Calculated and Measured Values of Qext 32
6. Conclusions 34
Appendix
A.1 ATwo Dimensional Model of the Superconducting Cavity 35
A.2 Excitation of the Superconducting Cavity from the Inside 39
A.3 Excitation of the Cavity at Non-fundamental Frequencies 44
A.4 Protrusion of the Coupler into the Beampipe of the SC Cavity 47
A.5 Table of the Side Coupler's External Quality Factor 50
A.6 Literature 51
JAERI-Research 99-018
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IV
JAERI-Research 99-018
1. Introduction
A proton linar accelerator is planned at the Japan Atomic Energy
Research Institute (JAERI). The proton accelerator is designed to
become the centrepiece of both JAERI's Neutron Science Project and
JAERI's actinide transmutation project called OMEGA (Options
Making Extra Gains from Actinides) [1].
While the research and development work on the low energy part of
the accelerator is well advanced and has been described in
numerous publications, the work on the high energy part of the
accelerator has recently lead to the construction of a single cell
superconducting accelerating cavity made from niobium. This cavity
was extensively tested; the results of those tests were given in
[2] . Five such cells are to be comprised in one accelerating
structure where the power is fed through a side coupler.
The side coupler under consideration has a coaxial shape and is
mounted on the beampipe perpendicular to the beam axis. For the
coupler design work, the external quality factor of the coupler
has to be estimated as a function of coupler dimensions in order
to achieve critical coupling. Important parameters are the
diameter of inner and outer conductor of the coupler, the distance
between the cavity cell and the coupler, and the protrusion length
of the coupler's inner conductor tip with respect to the inner
surface of the beampipe.
We have conducted low power measurements on a single cell cavity
made of copper which has the same shape as the superconducting
niobium cavity. In particular we have measured the quality factor
of the coupler. We have complemented the measurements with
calculations of the coupler quality factors in various settings.
We used the Mafia code to conduct the calculations numerically.
Hence, this report is concerned with the comparison of calculated
values of the side coupler quality factor to the values measured
on the normal conducting single cell cavity. We give an account on
how we obtained both the measurement results and the calculation
results, the latter requiring us to proceed through an simplified
cavity geometry with axial symmetry.
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JAERI-Research 99-018
2. Two dimensional model of the single cell cavity.
2.1 Introduction to the Two dimensional model of the single cell
cavity
In order to establish certainty about the predictive power of
calculations using the Mafia code concerning the superconducting
cavity we conduct calculations designed such that the result can
easily be compared to that of measurements.
In the experiment concerning the superconducting cavity, the
geometry of cavity including the axial coupler is axisymmetric.
The axisymmetric cavity includes the same axial coupler which is
used in the low temperature cavity tes t s . Hence, we can use
Mafia's two dimensional time domain solver T2 to perform
calculations and compare the results with measurements. The exact
dimensions of the cavity are given, e.g., in [3]. The wall
material in the Mafia time domain calculations is assumed to be
ideally conductive. The set-up of the cavity in the calculations
as well as the electric field of the fundamental mode are shown in
fig.2.1.
MAUA#ARROW
# 1
(m)
0.236
0.118
00.472 0.945
(m)
Fig. 2.1: Cross section along the beamaxis of the cavity which is used in the calculations. Theelectric field of the fundamental mode is shown as calculated by the Mafia eigenmode solver.
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JAERl-Research 99-018
We have calculated the cavity's scattering matrix using a time
dependent excitation at one port; all results concerning the two
dimensional cavity geometry are reported in Sections A.I to A.4 of
the appendix.
2.2 Determination of external Q of the axial coupler to the cavity
In Section A.4 we report the qualitative result that the coupling
to the fields inside the cavity is improved by increasing the
protrusion of the coaxial centre conductor far into the beampipe.
In this Section we attempt to quantify this coupling in terms of
the external quality factor Qext of the cavity ports. In particular
we shall determine the dependence of Qext on the length of the
protruding centre conductor. We conduct calculations that cover a
time interval of one microsecond.
We vary the length of the protruding centre conductor inside the
beampipe in steps of 20 mm from 120 to 220 mm. During the time
interval of 1 ^s we observe a monitor of the z-component of the
electric field inside on the cavity axis, and we record a voltage
signal that emerges from the cavity port. In fig. 2.2.1 we show
the monitored electric field in a case where the coupler protrudes
the beampipe by 220 mm; see fig. A.4.2 for the same result during
the first 100 ns. It appears that the signal's amplitude drops
exponentially after the excitation of the cavity by the dipole. By
looking at this graph we can read the amplitude of the
oscillations at various times. Various readings of the electric
field inside the cavity, each for a different length of the centre
coupler inside the beam pipe, are given in the table below:
Ez |.t/usec !length/mi
0.120.14|0.16]0.18:0.20!0.22!
005:
74.50;74.2073.8073.40:72.40:71.00
0.10!
74.30:74.0073.40!72.00!69. oo;61.60
0,20]
74.Q0|73.40]72.30J69.10!62.40;47.00!
0,30Ez(relative
73.60;72.60]71.1066,8057.00:35.90
0,40units) ;
.....7.3.50!...71.9069.9064.3051.4027.30
0.60;
73po;71,00]67,40|59.4o!42.30!15.50:
0.80!
72.40!69,80]65-0055,0034.50;
8.70
1,00
71,7068,6063.1051,002.8.604.70
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JAERI-Rcsearch 99-018
MAHA#1DGRAPH
OiOtWIll Kttrrmrn^uwt z
R 1
1 14!
MfCMEAi GttMtlNB
KEOVGMCI CCOtlCIMTK: 7VWW. . . . . . MKHLIME
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ic
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£ CUMfOKBMT Jl1 FUtCTBIC FfaLS
2E^07 4E-07 6E-07time (sec)
8E-07Hi
11i-06
Fig. 2.2.1: The electric field in the cavity. Axial component of the electric field recorded withmonitor Ez. A dipole excites the cavity with a Gaussian enveloped sine oscillation. (Referred toin the Appendix as Case (F) where the centre conductor fully protrudes the beampipe. )
From the field drop, or alternatively from the monitored port
voltage drop, we can calculate the loaded quality factor of the
cavity for each length of the centre conductor inside the
beampipe. The port voltage is
Vport = Vo exp (-oot/2QL) , (1)
where Vo is the initial voltage at t = to, and QL, the loaded
quality factor. The loaded quality factor is a sum:
QL = 1/Qo + Zi 1/Qiext, (2)
where Qo is the cavity quality factor and the sum i = 1..N is
taken over the external quality factors
Since the cavity is lossless, the cavity quality factor Qo is
infinite, i.e.l/Qo = 0 , so that QL is determined entirely by
external Qiext. The cavity has N = 2 ports with Qiext = Q2ext. Hence
the signal drops at twice the rate of that of a cavity with one
port only. In fig. 2.2.2 we show the values of the port's Qext.
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JAERI-Research 99-018
1Q Q faJl-off: L(Uref) = 22.9 mm
105
8
O104
103
Q fall-off: L(Ez2) = 23.5 mm
105 :
N
104 :
0.1 0.15 0.2 0.25
coupler length/m
103
• lit 1
— ^ J
...X-
1 1
Ml
• -
X
0.1 0.15 0.2 0.25
coupler length /m
Figs. 2.2.2: Qext of the axial cavity port determined from the port voltage and the electric field.
We can see that the values of Q themselves appear to increase
exponentially as we shorten the protrusion of the conductor in the
beampipe. This could be due to an exponential decrease of the
evanescent field of the fundamental mode along the beamaxis inside
the beampipe.
We show fig. 2.2.3 in order to test the idea of exponentially
decreasing fields inside the beampipe. The amplitude of the
voltage signal at the port to the cavity is plotted versus the
length of the coupler inside the beampipe. The voltage signal was
recorded immediately after the pulse of the exciting dipole inside
the cavity. Hence, it is proportional to the strength of the
electric field inside the beampipe not yet diminished by the
leakage through the ports. As expected, the amplitude of the
voltage signal appears to decrease exponentially as we shorten the
coupler. Note that the falloff length is twice as large for the
voltage as it is for the Q value, cf. figs. 2.2.2. This is in
agreement with the fact that the power flow through the port
indicated by the Q value is proportional to the square of the
field change.
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JAERI-Research 99-018
Iop.
3
103
102
mi
i ifall-off length:
o
^ ^
4tr^Z.
45.7 mm—
•; : \
^
r**7
:
0.1 0.12 0.14 0.16 0.18coupler length/m
0.2 0.22 0.24
Fig. 2.2.3: Post peak voltage at the cavity port calculated with Mafia's time domain solver intwo dimensions for cases where the length of the axial coupler was varied. Note that the voltageappears to increase exponentially with the protrusion of the axial coupler inside the beampipe.
We conclude that we are capable to use Mafia's time domain solver
in two dimensions to calculate the external quality factor of an
on-axis cavity port. In particular we can estimate its variation
with the coupler tip's distance to the cavity and, thus, we can
extrapolate to very high Q values. Such values, if they were to be
obtained in a simulation, would require that simulation to cover
very long time intervals. We can now continue to conduct
calculations with Mafia's T3 solver in three dimensions.
2.3 Optimised method for the evaluation of Qext
The voltage square is proportional to the power flowing through
the port. The more power flows through the port the smaller is the
value of Qext. We conduct one Mafia calculation in the time domain.
The calculation time is chosen sufficiently long to enable us to
well determine the time constant of the exponential fall of the
field E inside the cavity. We use a configuration of the port with
good coupling in order to benefit from the speedy falloff and thus
the relatively short calculation time.
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JAERI-Research 99-018
The energy W in the cavity is related to the field E:
W ~ |E|2 (3)
After the time t, the field amplitude in the cavity has the
strength:
|E| = |Bo | e-vt (4)
where Eo is the initial field amplitude. We wait for the time x'
for the field to fall to 1/e of the initial value:
|Eo|e-i = I Eo | e-W <=> %' = 1/Y (5)
Note however that after the time x' , the energy has fallen onto e~2
of the initial energy. Hence the x' value found from the fall of
the field inside the cavity has to be halved to determine the
external quality factor Qext of the port: T(W) = x' 12. Q is then
obtained by the relation:
Qext = co • t(W) (6)
The external quality factor is defined by the relation:
Qext := coW/P (7)
where P = dW/dt is proportional to the peak voltage square: |u|2.
We can rewrite equation (5) to obtain:
Qext = a • co/ | U | 2 (8)
where a is proportionality constant. Given the result of one Mafia
calculation, as shown e.g. in fig. 2.2.1, we extract x' from the
field's falloff and Qext from equation (4) . In a corresponding
graph showing the voltage we read the peak voltage and determine a
in equation (6). Once we have established a, we can use equation
(6) in all subsequent cases to calculate Qext on the basis of the
peak voltage U at the port.
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JAERI-Research 99-018
Since it takes only a small way into the time domain simulation to
attain this peak voltage - independent of the coupler's quality -
much calculation time can be saved with respect to the method
where we actually observe the time constant of the cavity field's
exponential decrease. This is particularly important in the cases
of high Qext values where the falloff is very slow and can be well
observed only after a long (calculation) time.
3 Calculations concerning a single cell cavity using
Mafia T3 time domain solver in three dimensions
3.1 Introduction to the model of the normal conducting cavity
This part of the report deals with the normal conducting copper
cavity. This cavity's shape is similar to that of the
superconducting cavity which has already undergone a number of low
power tests, see [3] . The shape of the cavity including the
coupler is axisymmetric. Therefore, it readily lends itself to
numerical modelling in two dimensions. Results of such
calculations, in particular concerning the values of the external
quality factor Qext of the coupler, were shown in the previous
chapter as well as in the appendix.
3.2 Model of the lossless cavity in three dimensions
In this Section we present the results of calculations conducted
in three dimensions using the MAFIA T3 time domain solver. The
excitation of the cavity is achieved by the fields emitted from an
ideal electric dipole positioned approximately in the centre of
the cavity. The time development of the signal is the same as the
one which excited the cavity in the case of the calculations in
two dimensions, cf. fig. 2.2.1.
- 8 -
JAERI-Research 99 0) 8
In order to optimise the calculation time and the usage of work
space we take advantage of the symmetry and calculate only one
eighth of the full brick: first of all, the full cavity is cut in
half in a plane perpendicular to the beamaxis (z-axis) . The
boundary condition at the cut corresponds to that of an ideally
conducting plate in the plane of the cut where only the
perpendicular components of the electric field are non-zero. The
remaining half-cell is twice cut radially. Each boundary in the
plane of the cuts is assumed to consist of ideally magnetic
surfaces in which the components of the magnetic fields vanish.
Thus we are left with one quarter half-cell i.e., one eighth of a
cavity, which is used in the calculations, see fig. 3.2.1.
A ,. ',, Anl An
H3DARROW
r- H S Mc aoo>L 3'iM
a«cn.
I.OE
MIK.I
t
IHTll'l'.UlTI'
A'
ruu-TS I- r r i.
Fig. 3.2.1: Mesh used to calculate the external quality factor Qext of the axial coupler. Thearrows show the direction and the relative strength of the electric field of the fundamentalmode.
Fig. 3.2.1 shows the electric field distribution in the excited
cavity, dominated by the fundamental mode. We can estimate the
frequency of the fundamental mode, f, under the assumption that
the phase velocity is the vacuum speed of light, c. We measure the
distance d between two field nodes on the coupler, d ~ 0.26 m, and
calculate f = 0.58 GHz.
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JAERI-Research 99 018
As a complement to fig. 3.2.1, we also show the distribution of
the magnetic field in fig. 3.2.2. Note that difference in the
radial distribution of electric and the magnetic field: the
electric field is strongest on the beamaxis while the magnetic
field is stronger in the periphery of the cavity. It should also
be noted that the fields were monitored at different points in
time i.e., the electric field shown was monitored approximately at
its respective maximum and so was the magnetic field. Thus, we
establish the result is in qualitative agreement with the fields
of the fundamental mode.
'•/ / Fliu i" ti w
#3DARROW
2X
Fig. 3.2.2: Mesh used to calculate the external quality factor Qext of the axial coupler. Thearrows show the direction and the relative strength of the magnetic field of the fundamentalmode.
In the next step we show agreement between the results of the two
dimensional calculations (see the previous chapter) and the three
dimensional calculations which are subject to the present
discussion. We install a dipole that excites the cavity almost in
the centre of the cavity. In addition, we install a 'monitor' of
the electric field component in the direction of the beam line in
two centimeters distance to the dipole, and another monitor to
record the voltage at the entrance to the port. This set-up is
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JAERl-Research 99-018
almost identical to the one used to document the results of the
calculations in two dimensions. The only difference is that we
cannot install the dipole directly in the cavity centre because -
due to our exploitation of the symmetry of the cavity - the centre
is also a corner point of the numerical mesh.
The cavity is excited by a pulse of Gaussian shape. The recorded
electric field component and the voltage signal at the port are
analysed to obtain the falloff time and thus the cavity quality
factor Qo. As in the previous calculations, we assume the walls
to be infinitely conductive. Therefore, the Q value is entirely
due to losses through the port opening i.e., thus Q is
proportional to Qext. When we evaluate the decrease of the signal
amplitudes over time, we have to bear in mind that the fields
leave the cavity through two ports. To give an example, in figs.
3.2.3 and 3.2.4 we show the amplitudes of the z-component of the
electric field inside the cavity (recorded by monitor Ez), and the
voltage at the port (recorded by porti_out) . In the case shown,
the length of the coupler inside the beampipe was 19 cm.
MAHA#1DGRAPH
riZKD COUtDHUVtt ion . . wnR.cn>
% ir t& TS
(•MB 1* K1O1
F i t * V
nuuMi
ield
o
8
5E+O5-J
4E+05-
3E+05-
T105 •In
1E+05-9H
OE+OO-PPfi0E+00
1 ViMalCSlV) 1 ! . SI • m m , EMC 1
z. oTwanw rr OJKtHK Pitto at v/M
^ 1 12E-07 4E-07 6E-07 8E-07
time (sec)1E-06
Fig. 3.2.3: Typical time dependence of the axial component of the electric field in the threedimensional calculations in Mafia's time domain solver.
- 1 3 -
JAERI-Research 99-018
MAHA• 1DGRAPH
DIM HIM 1 m
LBUK or »om_wr3
fOOTKKNCX COOWTKWW; VVAKI ...MUMLIHB
TO 4SSi iO
m w i i j*/o*^T - lev .0) vnci
BMTUt &n»/M 4.*lMI)«tiiIS41-ai
50-j
40-
i3o B k1 2 0 J H H |
OE+OO jWWiW^^WOE+00 2E-07 4E-07 6E-07
time (sec)8E-O7 1E-06
Fig. 3.2.4: Typical time dependence of the port voltage in the three dimensional calculations inMafia's time domain solver.
fall-off length: 23.2 mm106. , t • , . , ,
MWO
105
104
1030.1 0.12 0.14 0.16 0.18 0.2
coupler Jeng th/m
0.22 0.24
Fig. 3.2.5: Qext versus the length of the axial coupler inside the beampipe. The value of Qext isobtained from the falioff time of the z-component of the electric field inside the cavity, (x)mark the values obtained by a MAFIA calculation in two dimensions, (o) those values resultingfrom a calculation in three dimensions.
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JAERI-Research 99-018
The values for Qext versus the length of the coupler inside the
beampipe which result from the calculations in two dimensions and
the calculations in three dimensions are shown in fig. 3.2.5.
They are in excellent agreement.
However, it should be noted that there is a difference between
these Qext values and those resulting from calculations shown in
the previous chapter, figs. 2.2.2. There, the Qext values are
higher as if the coupler were shorter by almost two centimeters.
One explanation could be that we changed the radius of the coupler
in the beampipe. In the calculation of the previous chapter we
modelled the superconducting cavity (niobium cavity) of which the
coupler radius is 7.7 mm. In the calculations presented here, we
model the normal conducting cavity (copper cavity) of which the
coupler radius is almost one centimeter larger: 17.2 mm.
Measurements on a cavity with an axial coupler
4.1 Measurements on an axi-symmetric normal conducting cavity
In order to validate the results of the calculations presented in
the previous Sections we have conducted measurements on a single
cell cavity similar to the one modelled in the calculations. The
cavity design is shown in fig. 4.1.1. The cavity itself is shown
in fig. 4.1.2.
In order to obtain a full understanding of the cavity's electro-
dynamic properties we have conducted three series of measurements:
First of all, in series (A) we measured the reflection coefficient
at the entrance to the axial coupler while the port to the
beampipe of the opposite side was closed, the situation shown in
fig. 4.1.1. By inserting 'outer conductor spacers' that added to
the length of the outer conductor we in effect varied the length
of the axial coupler inside the beampipe which, in fig. 4.1.1, is
shown on the right side.
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JAERI-Research 99-018
In the second series, (B), we inserted an axial wire probe such as
shown in fig. 4.1.3; this probe, in fig. 4.1.1, would be drawn
protruding through a port on the flanges that close the beam pipe
section on the left side. We measured the scattering parameter
corresponding to the wire probe for varying lengths of the axial
coupler.
In the third series, (C), we varied both parameters, spacer length
and wire length.
53?
Outer conductor spacers
50 ohm n-type adaptor
Fig. 4.1.1: Single cell cavity with axial coupler. One main characteristic is that the 77mmouter conductor of the 50 Ohm feed line can be changed in length by the insertationfrgg++ ofspacers. Thus the protruding length of the center conductor into the beam pipe can be varied.
To evaluate the measurements of series (A) and (B) we determine
the values of cavity Q, denoted by Qo, and the values of Qext of
the coupler, Qext, by an analysis of the impedance curve such as
plotted on the Smith chart in fig. 4.1.4. In order to determine
the frequencies which are required for the extraction of Qo, Qext
and QL, the resonator load has to be moved into 'retuned short'
position. In this position the impedance tends towards zero the
further the frequency is away from the resonance. Hence, in order
to analyze the measured data, the phase of the measured reflection
coefficient has to be offset accordingly.
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cavity beampipe flange 50 Q. line axial coupler
Fig. 4.1.2: Single cell copper cavity with an axia! coupler during the set-up for normalconducting measurements. The flanges between the beampipe and the 50 Ohm feed line can beseen and also the feed line itself. The centre conductor of the feed line is about to be inserted. Itstip will protrude into the beampipe to constitute the axial coupler. The length of the coupler canbe reduced by inserting 'spacers' i.e. additional pieces of outer conductor at the position where,in the picture, the feed Sine is opened.
Fig. 4.1.3: One of the wire probes used in the measurement series (B) and (C).
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JAERI-Research 99-018
t.0
-1.0
Fig. 4.1.4: Smith chart with an impedance curve such as obtained in the measurement series.The values of Q0, Qext and QL are found by division of the resonance frequency by thedifferences If5-f6l, If3-f4l, and If1-f2!, respectively.
In figs. 4.1.5, we show typical curves resulting from such
measurements. The graphs in the box on the left side correspond to
a case of overcoupling (Qext < Qo), and those in the box on right
side correspond to a case of undercoupling (Qext > Qo). Note the
difference in the phase curve of the reflection coefficient in the
cases of overcoupling and undercoupling. At resonance, the phase
in the case of overcoupling does not change while in the case of
undercoupling it changes by n. The respective behaviour of the
coupler is that of a line terminated in an open circuit, and that
of a line terminated in a short ciruit.
- 18 -
JAERl-Research 99-018
0.5
la)
(b)11
A1 Aft: JL.
-0.55.862 5.863 5.863 5.864 5.864
flHz
Figs. 4.1.5: In the boxes typical curves are shown of: the normalized amplitude of the reflectioncoefficient (a), the phase of the reflection coefficient, offset and normalized to n (b), thenormalized real and imaginary parts of the impedance curve, respectively (c) and (d), and thenormalized susceptance curve (dashed line, e). The boundaries which mark the frequencyintervals to determine Qo and Qext are marked respectively (o) and (x). In the box on the leftside we see the case of overcoupling, on the right side we have undercoupling.
In measurement series (B) we first excite the cavity and then we
measure Qext of the coupler. The excitation of the cavity is
accomplished by a thin wire probe inserted axially in the beampipe
opposite to the axial coupler which we wish to examine.
First, we determine Qo of the cavity while the axial coupler at
its entrance is terminated in a short circuit (Qo = 22602). Then
we connect the measurement cable to the axial coupler. Thus, when
we use the wire probe to measure the value of Qo', this value
corresponds to the combined effect of the cavity Qo plus that of
Qext of the axial coupler. Both quantities contribute to the losses
that are expressed by Qo' . Hence, we can extract Qext from Qo' :
1/Qext = 1/Qo' - 1/Qo. (1)
During the measurement series (B) we measure Qext for various
lengths of the coupler inside the beampipe. The results of these
measurements are shown in fig. 4.1.6. As a reference, we plot the
results for Qext obtained from the (phase-shifted, but otherwise
uncorrected) reflection coefficient of the axial coupler, i.e.,
measurement series (A) . The falloff length of the coupling
obtained from these measurements is 18.6 mm. Note that the results
of the measurement series (B) agree well with those of series (A).
-19-
JAERI-Research 99-018
external Q of axial coupler
&
105
104
1 1
Mil
iiiiii i i
s : : : : : : : : : :
11 1
J
" fr
::::::::::::#:::I:*!::::
:::
* . .
: : : : : : : : : :
. .„. . . . ,
: : : : : : : :
x- •i
: : : £ : : :
•if
i ; $ i ; i ; ; • • •; • =
;
: : : : : : : : : : : : : : : :
0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12spacer length: z/m
Fig. 4.1.6: Results of measurement series (A) and (B). Qext of the axial coupler is plottedversus the length of the coupler spacers. Long spacers cause the coupler to be short inside thebeampipe. The values measured in (A) (reference values) are plotted with (x). They wereobtained by offsetting the phase of the coupler reflection coefficient. The values plotted with(*) were obtained from Qo'(QO, Qext), measured with a wire probe opposite to the axialcoupler.
Finally, we conduct the measurement series (C) to see whether the
length of the wire probe would have any significant effect on the
results for the falloff length and the absolute values of Qext of
the axial coupler.
The length of the wire probe is chosen such that its coupling is
approximately critical. Hence, a reduction of the length of the
axial coupler (by the insertation of longer spacers) requires the
wire probe to be shorter as well. In Fig. 4.1.7 we show which
combinations of wire length and spacers are used in the
measurement series (C) . The rate of change is Alenwire/Alenspacer ~ -
0.9; however, it should be noted that this linear approximation
can only be valid over a small range of wire length (we chose 75
to 100 mm to obtain the value stated above). The reason for this
limitation is the dependence of the measured Qo' not only on the
external quality factor of the axial coupler but also on the Qo of
the cavity as expressed in equation (1).
- 20 -
JAERI-Research 99-018
0.220.21
0.20.190.180.170.160.150.1J
•x *
i
* * • • -x-
04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12spacer length 1/m
Fig. 4.1.7: Combinations of wire length and spacer length used in measurement series (C). Thelength of the wire probe was reduced in step with the increase of length of the spacers on theaxial coupler such that the coupling of the wire probe was approximately critical.
The values for Qext obtained in the measurements of series (C) are
shown in fig. 4.1.8. They are in good agreement with the results
of the reference measurement shown in the same graph. The falloff
length of the coupling is 1 = 15.6 mm. Thus, we have established
the equivalence of the various methods, (A) , (B) and (C) , to
measure the value of Qext of the axial coupler that is best
regarded as a probe.
^ 06 external Q of axial coupler
x&
105 :
104 =
103
rTiT
m
-;:::::::;:
iiiiii
- i
;;;;;;;;;;;;
; ; • • ; • • ; ; ; ; ;
r
jiiim::::!1
;;;;;;;;;;;;
I.....T.....
;;;;;;;;;;;<
f
;;;;;;;;;;;j
&
o
0.04 0.05 0.06 0.07 0.08 0.09 0.1spacer length: zlm
0.11 0.12
Fig. 4.1.8: Results of measurement series (C). Qext of the axiai coupler is plotted versus thelength of the coupler spacers. Long spacers cause the coupler to be short inside the beampipe.The reference values are plotted with (x). The values obtained for a variety of wires with theirlength being different are plotted with (o).
- 21 -
4.2
JAERI-Research 99-018
Comparison of calculations and measurements
In the previous chapters we presented the results of coupling
calculations obtained using the MAFIA time domain solver. In
Section 4.1 we reported the results of measurements conducted to
determine the value of the external quality factor Qext of an axial
coupler in a single cell cavity. In this Section we compare the
results of calculations and measurements.
Fig. 4.2.1 shows the results of both the calculations and the
measurements. The figure shows that the agreements between
calculated and measured results are very good. The coupling
falloff lengths of the external quality factor as the coupler tip
were estimated from the calculations and measurements to be 17.8
mm and 17.3 mm, respectively, which are also in good agreement.
10*
icr
104
10
external Q of axial coupler
I ' ' ' ' r
I I I I I I I I I I I I I I I I I
0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12
Spacer length (m)
Fig. 4.2.1: Qext of the axial coupler versus the length of the outer coupler spacers. Themeasurement results are marked (x), the results obtained from calculations with Mafia's two-and three dimensional time domain solvers are marked with (o).
- 2 2 -
JAERI-Research 99-018
5 The superconducting cavity with a sidle coupler
5.1 introduction to the superconducting cavity with a side coupler
In chapter 4 we have established the agreement of measured and
calculated values of Qext in the case of the axial coupler. However
the ultimate goal is to determine, for a design value of Qext, the
shape and position of a side coupler, which will be applied to the
actual accelerator system. For this reason, to show the agreement
between measured and calculated values of Qext in the case of a
side coupler shall be the aim of this section.
beampipe flange cavity side coupler beampipe spacers
Fig. 5.2.1: Single cell copper cavity with a side coupler for normal conducting measurements.Between the cavity and the beampipe a flange can be seen. The side coupler is connected per-pendicularly to the beampipe. Its distance to the cavity can be modified by changing the ioactionof spacers from the endplate, as shown on the right, to the flange between cavity and beampipe.
- 2 3 -
5.2
JAERI-Research 99-018
Measurements to determine the side coupler's external Q
For the purpose of the measurements on a side coupled cavity we
modified the copper cavity, shown in fig. 4.1.2, which we used for
the axial coupler measurements. The modified cavity is shown in
fig. 5.2.1. The coupler, familiar to us from the axial coupler
measurements, is now fixed on the beampipe perpendicular to the
cavity axis. This is shown in the drawing of fig. 5.2.2. For a
view of the coupler from the inside of the cavity see fig. 5.2.3.
The beampipe is cut off the cavity. The connection between the
cavity and the beampipe is made by flanges. Note that the distance
of the side coupler to the cavity can be varied by inserting rings
between the cavity and the beampipe. The spacers which are not in4use' are inserted between the beampipe and its endplate in order
to keep constant the length of the beampipe from the cavity to the
endplate.
Fig. 5.2.2: Single cell copper cavity with a side coupler for normal conducting measurements.We denote the direction of the beamaxis (the on-axis distance) 'z'. The perpendicular directionpointing into the beampipe is called 'y'. Note the reference positions on z and y axis: z =0 at theiris on the coupler side of the cavity where the beampipe flange is welded to the cavity; y = 0 atthe wail of the beampipe on the side of the pipe where the coupler is welded onto the beampipe.
- 24 -
JAERI-Research 99-018
cavity nange siae coupler oearrppe
Fig. 5.2.3: Inside view of the single eel! copper cavity and the beampipe with a side couplerprepared for norma! conducting measurements. The flanges between the cavity and thebeampipe are a bit hard to see. In the text, we frequently refer to the 'on-axis' distance of thecoupler to the cavity. This distance is indicated in the picture by the double flesh.
Concerning the opposite side of the cavity, there the beampipe is
not modified with respect to the set-up used during the axial
coupler measurements. As in those measurements, a wire probe is
mounted on the beamaxis. The Hewlett Packard network analyzer is
connected to a wire probe which is excited by the analyzer's
signal (port 1). The transmitted signal is picked up from the side
coupler and recorded by the analyzer (port 2). The evaluation of
the measured data is done as discussed in chapter 4 in order to
extract the values of cavity Qo, Qext of the wire probe, and
ultimately the external quality factor of the side coupler.
Note that our set-up of the side coupled cavity permits us to vary
both parameters, the length of the coupler i.e., the distance of
the coupler tip to the wall of the beampipe, and the on-axis
distance of the coupler to the cavity, cf. figs. 5.2.2. and 5.2.3.
The measurement results of Qext of the side coupler are presented
below. In fig. 5.2.4 we show the values obtained (for several
settings of the coupler length) while the coupler's on-axis
distance is varied. In fig. 5.2.5 we show the values obtained (for
several settings of the on-axis distance of the coupler) while the
coupler length was varied i.e., the distance of the coupler tip to
the wall of the beampipe.
- 25 -
JAERI-Research 99-018
108
107
&
105 :
104
X
+
rm
*
X
• : : : : : : : o : : : : ;
* :
X
+
: : : : Q : : : : : : :
. «
.X
"4
»••: : -
X"
::::::::::$::
o
::::«:::::::
: : : :^: : : : : : :
Liii
O
uli
80 85 90 95 100 105
coupler distance to cavity (zlmm)
110 115
Fig. 5.2.4: Measured values of external quality factor Qext of the side coupler to the normalconducting cavity versus the on-axis distance of the side coupler to the cavity. The radialdistance of the side coupler's tip to the beampipe wall is (y/mm): 40 (o), 20 (+), 0 (x), and-20 (•).
-20 -10 0 10 20 30 40
side coupler tip distance to beampipe vail (ylmm)
Fig. 5.2.5: Measured values of external quality factor Qext of the side coupler to the normalconducting cavity versus the radial distance of the side coupler's tip to the beampipe wall. Theon-axis distance of the coupler to the cavity is (z/mrn): 80 (*), 88 (x), 96 (+), 104 (o),and 112 (•).
- 26
JAERI-Research 99-018
Note that in fig. 5.2.4 we observe an exponential rise of the
coupler's Qext value when the coupler's on-axis distance to the
cavity is increased. The rate of increase does not depend on the
actual length of the coupler tip. Moreover the falloff length of
the coupling (X = 15.4 mm) appears to be in reasonable agreement
with the results obtained in the course of measurements on the
axial coupler (X' = 17.3 mm), cf. chapter 4.
We turn our attention to fig. 5.2.5 which shows the dependence of
the coupling on the length of the coupler i.e. the distance of the
coupler tip to the wall of the beampipe. We distinguish between:
a) the cases where the coupler is protruding sidewise into the
beampipe, and b) those where the coupler is recessed inside the
feed line; the latter are those cases where the distance between
the coupler tip and the beampipe wall is negative.
Concerning the cases a) we do not observe an exact exponential
drop of Qext when the coupler tip is extended towards the beamaxis.
However, in the cases b), where the tip is well recessed in the
feedline, the values of Q can be interpreted to rise exponentially
as the distance between the coupler tip and the beampipe wall is
increased. Under the assumption of an exponential dependence on
the coupler length in b) the falloff length is X" = 8.4 mm.
5.3 Calculation of the side coupler's external quality factor
For the purpose of the calculation of the value of the external
quality factor Qext of the cavity we use a three dimensional grid,
shown in fig. 5.3.1, which is similar to the one used in the case
of the axial coupler, cf. fig. 3.2.1. Note that the side coupler
can easily be accommodated without an enlargement of the grid
block. Rather, the block has become smaller as the feedline on the
cavity axis is omitted. Note that the ratio of coupler fraction to
cavity volume is half a coupler in one eigths of a cavity (axial
coupler: a quarter coupler in one eighth cavity). Hence, the
falloff time of the field inside the cavity is calculated four
times too short and we have to multiply the corresponding Q value
by a factor of four in order to obtain Qext of one side coupler.
- 2 7 -
JAERI-Research 99-018
Fig. 5.3.1: Grid used to calculate the external quality factor Qext of the cavity. To fully exploitthe rotational symmetry (apart from the side coupler), the grid comprises one eighth of thefull cavity and one half coupler. The arrows indicate the direction of the electric field of thefundamental mode.
We optimise the calculation method which was applied in the case
of the axial coupler, cf. chapter 4. Once we establish the
relation between the falloff time of the field inside the cavity
and the peak voltage at the port to the cavity the optimisation is
achieved by obtaining Qext in all further calculations from the
maximum voltage amplitude U at the port of the feedline. See
Section 2.3 for a detailed account of the full Q evaluation
method.
We have conducted an extensive series of calculations while
scanning both parameters, the on-axis distance of the side coupler
to the cavity and the distance of the coupler's tip to the wall of
the beampipe. The results are shown in fig. 5.3.2. Note that we
can observe the coupling to decrease exponentially with increasing
on-axis distance of the coupler to the cavity. The falloff length,
X - 16.4 mm, is independent of the coupler setting.
- 29 -
JAERI-Research 99-018
109
xo
104
: : : ! : ! : : : : : : j? : : : : : : : : : : : : \% i i i : : : : : : : : : : j : : : i : : : : : £ : : 1 1 | : : ! : : : : : : : : i : f : : ! : : T T T T T T T T T : ! : : : : : : : : : : :
• : • • • • • : • ; • ; • : : ; ; : ; : ; ; ; ; ; ; ; : • • • • • : • • ; • • • •
J • • • • • • • : • • • : • < • :::>:::::•;•••:•:>:;••••:;•::•
:::::::::':::: r::::::::::::: r::::::::::;::
80 90 100 110 120 130 150
z/mm
Fig. 5.3.2: Values of Qext calculated for the side coupler mounted on the beampipe versus theon-axis distance of the coupler to the cavity. The results correspond to various settings of thecoupler. The distance of the coupler tip to the wall of the beampipe is (y/mm): 40 (*), 20(x), 0 (+), and -20 (o).
Xa>O-
105
104-20 -10 10 20 30
z/mm50
Fig. 5.3.3: Values of Qext calculated for the side coupler mounted on the beampipe versus thedistance of the tip of the side coupler to the wall of the beampipe. The results for various on-axis distances of the side coupler to the cavity are shown (z/mm): 65 (•), 50 (*), 35 (x), 20(+), and 5 (o).
- 31 -
JAERI-Research 99-018
In fig. 5.3.3 we show the same calculation results, however, the
values of Qext are plotted versus the distance of the side coupler
tip to the wall of the beampipe. We distinguish between: a) the
cases where the coupler is protruding sidewise into the beampipe,
and b) those where the coupler is recessed inside the feed line;
the latter are those cases where the distance between the coupler
tip and the beampipe wall is negative.
Concerning the cases a) we observe a decreasing rate of drop of
Qext when the coupler tip is extended towards the beamaxis.
However, in the cases b) , where the tip is well recessed in the
feedline, the values of Q can be interpreted to rise exponentially
as the distance between the coupler tip and the beampipe wall is
increased. Under the assumption of an exponential dependence on
the tip distance to the wall b) the falloff length is X' = 9.3 mm.
5.4 Comparison of calculated and measured values of Qext
We now shall compare the results of measurement and calculation,
discussed in Sections 5.2 and 5.3, respectively, concerning the
value of external quality factor of the side coupler to the normal
conducting cavity. In fig. 5.4.1 we show the values of the coupler
Qext for various settings of the coupler length. Note that the
agreement within the uncertainty of the measurement is very good
over the full range of the coupler distance.
Considering the results, we should also bear in mind that there is
still room for more precise measurements by narrowing the
frequency band in which the network analyzer excites the cavity.
Concerning the calculations we can easily afford to refine the
grid at the cost of higher calculation times because of the
introduction of the peak port voltage reading method, discussed in
Section 2.3.
- 3 2 -
JAERI-Research 99-018
109
109
107
106,=
105
104
• • • • • ; ; ; ; ; =
= • • • : • • • ? { • <
imn
£ x<i:::::::*:'I
; ; • : ; ; ; ; ; • ; ; !
I : : : : : : : : : : :
:::::x
X (
P l i l l l l l l l l l
x . . J9
j i i l i i i x : : : '
' • ; : : : : : : : i : > : : : : : : : : : : : : 1
: : : : : : ; : : : : r : : : : : : : : : : : :
• x t» X H>n::::::!:::t::::!:::::::::::::::::: :::::::::::::
• ic ia *
> X 7l l l i l i l i l l i H i l l i i l l l l i l
':s..lits,:::..Lx ::J
m
::::::::::::
• • • • • • • : : : : :
x-\Mi!;;!;!;;!
* * •
! : : : : : : ! : : : :
; : : : : : : : : « :
f..
; • • • • • • • • ; • •
: : : : ! : i : : : : :
; ; ; ; ; ; • ; • • • •
: : : : : : : : : : : :
. : : : : : : : : • : :
> y
! : : : • : : : : : : :
:::: M ::::::
;:::x:::::5::::::::::::
• : : : : : : : : : : 1J ; ; • -
• • • • ; • : • • • ; =• : : : ! : : : : : : :
i l l l l l l l i i l i
>
: :::: s'.:::::::::::
80 85 90 95 100 105 110 115 120
on-eocis distance of side coupler to cavity z/mm
Fig. 5.4.1: Measured (x) and calculated (o) values of Qext of the side coupler obtained forvarious settings of the coupler tip distance to the wall of the beampipe (y/mm): 40 (a), 20(b), 0 (c), and -20 (d); the negative distance in (d) corresponds to the case where the tip isrecessed inside the feedline of the side coupler.
However, more refined methods of either measurement or calculation
are hardly required for we have well established the falloff
lengths corresponding to the parameters which enter the design
considerations: the distance of the side coupler to the cavity and
the protrusion of the coupler tip into the beampipe. Furthermore,
the fact that, in the calculation, we fully exploit symmetries to
keep the size of the grid small does not appear to have any
noticeable effect onto the validity of the resulting Qext values.
Perhaps an exception to this rule are those cases where the
coupler tip protrudes close to the beamaxis. The coupler in such
cases 'sees' its mirror image which in the true geometry, of
course, is not implemented. We reckon that the tip's protrusion
has to exceed 30 mm into the beampipe for the mirror effect to
become noticeable. However, such far protrusion has little
practical relevance.
- 3 3 -
JAERI-Research 99-018
Conclusions
Using the time domain solvers of Mafia, we have calculated in two
and three dimensions the quality factor Qo of a single cell copper
cavity of the superconducting high beta section of the accelerator
which is proposed for the Neutron Science Project of the Japan
Atomic Energy Research Institute (JAERI) by the Proton Accelerator
Laboratory group.
We have calculated, using Mafia's time domain solvers, the Qext
values of an axial coupler in the beampipe to the accelerator
cavity. Moreover, we have calculated the Qext values of a side
coupler mounted onto the beampipe to the accelerator cavity.
Measurements were conducted in all cases and the calculation
results were found to agree well with the measured values. Hence,
we have established the Mafia calculation, in particular of the
side coupler's external quality factor, as a valid tool that can
be reliably applied to establish certainty about the electrical
qualities of a side coupler under design for the accelerator.
- 3 4 -
JAERI-Research 99-018
Appendix
A.1 A two dimensional model of the superconducting cavity
The cavity constitutes a two-port. We would like to calculate the
scattering parameters using Mafia's eigenmode solver. In order to
do so we choose the time dependence of the input signal in
accordance with the Mafia instruction manual i.e.,
f (t) = sin(an) sin(an/2) • 0.75 • 3 for 0 < an < 2%, or
f(t) = 0 otherwise,
where co = 4JC fres and x = t in the case. We begin the pulse at the
start of the simulation. The pulse length is one oscillation
which, however, is not just sinusodial. The exciting signal i.e.,
the forward voltage at port one, U^or, is shown in fig. A.1.2. Its
duration is that of a half cycle of the resonance frequency, which
is less than one nanosecond.
Parts of the coaxial feedlines on either side of the cavity are
included in the simulation area. The signal Uref returning at the
entrance to the coaxial feedline and the signal transmitted
through the cavity and obtained up at the pick-up exit Utrans is
shown in figs. A.1.3 and 4, respectively.
Concerning the output signal Uref we note, first of all, that a
time delay At occurs between the input signal and the reflected
signal. Assuming that waves in the coaxial waveguide propagate
without dispersion at the vacuum speed of light we can obtain the
length 1 of the coaxial guide: 1 = c At/2 » 0.195 m which is in
good agreement with the programmed value (l'= 0.18 m plus the tip
length of 0.02 m inside the beampipe). Secondly, we note that the
amplitude of the reflected signal at port one is falling off
during the observed time interval. Nevertheless, we are able to
observe the signal for a much longer time span than the duration
of the input oscillation. In order to estimate the frequency of
the "reflected" signal we simply count the number of peaks and
divide by the observed timeinterval: festimate = 53/(3e-8 - 0.25e-8)
Hz ~ 1.9 GHz which is well above the fundamental resonance of the
cavity at approximately 580 MHz.
- 35-
JAERI-Research 99-018
MAFIA#1DGRAPH
0.5-
OE+00-
-0.5-
OE+00 5E-10 1E-09 1.5E-09 2E-09 2.5E-09 3E-09time (sec)
Fig. A.1.2: The pulse signal we use in Mafia's time domain solver to excite the cavity.
MAHA#1DGRAPH
TITO. COCASl
V I
OE+00
-0 .5-
OE+00 5E-9 1E-08 1.5E-08 2E-08 2.5E-08 3E-O8
time (sec)
Fig. A.1.3: The signal reflected at the exciting port to the cavity.
- 3 6 -
JAERI-Research 99-018
MAFIA• K S AMVl ITOK Hi
#1DGRAPH
PtUD COCCI'<«*TKS:5E-02-
0E+00
-5E-02-
-0.10E+00 5E-9 1E-08 1.5E-08 2E-08 2.5E-O8 3E-08
time (sec)
Fig. A.1.4: The signal transmitted to the port opposite to the exciting port of the cavity.
MAHA41DGRAPH
UTOIHMVi ijllMl
VWiO ';(k.ia.iKATiei;
AteCtuif,: (.(ATtiKI.I' .!"•'i n , : i r r v i iu i i
VMIV. . . . . . HlWIl.lNK
11 -
0.8-
0.6-
0.4-
0.2 i
OE+00OE+00 5E+08
1
1E+09 1.5E+09
frequency (Hz)
2E+0S
A
) 2.5E+O9
Fig. A.1.5: The scattering parameter S11 of the cavity with short axial couplers.
- 37 -
JAERI-Research 99-018
In fig. A.1.5 the amplitude of the scattering parameter sn is
shown. Note the absence of resonant absorption at the frequency of
the fundamental cavity mode. Apparently, "knocking onto" the
cavity with a short pulse does not lead to an excitation of the
fundamental mode. We assume the value of Qext of the fundamental
mode, Qfundext, is much higher than the corresponding value of the
i-th higher order mode (HOM, hence QiH0Mext) . Consequently, it takes
a longer time to fill the cavity with field energy corresponding
to the fundamental mode than it takes in the case of the HOM.
Thus, we expect that the overwhelming part of the energy provided
by a short pulse should be stored in HOMs with low Qext values. In
particular, we bear in mind that the fundamental mode does not
propagate in the beampipe. The coupling to the fundamental mode
should therefore be much reduced with respect to the coupling to
such HOMs which propagate in the beampipe.
In order to check our assumptions we extend the tip of the inner
conductor of the coaxial feed line well into the beampipe as shown
in fig. A.1.6. We repeat the excitation with the same signal as in
the case discussed previously, see fig. A.1.2.
MAFIApSs.ouNjv.Ji2--: I ' ' r
TIMS ilftBMOfrr •3I.KTHC
HARROW
(m)
0.236
0.118
0 0.472 0.945(m)
Fig. A.1.6: The cavity with long axial couplers and the electric field of the fundamental mode.
- 38 -
JAERI-Research 99-018
MAHA#1DGRAPH
55£ 0.6-
0.4 -
0.2 -
0E+000E+00 5E+O8 1E+09 1.5E+09
frequency (Hz)
2E+O9
Fig. A.1.7: The scattering parameter s11 of the cavity with long axial couplers.
The amplitude of sn is shown in fig. A. 1.7. We can clearly see a
peak in the absorption spectrum at 580 MHz. As a result we note
that the inwards prolongation of the centre conductor of the
coaxial cable through all the beam pipe close to the cavity itself
leads to an excitation of a mode at the fundamental frequency.
A.2 Excitation of the superconducting cavity from the inside
In Section A.I we discussed the excitation of the cavity by a
pulse fed via one of the coaxial feed lines. Now we examine the
response due to an exciting electric dipole placed inside the
cavity. We observe the voltage signals which emerge from the
cavity. We stick to the practice to label the signals "reflected"
while bearing in mind that the signal source is inside the cavity:
hence the "forward" voltage signal on either port is zero because
no voltage wave is incident to the cavity.
In this Section we examine the cavity with the probe tips in their
standard recessed position while in the following Sections we
- 3 9 -
JAERI-Research 99-018
shall discuss the cavity with the tips protruding far into the
beam pipe. We conduct two kinds of calculations. The difference
between the calculations is the shape of the signal exciting the
cavity. We observe the component Ez of the electric field in the
direction of the cavity axis. To do so we install "monitors" on
the beamaxis. In Mafia, monitors can record the values of field
components as the calculations proceed in time.
MAFIAPKMtti 4 J1/3V»1 - 15'. I )
0 .4OM4000MUOOBHKI
#1DGRAPH100
13
0E+00-
-1000E+00 2E-09 4E-09 6E-09
time (sec)
8E-09 1E-08
Fig. A.2.1: Component of the electric field in the axial direction recorded with monitor Ez whenthe cavity is excited with a pulse signal by the dipole in the centre of the cavity.
Signal shape A) is a single oscillation (T < 1 ns) such as used in
the previous Section, cf. fig. A.1.2. The single oscillation ex-
cites the cavity over a broad frequency spectrum. In fig. A.2.1 we
see how the perturbation of the pulse (see signal at t < 0.8 ns)
causes the field Ez to oscillate. We perform the Fourier
transformation of the signals to obtain the frequency spectrum of
the oscillating field. The spectrum of the field in the frequency
range from 0 to 2 GHz is shown in fig. A.2.2. Note that spikes at
580 MHz and at 1260 MHz indicate the presence of resonances.
- 4 0 -
JAERI-Research 99-018
MAFIA#1DGRAPH
OftDIIMTS: BX3AM_TU
TTJV3 CTOROINUKS;DIM KKSHMM
[SWZt OF n U N _ r U ] ~"
VMTt KHKLMnm u
TO * H J 1
1
ampl
1E-05 -j
8E-06-
•
6E-06-
4E-06 -
2E-06-
OE+00 5E+O8
«™'«r
L1E+09 1.5E+09
frequency (Hz)2E+09
Fig. A.2.2: Fourier spectrum of the electric field component recorded with monitor Ez.
MAHA#1DGRAPH
M B . . . HKbULlNK
1
1
0.5-
-0.5-
0E+00 5E-09
^ A/- vy
1E-08
MuU MtrUtVOC IN
AM
1.5E-08time (sec)
ill-
2E-O8 2.5E-O8 3E-08
Fig. A.2.3: The Gaussian signal we use in Mafia's time domain solver to excite the cavity.
- 4 1 -
JAERI-Research 99-018
MAFIA AIIWAMU. OMMR
Ci» w,Tn-f "* FT1LI) I
tlDGRAPH
2000
1000-
0E+00
-1000-
-2000OE+00 2E-08 4E-08 6E-08 8E-O8 1E-07
time (sec)
Fig. A.2.4: Axial component of the electric field recorded with monitor Ez. A dipole excites thecavity with a Gaussian enveloped sine oscillation.
MAMA#1DGRAPH
I 9-«Do«+li*, a JWiflO]
( 9 ooim.oo, Q.iOM-ai]Mscidiut! iMtunat / . ] (
! 0.0001*40, a.3DM*10] tade
ampl
i
Ih-u4 -
8E-05-
6E-05-
4E-05 -
2E-05-
OE+00
VKBICW1V)32 0]
A/A5E+O8 1E+09
frequency (Hz)1.5E+09 2E+09
Fig. A.2.5: Fourier spectrum of the electric field component recorded with monitor Ez. A dipoleexcites the cavity with a Gaussian enveloped sine signal.
- 42 -
JAERI-Research 99-018
MAFIA umi tva.
#ARROW
•I 3.00DO. 9.3MW)
SI 0.179H, 0.7MMI
ITIHtmm.... ,;
(m)
0.236
0.118
00.180 0.472 0.765
(m)
Fig. A.2.6: Electrical field in the cavity after the excitation by an electric dipole.
Signal shape B) is that of a Gaussian shaped wave package (tpeak <
10 ns) where the frequency is the resonance frequency of the fun-
damental cavity mode. Such a wave package is shown in fig. A.2.3.
The monitored signal is shown in fig. A.2.4. After the Gaussian
dipole signal (i.e., t > 15 ns) we can still observe an oscil-
lating field of the same amplitude. Fourier transforms of the
signal (at two positions inside the cavity) are shown in fig.
A.2.5. The cavity field oscillation after the end of the dipole
excitation can be seen as little "spikes" at 580 MHz. Note that
the Gaussian package does not significantly excite the cavity at
any frequencies other than 580 MHz.
In order to determine the mode we record the full electric field
inside the cavity (and the adjacent beampipe) at 80 ns. At this
time, the electric field can be seen to be at maximum, cf. fig.
A. 2.4. The full field in the cavity is shown in fig. A.2.6. It
looks similar to that in the space between the parallel plates of
a capacitor. Thus, we know to have excited the cavity at the
fundamental TMoio mode. The field is strongest on the beamaxis and
weakest in the periphery of the cavity. In particular, it should
- 43 -
JAERI-Research 99-018
be noted that the strength of the field appears to drop off to
negligible strength in the extremities of the beampipe. We see
that the probe couplers do not really get "in touch" with the
field. As stated in Section A.I, the fields inside the beampipe
are evanescent. This is why coupling an external signal to the
TMoio mode of the cavity is so difficult.
A.3 Excitation of the cavity at non-fundamental frequencies
In Section A. 2 we discussed the excitation of the cavity by
different types of signals emitted from a dipole placed in the
center of the cavity. In this Section we shall complement our
observations by calculating the cavity time response when the
dipole oscillates at frequencies other than the resonance of the
fundamental TMoio mode.
Earlier, we noticed the existence of another resonance than that
of the TMoio mode at a frequency of approximately 1260 MHz, cf.
fig. A. 2.2. Now, we shall excite the cavity at this higher
frequency in the same way as in Section A.2, case B), where the
envelope of the signal was chosen Gaussian. Likewise, we observe
the z-component of the electric field inside on the cavity axis
with Mafia's field monitor.
The monitored field is shown in fig. A.3.1. The time development
of the field proceeds in the way which is already familiar to us
from the calculations at the fundamental mode: At first the
Gaussian shaped dipole signal dominates the observed fields.
However, after the vanishing of the pulse the cavity can be seen
to oscillate at the resonance frequency of the mode.
As a complement we calculate the Fourier spectrum of the voltage
signal emitted from the coaxial ports of the cavity, see fig.
A. 3.2. The resonance is clearly visible in the spectrum. In
addition, we monitor the complete electric field in the cavity at
t = 80 ns. This field is shown in fig. A.3.3. The fact that the
field lines lie parallel to the cavity axis supports the assump-
tion, stated in Section A.2, that the resonance at 1260 MHz
corresponds to the TM020 mode.
- 44 -
JAERI-Research 99-018
MAFIAcaoaam or njEntc rino IN V
K1DGRAPH
USCJ 8S*: OaCHTTMI|BL» at nil
2000
1000-
"OE-KX)
-1000-
-2000OE+00 2E-08 4E-08 6E-08 8E-O8 1E-07
time (sec~>
Fig. A.3.1: Electrical field in the cavity recorded by Ez. An electric dipole excites the cavitywith a Gaussian shaped sine signal at 1260 MHz.
MAFIAttlDGRAPH
2E-10
DUt M
OE+00OE+00 5E+08 1E+09 1.5E+O9 2E+09
frequency (Hz)
Fig. A.3.2: Fourier spectrum of the port voltage when the cavity is excited with a Gaussianenveloped sine signal at the frequency of 1260 MHz.
- 4 5 -
JAERI-Research 99-018
Fig. A.3.3: Electrical field in the cavity after the excitation by an electric dipole at 1260 MHz.
MAFIAs OOWUMMT =r s u i m i c
#1DGRAPH200a
TO 135»>
-2000OE+00 2E-08 4E-08 6E-O8 8E-O8 1E-07
time (sec)
Fig. A.3.4: Electrical field in the cavity recorded by Ez. A dipole excites the cavity with aGaussian shaped sine signal at 950 MHz.
- 46 -
JAERI-Research 99-018
So far, we have shown the results stemming from an excitation of
the cavity at one of its resonances. What happens if the dipole
oscillates at a frequency well apart from a resonance? In order to
answer this question we conducted a calculation where the dipole
oscillates at approximately 950 MHz. The resulting field at the
monitor Ez in the time domain is shown in fig. A.3.4. We can see
the Gaussian envelope of the dipole signal. However, no
significant excitation of the cavity can be observed. Compare this
result to figs. A.2.4 and A.3.1 where the cavity is shown when
excited at its TMoio and TM020 resonances, respectively.
A.4 Protrusion of the coupler into the beampipe of the sc cavity
In Section A. 3 we discussed the excitation of the cavity at
frequencies higher than that of the fundamental mode. At these
frequencies we could observe a tiny voltage signal at the ports to
the cavity resulting from leakage through the coaxial opening, cf.
fig. A.3.2. In this Section we examine the effect of a protrusion
of the centre conductors of the coaxial lines into the beampipe
while the cavity is excited at the resonance frequency. Note that
we have already briefly discussed such a protrusion earlier, when
we calculated the broadband frequency response of the cavity, cf.
Section A.I.
The case similar to the experiment, where the centre conductor of
the coaxial line protrudes only two centimeters into the beampipe,
cf. fig. A.2.6, serves as reference case, labeled (R) . In this
Section, we calculate the case (H) where the centre conductor of
the coaxial feed protrudes by 12 cm i.e., half of the length of
the beampipe, and the case (F), where the conductor protrudes by
22 cm i.e., almost the full beampipe length. In figs. A.4.1 and
A.4.2 the outgoing voltage signal is shown for cases (H) and (F);
mind that, in the reference case (R) , we could not observe any
output signal. Note also that the different scale in figs. A.4.1
and A.4.2: the scale of the graph corresponding to case (F) is ten
times larger than that of case (H).
- 47 -
JAERI-Research 99-018
In case (H) the port signal rises as long as the dipole pulses
inside the cavity (t < 15 ns) . Then its amplitude appears to
decrease slightly (approximately by 1 % in 80 ns). However, the
signal in case (F) where the conductor protrudes the beampipe
almost at full length, first of all, is stronger by almost one
order of magnitude and, secondly, after the time (t < 20 ns) where
the signal's amplitude rises, it appears to decrease markedly (by
almost 20 % in 80 ns). Moreover, we can see that the rate of the
signal's decrease, itself, drops with time, exponentially.
Hence, we conclude that coupling to the fields inside the cavity
is, indeed, improved by the increased protrusion of the centre
conductor into the beampipe. The port voltage signal is in
agreement with the assumption that the field inside the cavity
should drop exponentially as it leaks outside. Concerning the
quality factor Qext of the cavity ports, in order to establish
quantitative results, calculations are needed that cover a longer
time interval than the one observed here (100 ns).
MAFIA#1DGRAPH
3E-O3-
2E-O3-
-2E-03-
-3E-03
i in
0E+00 2E-08 4E-08 6E-08 8E-08 1E-07
time (sec)
Fig. A.4.1: Case (H) where the centre conductor protrudes half of the beampipe. Port voltagewhile the cavity is excitated by an electric dipole at 580 MHz.
- 4 8 -
JAERI- Research 99-018
MAFIAwoe* Mcniiun ut '
ttlDGRAPH
3E-02
VAKI
TO 131
-3E-024OE+00 2E-08 4E-08 6E-08
time (sec)
8E-O8 1E-07
Fig. A.4.2: Case (F) where the centre conductor fully protrudes the beampipe. Port voltagewhile the cavity is excitated by an electric dipole at 580 MHz.
- 4 9 -
JAERI-Research 99-018
A.5 Table of the Side Coupler's External Quality Factor
Values of Qext of the side coupler to the accelerator cavity
z/mm
80
84
88
92
%
100
104
108
112
80
85
90
95
100
115
130
145
y/mra -20
experiment
9423874
14277533
13114172
22846861
37932836
Mafia calculation
8634645
11625541
15710207
21200964
52056362
128629363
325352260
-15
5181329
7426610
4030678
4643520
6905889
9298612
12561461
-10
2342947
2838601
4286075
4126801
6811152
10991863
2313726
2894161
3961483
5345834
7183486
17621724
43514869
110494230
-5
1171621
1620660
2354703
2345987
3821964
6118884
1726472
2281404
3085988
4137920
10141396
25113683
63383727
0
781324
1214167
1354384
1319458
2256803
3524936
5820490
773598
959405
1320823
1776668
2391868
5942139
14529081
36846023
10
260583
331127
506547
489724
798544
1287313
2129656
339191
417917
581163
788546
1073299
3154184
6708118
17305645
20
117262
138908
210143
216739
351295
552975
892061
141264
176217
244272
330206
444167
1115802
2804886
7183486
30
57207
69085
107633
58186
72555
97532
132496
179465
40
30461
36284
54367
57890
89419
143569
230750
36152
45221
61068
82551
112195
276236
679920
1740595
50
18042
20307
34086
23467
31891
43264
58360
79001
- 50 -
JAERI-Research 99-018
A.6 Literature
[1] N. Ouchi et al., "Proton Linac Activities in JAERI", Proc. of
the 8th workshop on RF Superconductivity, Abano Terme, Italy 6-10
Ocotber 1997
[2] N. Ouchi et al. R&D Activities for Superconducting Proton
Linac at JAERI, Proc. of the first Asian Particle Accelerator
Conference, Tsukuba, Japan, 23-27 March 1998
[3] N. Ouchi et al. , "Design and development work for a
superconducting proton linac at JAERI", Proc. of the 8th workshop
on RF Superconductivity, Abano Terme, Italy 6-10 October 1997
[4] MAFIA The ECAD System Operation Manual, The Mafia
Collaboration, 9. December 1996 (http://www.cst.de)
- 51 -
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