measurements on iris-loaded...
TRANSCRIPT
October 22, 1963
MEASUREMENTS ON IRIS-LOADED WAVEGUIDES
S. Giordano Yale University
This report deals with some preliminary measurements
of iris-loaded waveguide structures, when these structures
are operated as v-mode standing wave accelerators.
The parameters considered are the shunt impedance
per unit length (R), bandwidth (BW) , and tank flatness. s
This paper discusses some preliminary meaSU'L'cments of
the above parameters, in an effort to establish design
criteria.
Table I lists the various parameters of the three
types of iris-loaded structures considered. All cal
culations and measurements are for the v mode. The
shaped irises are based on the calculations of R. L.
Gluckstern.(l) The waveguide with flat irises is of
the type usually referred to as a "standard disk-loaded
structure." The slotted structure has four radial slots
as shown in Fig. 1. An improvement in the shunt impedance
was obtained with the addition of nose cones. In all
three structures, the center hole was 2 in, and outer
wall diameter, 10 in. The operating frequencies of
the various structures were between 800 and 900 Mc/sec,
but all measurements shown in Table I are scaled to
880 Mc/sec.
The test model was made of unit cells, which were
held together with tie rods. The unit cell length was
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
153
~ R s
Q *
6f **
BW
~ R s
Q *
6f **
BW
TABL
E I
SHA
PED
IR
IS
FLA
T IR
IS
SLO
TTED
IR
IS
Calc
ula
ted
M
easu
red
C
alc
ula
ted
M
easu
red
C
alc
ula
ted
M
easu
red
.55
.5
5
· · ·
.5
5
· ·
· .5
5
12
.3 M
O/m
12
Mn/
m
· · ·
1
2.3
MO
/m
· ·
· 1
3.8
MO
/m
19
,00
0
18
,50
0
· ·
· 1
9,0
00
·
· ·
19
,00
0
136
kc/s
ec
140
kc/s
ec
· · ·
138
kc/s
ec
· ·
· 14
6 k
c/s
ec
. . .
+
2.7
Mc/
sec
· ·
· +
5.2
Mc/
sec
· ·
· -2
5.0
Mc/
sec
1.1
·
· ·
· ·
· ·
· ·
1.1
37
M0/
m
· · ·
·
· ·
· ·
· 30
M
0/m
31
,00
0
· ·
· ·
· ·
· ·
· 2
0,0
00
86
kc/s
ec
· ·
· ·
· ·
· ·
· 80
kc/s
ec
. .
. ·
· ·
· · ·
·
· ·
-11
. 3 M
c/ s
ec
* 6
f is
th
e
freq
uen
cy p
ert
urb
ati
on
of
a 1
/4 in
d
iam
eter
met
al
sph
ere
at
the
cen
ter
of
a si
ng
le c
ell
.
** B
W is
th
e
ban
d w
idth
defi
ned
h
ere
to
be
the d
iffe
ren
ce in
fr
equ
ency
bet
wee
n
the
"0"
mod
e an
d t:h
e 1T
m
ode.
T
he
(+)
sig
n is
a
forw
ard
w
ave,
and
the
(-)
sig
n is
a
bac
kw
ard
wav
e.
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
154
designed for r3 = 0.55, and by stacking two such cells
together, a cell for r3 = 1.1 was obtained. Spring
rings were used to obtain electrical contact.
For the slotted iris, a plot of bandwidth vs. slot
angle is shown in Fig. 2, and the corresponding shunt
impedance vs. bandwidth is shown in Fig. 3. The values
for the slotted iris cavity listed in Table I are for
the optimum values of shunt impedance.
Also of interest in the case of the slotted irises,
are the radial field variations. Both metal and di
electric spheres were pulled radially across the cavity.
The electric field perturbation of the dielectric
sphere was scaled to match the electric field pertur
bation of the metal sphere. Figures 4 and 5 are plots
of the radial field taken along two different direc
tions. The difference between the two curves is propor
tional to the magnetic field squared. A rotatable pertur
bation device was used to give a more accurate measure
ment of the circumferential field variation. At a
radius of 0.75 in, measurements were made at various
points along the length of the cell, and within the
accuracy of the measuring equipment, the circumferential
variation was less than 5%.
Tank flattening refers to the variation of electric
field along the axis of the tank due to the tuning errors.
These tuning errors are the results of machining tolerances,
temperature variations, etc. It would be useful to obtain
an analytic functional relationship relating the tuning
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
155
~--------~--~ CAVITY SECTION
FIG.l SLOTTEO IRIS
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
156
~= 0.55
o 10
o 10 20 30 40 60 70 BANDWIDTH (M,)
FIG. 2
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
157
/4
13
~ ~ 12
~ ~ I
~ II ° /
~II\
/0
o 10
/0" I \ I \ I \ I \ I
\ I I '0
° ,
I , "
40
Flo. 3
~ = 0,55
"-" 0 .........
"'-- --0
60 70 BANOW/Oil-l M,
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
158
~ <J
o I
/ /
-.0 I
t1 (0 I
01
.\0
" /0 ":t • ~
-J il: ..... ~ ~ .... -"> 'q:: \,)
\
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
159
...... .....,
~ ....J
~
~ q: ~
~ ~ \j <::)
-.1"" ~lli ~l'
I
~
"'~ I
V')\lJ
~
~....J
~
tQ~ .. \J
~
...... I~ \f')
I
~
I
't... I
" "l I
~ , ..... 0, • .. ,
" ~ ~
to ~~
-i:::
..oJ ~
V)~
....., G:
~~
~ ....,q ~llJ ~CQ
).... ).... ~~ ....... ~
~
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
160
error to the properties of a structure, as has been
done for a hollow cylindrical structure in the TM010
mode. (2) For iris-loaded structures the problem becomes
extremely complex. The following is an experimental
approach to the problem, in which various measurement
techniques are used to derive an empirical relation
ship.
The tuning errors along the length of a cavity can
be written as a Fourier series.
F(z) = n1rZ (1 + Pn cos L ) , (1)
where L is the length of the cavity and f is the o
resonant frequency. Corresponding to the tuning error,
there is an electric field variation, which can be
written as
co
E(z) = E \' (1 n1rZ ) o~ + €nCOS L
n=l
(2)
where E is the average electric field along the length o
of the cavity. We now want to find a functional rela-
tionship between P and € , depending on the particular n n
structure being considered. We first define the
following function
en = K F(L) G(n) Pn ' (3)
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
161
and by various measurements show that Eq. (3) is valid
and derive the quantities K, F(L), and G(n).
PICKUP LOtJPS
PERTUR8ATION TUNER.5
F/G,G In Fig. 6 is shown a cavity with 7 shaped irises,
matched pickup loops and perturbation tuners in each
cell. Figures 9 and 10 are photographs of the assembly.
Operating at a frequency of 880 Mc/sec in the 1f mode
at t3 = 0.55, the structure has a bandwidth of 2.7 Mc/sec
and a Q of 18,500. (Bandwidth is defined here to be
the difference in frequency between the O-mode and the
1f-mode.) An rf drive loop was placed at the center
of the cavity, and the tuners were adjusted to make
the field flat (all eight pickup loops had the same
output reading). From a previously determined tuning
curve, the tuners were adjusted to obtain a first
harmonic variation of the frequency along the cavity as
in Fig. 7a. Figure 7b shows the variation of the electric
field along the cavity, as measured at the pickup loops.
From Fig. 7 we get the relations: PI = !:If/fo and
E:l = !:lE/Eo· Repeating the process for the 2nd, 3rd, and
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
162
o I o
(A) L
(8) FIr,. 7
4th harmonics, and substituting in Eq. (3), we obtain
€:l K F (Ll ) G(l) 4550 = = Pl
82 K F(Ll ) G(2) 2180 = = P2
83 K F(L
l) G(3) 1140 = = P3
84 K F(L
l) G(4) 825 - = = P4
where Ll = 0.80 m, the length of a seven-iris cavity.
The above values can be approximately represented by
the following relations:
E: n
P = K F(Ll ) G(n) n
(4)
L
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
163
Since Ll is a constant for all of the above measure
ments
G(n) 1 1.2
n (5)
We now want to determine the dependence on L of
the function F(L). Consider a cavity of some arbitrary
length L. The tuners are adjusted so that the fre
quency varies linearly along the cavity (i.e., has the
shape of a ramp function) as shown in Fig. 8a. Figure
8b shows the corresponding electric field variation in
the cavity. With the ramp-function variation, Eq. (1)
~ ---
It (A) (8)
Flu ~
may be written as
[ 7rZ 1 37rz
F(z) = fo 1 + Pl(cos ~ +:z cos L '3
1 57rz ] + 52 cos L + . . .) (6)
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
164
We have previously shown, from Eqs. (4) and (5) that
8 Ip ~ 1/n1
.2
, and may therefore write Eq. (2) as n n
[ 11"Z 1 311"z+
E(z) = Eo 1 + 8 1 (cos ~ + 33.2 cos L
1 511z J + 53 . 2 cos L + ... ) (7)
At z = L, Eqs. (6) and (5) become
F(L) f [1 + PI (1 1 1 )] = +-+--;;-+ . . .
0 ~2 r:"-j .J
= f + 6f 0
(8)
E(L) E [1+c1 (1 1 1 )] = +- + 53 . 2 + . . .
0 33.2
= E + 6E 0
(9)
where 6F and 6E are shown in Fig. 8.
From Eqs. (8) and (9) we may write
Af PI (1
1 1 ) f +-+ -+ . . . P 0 32 52
1.18 ~ (10) = ~
AE (1 1 1 ) 8
1 81
+ ---1 --"- -I- . . . E 33.2 53 . 2
0
z=L
From Eq. (4), for n = 1 and z = 1, we get
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
165
F(L) = 1 1 - . Substituting Eq. (1) in (11) we obtain
F(L) = 1.18 (~)
K (~f) o
For four different cavity lengths of 0.80, 0.70,
0.60, and 0.50 meters (corresponding to 7, 6, 5, and 4
irises, respectively) , the tuners were adjusted to pro
duce a ramp function frequency variation with 6f = 68 kc/sec. For each of the four cavity lengths, the
electric field along the cavities was plotted, as
shown in Fig. 8, and the values of E and 6E were o
found. Substituting the value of E , 6E, f and 6f o 0
in Eq. (12) we obtain: F(0.80) ~ 4800, F(0.70) ~
3460, F(0.60) - 3000, and F(0.50) - 2000. The above
F(L) values can be represented by the following
approximation:
F(L) ex: L2
Substituting Eqs. (5) and (8) into (3) we get
L2 € =K
3-P
n 1.2 n n
The independent numerical results from Eq. (3) can
now be substituted in Eq. (14) to evaluate K .
(11)
(12)
(13)
(14)
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
166
Equation (14) becomes
e: = n
7500 L2 1.2
n p
n (15)
The above measurements were made with a low-level
signal generator (5 mW). With the calibrating equip
ment available, t~e probes and detectors may have an
error of 5 to 10%.
It is interesting to note that for the narrow
bandwidth (2.7 Me/sec) structure measured above, the -1 2 higher order harmonics go as (n) '. Similar measure-
ments were made on a structure having a bandwidth of
40 Me/sec, and it was found that the higher order
harmonics varied as (n)-2. It would be interesting to
run a series of measurements on structures of different
bandwidths, to evaluate the function
e: n
= K H(BW) F(L) G(n) p R(BW) n
n (16)
Unfortunately, time has not permitted this to be done.
Equation (15) clearly indicates the extreme tuning
and stability requirements of the narrow band structure
considered. Using short sections would obviously help
the tank flattening problem but would increase the total
number of individual cavities required. Another big
improvement can be obtained with wider bandwidth struc
tures, which would reduce the value of K3
.
(The discussion following this paper has not been
reproduced. )
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
167
References
(1) Gluckstern, R. L., Proceedings of the 1961 Inter
national Conference on High Energy Accelerators,
p. 129.
(2) Alvarez, L. W., et ale R.S.I., February 1955,
p. 116.
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
168
A SHAPED I RIS FOR f3 = 0.6 AT f = 880mc/s. THE HOLE DIA IS 2.111". THE STEEL SCALE IS 6"LONG. NOTE SPRING RING AT 10.125 DIA
FULL SPACER SECTION FOR {3= 0.6. AT LOWER LEFT IS AN ADJUSTABLE TUNER. UPPER 8& LOWER RIGHT ARE COUPLING LOOPS
FIGURE .9
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
169
EXPLODED VIEW OF ONE CELL SEND HALF CELL
ASSEMBLED FOUR CELL MODEL
FIGURE 10
Proceedings of the 1963 Conference on Proton Linear Accelerators, New Haven, Connecticut, USA
170