measurements on iris-loaded...

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.


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


155

~--------~--~ CAVITY SECTION

FIG.l SLOTTEO IRIS


156

~= 0.55

o 10

o 10 20 30 40 60 70 BANDWIDTH (M,)

FIG. 2


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,


158

~ <J

o I

/ /

-.0 I

t1 (0 I

01

.\0

" /0 ":t • ~

-J il: ..... ~ ~ .... -"> 'q:: \,)

\


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

).... ).... ~~ ....... ~

~


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)


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


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


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)


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


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)


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. )


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.


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


169

EXPLODED VIEW OF ONE CELL SEND HALF CELL

ASSEMBLED FOUR CELL MODEL

FIGURE 10


170

measurements on iris-loaded...

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