1 LANL2G.doc

Dale Schrage, MS H817Richard LaFave, MS H8175-0029/5-2904LANSCE-1:01-002January 11, 2001rpl@lanl.gov

SUBJECT: Structural and RF Analysis of LANL 2 Gap, 350 MHzSpoke Resonator Cavity

Introduction:

As requested, a combined structural and RF analysis of the LANL 2-gap, 350MHz spoke resonator has been performed. This memo summarizes the modelpredictions for maximum end flange deflections and reaction forces during tuning, cavitystress and deflections under vacuum loads, and resonant structural frequencies. Inaddition, predictions for shifts in resonant RF frequency are presented. The resultsshown in Tables 1 through 4 summarize the model predictions for the various conditionsconsidered. Material properties are listed in Table 5.

Models:

Figures 1, 2a, and 2b show external and a section views of the cavity. Figures 3aand 3b show the section views along with some dimensions to indicate the overall sizeof the cavity. Although Figure 3a shows the annular stiffener diameter as 26 cm, 24 and28 cm diameters were also considered. Four models of the spoke resonator have beenconstructed for MICAV and COSMOS/M. The first is a solid model of the RF volume thatis used to predict RF resonant frequencies, while the three remaining models are shellmodels of the cavity structure with the various annular stiffener diameters mentionedpreviously. The structural models were constructed such that the resulting nodaldisplacements could be imposed directly on the RF volume model, resulting in resonantRF frequency shift predictions for the deformed geometries. Figures 4 and 5 show themesh used in the RF volume model while Figures 6 and 7 show the structural mesh forthe 26 cm diameter annular stiffener model. Material properties were taken as theambient temperature niobium properties listed in Table 3 of LA-UR # 99-5826 and arereproduced in Table 4.

The RF model was meshed with four node tetrahedral elements resulting inproblems with approximately 60,000 elements while the structural models were meshedwith three node shell elements resulting in problems with approximately 10,000elements.

Boundary Conditions:

Two sets of boundary conditions were imposed on each of the three structuralmodels to simulate two methods of tuning the cavities. In the first the annular stiffenersare fully constrained while a fixed deflection is imposed on each of the bore tube end

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2 LANL2G.doc

flanges. In the second the fixed deflection is imposed on both the annular stiffeners andthe bore tube end flanges. The amount of the fixed displacement was varied until theresulting peak stress reached the level specified in Table 1 of 7000 psi, correspondingto the yield point of room temperature niobium. Since the model was linear this trial anderror procedure was trivial.

The cavities were also analyzed under vacuum loading conditions. In thesecases both bore tube end flanges and both annular stiffeners were fully constrained while2X atmospheric pressure (29.4 psi) was applied to all external surfaces.

Lastly the cavities were also analyzed in order to predict resonant structuralfrequencies. In these cases, as with the vacuum loading cases, both bore tube endflanges and both annular stiffeners were fully constrained.

Results and Discussion:

Results for each tuning sensitivity case considered are shown in Table 1. In aneffort to test the MICAV RF predictions, similar simulations were run for the ANL 2-gapcavity for which some experimental results are available. Table 2 summarizes theMICAV predictions for the ANL cavity as well as some of the experimental resultsobtained by Tsuyoshi Tajima, Robert Gentzlinger, and Alan Shapiro. It should be notedthat the MICAV RF predictions show good agreement with available data. This is asignificant benefit since in the past MICAV has only been tested against other computercodes without the benefit of experimental data.

The maximum tuning sensitivity of 46 KHz/mil occurs with the 24 cm diameterannular stiffener although there is not a large difference in the sensitivity between thevarious sizes of stiffeners. As the table indicates, the significant improvement in tuningsensitivity occurs when driving the annular stiffener along with the bore tube end flangeas opposed to fixing the stiffener. Figures 8 and 9 are typical of the stress anddisplacement plots for the case when the stiffener and end flange are driven together.

Table 3 lists the results for the vacuum loading cases and indicates peakstresses with 2X atmospheric pressure of 5181 psi, 74% of the room temperature yieldstrength of niobium. As the table indicates there is not a significant difference betweenthe various sizes of stiffeners. Figures 10 and 11 are stress and displacement plots forthe vacuum loaded 26 cm diameter cavity. These figures show that the areas of peakstress are in the spoke and not on the cavity exterior, so they are not affectedsignificantly by the size of stiffener.

Table 4 summarizes the resonant structural frequency predictions and indicates avery stiff structure with the lowest structural resonant frequency predicted to be 270 Hz.

Summary:

A structural analysis of the 2-gap, 350 MHz spoke resonator cavity has beenperformed in order to determine maximum end flange deflections and flange reactionforces during tuning, cavity stress and deflections under vacuum loads, and resonantstructural frequencies. The analysis indicates that there is not a significant variation inperformance with stiffener diameter over the range considered, however a significantimprovement in tuning sensitivity can be realized by moving the annular stiffeners with

3 LANL2G.doc

the bore tube end flanges. This improvement stems from the larger endwall deflectionsthat can be imposed on the structure in this configuration before peak stresses reach7000 psi.

Fig

ure

1: E

xter

nal V

iew

of L

AN

L 2

Gap

Cav

ity -

Sol

idw

orks

Fig

ure

2a: S

ectio

n V

iew

of L

AN

L 2

Gap

Cav

ityF

igur

e 2b

: Sec

tion

Vie

w o

f LA

NL

2 G

ap C

avity

Figu

re 3

a: L

ater

al C

avity

Sec

tion

View

with

Dim

ensi

ons

All D

ims

cm.

Figu

re 3

b: L

engt

hwis

e C

avity

Sec

tion

View

with

Dim

ensi

ons,

All

Dim

s cm

.

Figu

re 4

: RF

Volu

me

Mes

hFi

gure

5: R

F Vo

lum

e M

esh,

Cut

away

Vie

w

Figu

re 6

: Stru

ctur

e Sh

ell M

esh

Figu

re 7

: Stru

ctur

e Sh

ell M

esh,

Cut

away

Vie

w

Figu

re 8

: Von

Mis

es S

tress

Plo

t, 26

cm

Stif

fene

r, St

iffen

er a

nd F

lang

e m

ove

toge

ther

= 70

00 p

si

= 58

67 p

si

Figu

re 1

0: V

on M

ises

Stre

ss P

lot,

26 c

m D

iam

eter

Stif

fene

r, 2X

Vac

uum

Loa

d, C

utaw

ay V

iew

Figu

re 1

1: D

ispl

acem

ent P

lot,

26 c

m D

iam

eter

Stif

fene

r, 2X

Vac

uum

Loa

d, C

utaw

ay V

iew

= .0

0471

in

Annu

lar

Stiff

ener

Tota

lPe

akD

ispl

acem

ent

Dis

plac

emen

tR

FR

FEq

uiv

Stiff

ener

Boun

dary

Rea

ctio

nVo

n M

ises

(Eac

h En

d)(E

ach

End)

Res

onan

tFr

eque

ncy

Tuni

ngTu

ning

Sprin

gD

ia.

Con

ditio

nFo

rce

Stre

ssFr

eque

ncy

Shift

Sens

itivi

tySe

nsiti

vity

Stiff

ness

(cm

)(lb

s)(p

si)

(m)

(in)

(MH

z)(K

Hz)

(KH

z/m

il)(K

Hz/

lb)

(lb/m

il)

28M

oves

With

Fla

nge

1701

7000

0.00

0339

0.01

3335

0.71

4139

-602

.565

-45.

148

-0.3

542

127.

450

28Fi

xed

457

7000

0.00

0140

0.00

5535

1.17

4658

-142

.046

-25.

845

-0.3

108

83.1

5126

Mov

es W

ith F

lang

e16

4970

000.

0003

610.

0142

350.

6712

64-6

45.4

40-4

5.40

4-0

.391

411

6.00

026

Fixe

d40

270

000.

0001

390.

0055

351.

1758

57-1

40.8

47-2

5.66

4-0

.350

473

.248

24M

oves

With

Fla

nge

1662

7000

0.00

0368

0.01

4535

0.64

9922

-666

.782

-46.

076

-0.4

012

114.

847

24Fi

xed

399

7000

0.00

0139

0.00

5535

1.17

7459

-139

.245

-25.

370

-0.3

490

72.6

97

MIC

AVM

easu

red

COSM

OS/M

Erro

rRe

sona

nt Fr

eque

ncy (

MHz

)33

9.69

9401

338.

8214

950.

26%

Tunin

g Se

nsitiv

ity (M

Hz/in

)9.

356

11.3

221

.03%

Stru

ctura

l Stiff

enes

s (lb/

mil)

34.3

644

.429

.22%

(KHz

/lb)

0.27

20.

255

6.35

%

Tabl

e 1:

Stre

ss a

nd D

efle

ctio

n D

urin

g Tu

ning

Unp

ertu

rbed

RF

Res

onan

t Fre

quen

cy =

351

.316

704

MH

z

Tabl

e 2:

AN

L 2

Gap

Cav

ity R

esul

ts

4 LANL2G.doc

CC:K. C. Chan, APT/TPO, MS H816P. Colestock, LANSCE-9, MS H851J. Delayen, JLABR. Garnett, LANSCE-1, MS H817R. Gentzlinger, ESA-DE, MS H821D. Gilpatrick, LANSCE-1, MS H817W. B. Haynes, LANSCE-9, MS H851A. Jason, LANSCE-1, MS H817J. P. Kelley, LANSCE-1, MS H817F. Krawczyk, LANSCE-1, MS H817P. Leslie, LANSCE-1, MS H817M. Lynch, LANSCE-5, MS H818W. Lysenko, LANSCE-1, MS H817M. Madrid, AR/TPO, MS H816T. Myers, Advanced Energy SystemsJ. Rathke, Advanced Energy SystemsB. Rusnak, LLNLD. Rees, LANSCE-5, MS H818E. Schmierer, ESA-DE, MS H821J. D. Schneider, APT/TPO, MS H816S. Schriber, LANSCE-1, MS H817R. Sheffield, APT/TPO, MS H816K. Shepard, ANLH. V. Smith, APT/TPO, MS H816T. Tajima, LANSCE-1, MS H817R. Valdiviez, LANSCE-1, MS H817T. Wangler, LANSCE-1, MS H817R. Wood, LANSCE-1, MS H817K. Zeroonians, SRACLANSCE-1 Reading File, MS H817