INFN-MI: StatusINFN-MI: StatusAngelo Bosotti, Nicola Panzeri,

Paolo PieriniAngelo Bosotti, Nicola Panzeri,

Paolo Pierini

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gPlanning

• Milestones :– Report on final tuner design by end 2005– Tuner construction and testing by mid 2006

• Parallel “historical” tuner activity– Started within TTF, now ILC/XFEL – In CARE/JRA1/WP8

• Report in preparation for 1.3 GHz β=1 cavities (Angelo Bosotti)

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gLFD compensation at high gradients (Δν = KL E2)

Stroke

Force

Displ

Structure

Piezo

δmax

Fmax

Evolution of the tuner concept, with integration of the fast LFD action1.3 GHz system under fabrication right now

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gCavity A characterization

JLAB Z501 Tests

1.0E+08

1.0E+09

1.0E+10

1.0E+11

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Eacc

Q

Test #1Test #2Test #3Design

Multipacting Cable failures...

0.177 N/(MV/m)2Lorentz reaction force at boundary

3.7 Hz/(MV/m)2Lorentz coefficient (constrained)

3.7 N/mbarVacuum reaction force at boundary

84.7 Hz/mbarVacuum freq. coeff. (constrained)

-353.4 kHz/mmFrequency sensitivity (longitudinal)

1.248 kN/mmCavity longitudinal stiffness (Kcav)

70 mmStiffening ring radial position

5.88 mT/(MV/m)Bpeak/Eacc

3.57Epeak/Eacc

160 OhmG

180 OhmR/Q

1.34 %Cell to cell coupling

40 mmIris radius

0.47Geometrical β

704.4 MHzDesign Frequency

ValueParameter

Previous estimation [7 Hz/(MV/m)2] only on half-cell geometry, but also, mechanical load condition was overestimated by a factor of 2. Present calculation on the full geometry.

1

X

YZ

-2841

-2453-2066

-1678-1290

-902.697-515.087

-127.477260.133

647.743

JUN 21 200513:45:48

ELEMENTS

PRES

X

YZ

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gWhere did we stand in tests with cavity A?

• Vertical tests: 3 at Saclay, 3 at JLAB

0 20 40 60 80 100 120 140 160 180 200

-3000

-2000

-1000

0

KL = -31

KL = -24

KL = -47

KL = -35

KL = -20

KL = -32

Δν[Hz]

E2acc [(MV/m)2]

Z502 Test #1 Z502 Test #2 Z502 Test #3 Z501 Test #1 Z501 Test #2 Z501 Test #3

Huge spread in static measurements!And off by a factor 10

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gInfluence of boundary conditions

cavext

accLL KK

EFzfKK

+∂∂

+=∞

∞2 • Linear superposition of 2 effects:

Shape deformation (fixed boundary)Cavity shortening (cavity+boundarycombined stiffness)

Analytical derivation of full behavior requires solution of only 2 load cases

-60

-50

-40

-30

-20

-10

0

1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06K ext [N/mm]

K L [

Hz/

(MV

/m)2 ]

AnalyticalANSYS

KL = -3.7Hz/(MV/m)2

KL = -54Hz/(MV/m)2

Cavity stiffness, Kcav

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gCavity frequency response under arbitrary b.c.

• Frequency response of the cavity can be then understood as a function of the external boundary condition

• Using values from the cavity mechanical characterization and Slater perturbation theorem

( )

( )⎪⎪⎩

⎪⎪⎨

⎧

+−=

+−−=

Hz/mbarin248.1

58.13077.84

Hz/(MV/m)in248.1

55.627.3 2

extextP

extextL

KKK

KKK

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gThe RF test frames

Saclay tests in 2004Jlab tests in 2003/2005

Q: Are they sufficiently stiff?

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gJLAB frame

• Cavity is held at He tank disks with a bar– Dish stiffness is greatly reduced!

~ 2.1 kN/mmJLAB load case

40 kN/mmNominal KDsmall

Large tube (FPC) side

~ 2 kN/mmJLAB load case

26 kN/mmNominal KDbig

Large tube (FPC) side

( ) 1kN/mm93.01111 −≈++=DsmallDbigframejlab KKKK

0.93 kN/mmOverall stiffness

~ 2.1 kN/mmHe tank dish, opposite side

~ 2 kN/mmHe tank dish, coupler side

11 kN/mmSupport plates (2)

142 kN/mmTi rods (4)

StiffnessComponent

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gSaclay frame

kN/mm39.2≈saclayK

2.39 kN/mmkframe

Average frame stiffness

0.444 mmMax δz

1.000 kNApplied force

Force load condition

2.536 kNReaction force

1 mmδz

Displacement load condition

A: NO, both are not stiff enough

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gCorrelation with measured KL

-60

-50

-40

-30

-20

-10

0

1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06K ext [N/mm]

KL

[Hz/

(MV

/m)2 ]

Semianalytical modelJLABSaclay

• Mechanical models assume perfect joints and no slack contacts between components– In reality: joints, screws, etc.

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gAlternative check

• From the Saclay data at low temperatures (2.2 to 1.7 K, where the bath pressure is more stable), an average value of Δν/ΔP of -462 Hz/mbar can be evaluated– Kext of 1.15 kN/mm can be estimated, coherent with the model

discussed before

• From the JLab data an average of Δν/ΔP of -1020 Hz/mbar in the same temperature range can be estimated. – Comparable to a nearly “free” cavity behavior (nominal -966

Hz/mbar), with a negligible external stiffness condition with respect to the cavity stiffness, again, coherent with the model discussed before

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gSummary on static KL

• RF test data is understood– Weak constraints for the cavity length– Low beta geometry very sensible to external boundary condition

(low cavity stiffness)

• Behavior of KL agains Kext allows to set tuner stiffness requirements under operating conditions

• Interaction with CEA (GD) has shown a nearly perfect agreement of static LFD modeling– both calculation modes based on Slater perturbation theorem, but

different and independent implementations, especially concerningthe mechanical part of the codes (ANSYS vs CASTEM)

• Planning for dynamic LFD calculations– harmonic analysis + Slater for cavity transfer function and piezo tf– time dependent analysis: overelongation?– need time for the development and check the procedures

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gRequirements for 704.4 MHz

• One of the uncertainties of the piezo materials is still their stroke capabilities at the low operating temperatures

• Assuming a 3 μm stroke to cavity (long piezos)– [safe? SRF/WP8 work in progress]

• a ~1000 Hz frequency offset can be compensated during the fast tuning action

• With a design accelerating field of 8.5 MV/m, this implies that the overall KL in the operating condition should be limited to around -10 Hz/(MV/m)2

– We took a 50% margin for dynamic LFD? [M.Liepe: factor 2]

• In order to achieve this condition with these rather soft cavities the combined stiffness of the He Tank and tuner system needs to provide ~ 10 kN/mm– At 20 kN/mm we are hitting limit with He tank dish stiffness

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gTuner requirements

• Extracting out the Tank and end dish stiffness contribution (total of 15 kN/mm), the requirement for the tuner becomes about 20 kN/mm

15 20 30

ktuner A kNÅÅÅÅÅÅÅÅÅÅÅÅÅmm

E

-12

-11

-10

-9

-8

LK

Actual experimental stiffness including leverage (TTF)

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gOn the road to finalize tuner design

Will ask for bids in late 2005 andOrder main tuner mechanical components before end of year(INFN contribution is available)Then fabrication time will take 4-6 months

Now we are fine-tuning the tuner stiffness by slight adjustments of the blade number length and slope for final optimization before emitting final drawings for Cavity A