Update on LHC 800MHz Crab Cavity Conceptual Design

Liling Xiao, Zenghai LiAdvanced Computations Department, SLACPresented at LARP-CM12, April 9, 2009

L. Xiao, Z. Li, CM12

Baseline Design (CM11) Cell Shape Optimization : (R/Q)_T, Bpeak

Baseline Design (CM11)Cell Shape OptimizationCell_l = 187.5 mm, R_disk = 70mmVT > 2.5MV, Maximum kick gradient limited by BpeakOptimize disk parameters for optimal Epeak and BpeakSquash or racetrackSquash ratio:0.8


TM110-pi modeE-fieldB-fieldTESLA TDR cavity peak fields for comparison (Eacc: 25-30MV/m):

Ep=50-60MV/m, Bp=107-128mTCrab Cavity RF Parameters

Frequency800MHz(R/Q)_T117ohm/cavityDeflecting Voltage VT2.5MVDeflecting Gradient Ekick6.67MV/mEpeak25MV/mBpeak83mTMode separation (Opt.-SOM)89MHz


Strongly damps unwanted modes in a compact structure because no cutoff for TEM mode in the coax

Node at the electric field rejects operating mode in the vertical planeLOM/SOM Coax-to-Coax Designd


There are two additional LOM modes due to the coupling of the cavity modes to the coaxial beampipe TEM modes. Coupler can be optimized to achieve Qext less than 100 for LOM/SOM with a smaller gap.Gap=10mmQext vs. Coax Position


Chart3

160.129155.613905.8431083.6796.5766

169159511636123.611739

224192261323180.681

294236188223224.787

434331149166280.9069939

1039.231802.561444114.731118.589431.937822

LOM-1

LOM-2

LOM-3

LOM-4

SOM

coaxial tube position d (mm)

Qext

l=300mm

one-celld2=65mm, d1=60mmtwo-cell w couplerd2=65mm, d1=60mmdz=150mmdepth=5mm

L=400mmpi-modebp-modeHOM-modeL=300mmpi-modeLOM1LOM2SOM

L=300mmpi-modebp-modeHOM-modedffQextfQextfQext

df0598.9647618603.30715549894.7344326

290799.9814954.295025600.02965823603.88678843893.8874883

250799.9830954.325050600.188357217604.03393210893.7666390

200799.9827951.1540?75

175799.9722877.2053955.1785100

150799.8685825.8720955.4832125

135798.8067804.5053955.8370150

125800.7576790.0846956.1510

115800.5145779.4513956.5429

100800.5081765.5646957.2996

75800.7431747.0513959.1609

50801.2509732.5261961.8771silo

25802.1704720.3054964.1903Qext re.LOM

Damp the dipole modes at the horizontal plane and reject the operating TM110 mode at 800MHz.

A two-stub antenna instead of the coupling loop is proposed.LOMOpt.HOM Coupler Design


There is significant coupling of input power to the LOM/SOM couplers in this baseline designDrawback in Baseline Design


Alternative Design Input coupler is between of the two cells to avoid the cross coupling Coax TM110-pi coupler rejects operating mode using field symmetry. LOM/SOM couplers reject operating mode using electric field node. HOM coupler rejects operating mode using filter.


LOM/SOM couplers reject operating mode using electric field node. Field symmetry is very important.The center conductors of LOM/SOM couplers will be slightly bent so that the rotating flange can adjust the tips of the center conductors to lie exactly along the E-field node of the operating mode field.Rejection of Operating Modeshift


Chart1

130000000

180000000

260000000

6700000000

9200000000

4000000000

280000000

60000000

larger LOM/SOM dimensions

LOM/SOM center conductor shift (mm)

Qext at LOM/SOM coupler

Operating mode's coupling at LOM/SOM coupler

filter

hook-filter

gap=0.55mmA(0,1)S12(dB)

Frequency7800000000.0001116514-79.0427195557

Frequency7825000009.51E-05-80.4404464401

Frequency7850000007.60E-05-82.3782945864

Frequency7875000005.40E-05-85.3600431971

Frequency7900000002.74E-05-91.2385147962

Frequency7925000006.64E-06-103.5553110145

Frequency7950000005.74E-05-84.8216903945

Frequency7975000000.0001699371-75.3942337646

Frequency8000000000.0125009088-38.0611682364

Frequency8025000000.0001530315-76.3043848623

Frequency8050000003.12E-05-90.1221164799

Frequency8075000002.90E-05-90.7481731315

Frequency8100000007.56E-05-82.4327042256

Frequency8125000000.0001181157-78.5538481921

Frequency8150000000.0001599546-75.9200640734

Frequency:7600000000.0001195621-78.4481264618

Frequency:7650000000.0001228528-78.2122969147

Frequency:7700000000.0001224008-78.2443121796

Frequency:7750000000.0001197623-78.4335957788

Frequency:7800000000.0001159939-78.7113005658

Frequency:7850000000.0001123816-78.9860962675

Frequency:7900000000.0001118886-79.0242813691

Frequency:7950000000.0001281756-77.8438927268

Frequency:7950000000.0001281756-77.8438927268

Frequency:8000000000.0027248777-51.293059597

Frequency:8050000001.12E-05-98.9899461084

Frequency:8100000002.96E-06-110.5629269469

Frequency:8150000003.80E-06-108.4134315812

Frequency:8200000001.68E-05-95.5030688255

Frequency:8250000003.32E-05-89.5838585753

Frequency:8300000005.21E-05-85.6586957362

0

filter

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

node

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Qext-dd=18.75mm

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

filter

fopt-d

small LOM/SOM couplerbig LOM/SOM coupler

shiftQextatLOM

-55.90E+05

-2.59.40E+05

02.20E+06

2.59.50E+064.81.30E+08

4.52.70E+084.91.80E+08

4.85.80E+0952.60E+08

4.97.70E+105.16.70E+09

55.80E+095.24.60E+085.159.20E+09

5.51.90E+085.24.00E+09

6.52.80E+075.252.80E+08

7.51.20E+075.56.00E+07

~

fopt-d

00

00

00

00

00

00

00

00

0

0

0

Qext for small LOM/SOM coupler

Qext for big LOM/SOM coupler

center conductor shift (mm)



lomsom-d

0

0

0

0

0

0

0

0

0

0

0

Qext for TM110-0 mode

center conductor shift (mm)



00

00

00

00

00

00

00

00

0

0

0

smaller LOM/SOM dimensions

larger LOM/SOM dimensions

LOM/SOM center conductor shift (mm)



damping results

bp__l=125mm

dd=15mmdd=18.75mmFc=1.47GHzD=22.5mm

fQextR/QfQextR/Qopt-dQextR/Q

578035774.90151.0044.30591150000.00196.8665.92598622671.60579.12129.20

578268315.20152.6241.90591233000.00191.7569.50598657350.50571.63143.88

607471797.20683.2860.80611038000.00253.9022.32621615194.80119.0913.39

607522812.40681.0797.00611070000.00245.9938.74621623477.90115.668.66

1.44E+091.94E+032.60E+01mono

1.45E+092.15E+032.14E+01mono

R/Q_T

884088000.00105.633.05

884097000.0098.6430.18

904252000.00111.522.05

909577000.00107.5033.01

985632000.00134.0316.01

996500000.00152.032.31

1119530000.00

1119690000.0011824.6024.47quad

1209800000.0011733.20199.21quad

1.21E+092.94E+035.88E-01R/Q-mono2935.490.59

1.34E+096.34E+031.07E+028.58E+00

1.34E+095.37E+034.05E+013.39E+00

1.35E+09

1.36E+094.19E+031.06E-02quad

1.36E+091.15E+037.34E-02quad

1.42E+091.15E+032.88E-01quad

1.44E+091.80E+058.02E-02quad

1.44E+098.30E+041.15E+00six

1.45E+091.94E+032.83E+022.60E+01mono

1.45E+094.80E+051.47E+00six

1.46E+092.21E+043.21E-01dipole2.15E+032.31E+022.14E+01mono

1.49E+091.45E+059.25E-01

TM110- coupler rejects operating mode using field symmetry.The misalignment of -mode coupler should be less than 1mm to avoid the cross coupling between the FPC and pi-mode coupler. TM110-0: (R/Q)_T=100/cavityTM110-: (R/Q)_T=0.3/cavityRejection of Operating Mode

Coax coupler misalignment 00.625mm1.25mm2.5mmF (MHz) for TM110-o mode799.982799.982799.982799.982Qext@coax>e111.4e93.5e88.2e7


Damping requirements for the LOM and SOM modes: Qext < 200.Monopole & Vertical Dipole Modes

LOM modesF (MHz)587.056587.218608.210608.288R/Q(/cavity)54.141.864.571.4Qext4950129129

Vertical Dipole modesF (MHz)888.130889.123899.865906.237985.622996.683(R/Q)_T(/cavity)35.31.20.930.916.42.3Qext414644445967


Horizontal Dipole Modes

Horizontal Dipole modes: TM110-o mode is the operating modeF (MHz)799.682 (pi mode)799.985(0-mode)897.095898.974982.510996.130(R/Q)_T(/cavity)1.199.50.081.011.24.1Qext3.6e4>e9143013959321359


2mmE-BCTrack3P - Multipacting StudiesTM110-0 modeVT=0.1~1.25MVResonant particles with impact energy between 50~2000eVMP in the Cell - zxyeVAvoid E: 200ev~600ev


Chart2

0

0.9722222

1.1305556

1.2222222

1.4388889

1.4777778

1.4861111

1.4416667

1.3777778

1.3138889

1.2583333

1.2138889

1.1666667

1.125

1.0916667

1.0611111

1.0333333

1.0111111

0.9861111

0.9666667

0.9444444

0.9305556

impact energy (eV)

delta

Nb SEY Curve

29871

IDtypeImpactxyzevphase

2987160-0.00126017690.02639948070.01881033354.46E-102001

2987131-0.00222314450.03893634820.04797023714.01E-09525.87678122493.56E-090.03175531971

2987132-0.00153922810.02695634130.04797346235.94E-09561.51202935235.49E-090.02916977961

2987133-0.00222173980.03893651220.04797354157.11E-09793.29620196426.67E-090.03175837631

2987134-0.00153661370.02695699680.04797718579.01E-09560.59100793738.57E-090.02917348981

2987135-0.00221745810.03893656880.04797769471.02E-08793.6033720329.74E-090.03176208311

2987136-0.00153457140.02695667550.04798165941.21E-08560.67960216081.16E-080.0291779371

2987137-0.00221471330.03893661940.04798220921.33E-08792.70703183111.28E-080.03176616621

2987138-0.00153318290.02695685890.0479862411.52E-08560.2880244791.47E-080.02918250811

24351320.00082075620.0269878750.02631347361.59E-08434.52735102511.56E-080.01222950931

2987139-0.00221283790.03893704810.04798679791.63E-08791.94242174591.59E-080.03177049311

29871310-0.00153258660.02695698230.04799069911.82E-08559.90352549141.78E-080.0291869621

29871311-0.00221190860.03893714170.04799117511.94E-08791.08773233271.90E-080.03177452211

29871312-0.00153244240.0269565350.04799524062.13E-08559.43175200942.09E-080.02919149251

29871313-0.00221184810.03893709420.04799579632.25E-08796.46233472512.20E-080.03177874551

29871314-0.00152723970.02695748670.04799995442.44E-08561.70243322842.39E-080.02919617541

29871315-0.00220482440.03893699530.04800009892.56E-08787.65481506562.51E-080.03178244851

29871316-0.00152753940.02695698120.04800453562.75E-08557.96208824872.70E-080.02920074861

29871317-0.00220484240.03893761430.04800523412.86E-08795.37603202582.82E-080.03178740951

29871318-0.00152360250.0269573460.04801005173.05E-08561.05198078533.01E-080.02920623471

29871319-0.00219855760.03893792520.04801148943.17E-08794.97861967263.13E-080.03179309131

29871320-0.00152027330.02695718090.0480164733.36E-08561.13650003513.32E-080.02921262171

29871321-0.00219399680.03893775990.04801819153.48E-08794.19925578683.43E-080.03179904761

29871322-0.00151753780.02695817570.0480233713.67E-08560.91665187193.62E-080.02921951291

29871323-0.00219011910.03893845560.04802515683.79E-08793.41911942693.74E-080.03180560621

29871324-0.00151530870.02695779440.04803054343.98E-08560.61158131843.93E-080.02922665681

29871325-0.00218703170.0389382280.04803241824.09E-08792.73140826734.05E-080.03181209631

29871326-0.00151347360.02695781170.04803811594.28E-08560.30631727254.24E-080.0292342121

29871327-0.00218432790.03893844270.04803984324.40E-08791.92105891214.36E-080.03181892291

29871328-0.00151226230.02695792520.04804608764.59E-08559.93174541864.55E-080.02924217371

29871329-0.00218249030.03893881790.04804814614.71E-08791.13398087034.66E-080.03182664491

29871330-0.00151166170.02695844870.04805463544.90E-08559.46055286784.85E-080.02925072441

29871331-0.00218186880.03893887360.04805704695.02E-08796.41297384114.97E-080.03183482581

29871332-0.00150613710.02695869330.04806378215.21E-08561.68268678415.16E-080.02925982681

29871333-0.00217450530.03893871460.04806577765.32E-08787.68306916575.28E-080.0318425721

29871334-0.0015059330.02695808930.04807309655.51E-08557.98849762055.47E-080.0292691261

29871335-0.00217385590.03893931690.04807571875.63E-08795.39744616715.59E-080.03185192411

29871336-0.00150166220.02695856210.04808363265.82E-08560.97834242595.78E-080.02927963331

29871337-0.00216717830.03893939140.04808713645.94E-08794.97603455895.89E-080.03186225351

29871338-0.00149781180.02695905710.0480953796.13E-08561.12055810856.08E-080.02929135511

29871339-0.00216156080.03893966870.04809915276.25E-08794.10206280546.20E-080.03187324491

29871340-0.00149404390.02695864190.04810833116.44E-08560.8444271676.39E-080.02930426621

29871341-0.0021562590.03894034690.04811229176.55E-08793.46599374456.51E-080.03188543621

29871342-0.00149091060.0269590550.04812174876.74E-08560.53551061726.70E-080.02931766391

29871343-0.00215200270.03894046280.04812601716.86E-08792.70562484086.82E-080.03189797621

29871344-0.00148858960.02695956210.04813629017.05E-08560.23313706167.01E-080.02933219381

29871345-0.00214871870.03894048010.04814069547.17E-08791.88519120717.12E-080.0319113821

29871346-0.00148669410.02695913990.04815144427.36E-08559.83927011877.31E-080.02934732191

29871347-0.00214613070.03894042010.04815608597.48E-08791.10763075227.43E-080.03192543271

29871348-0.00148582630.02695977270.04816765217.67E-08559.39676410977.62E-080.02936353181

29871349-0.00214464370.03894092410.04817238657.78E-08796.35655846517.74E-080.03194057351

29871350-0.00148010560.0269594530.04818553867.97E-08561.70705849727.93E-080.0293813651

29871

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sey-curve

coppernb

000.00E+000.00E+00

500.2461673815.00E+019.72E-01

1000.46870224087.50E+011.13E+00

1500.66351426341.00E+021.22E+00

2000.83006420642.00E+021.44E+00

2500.96948623183.00E+021.48E+00

3001.0838245474.00E+021.49E+00

3501.17559000185.00E+021.44E+00

4001.24747571176.00E+021.38E+00

4501.30217061857.00E+021.31E+00

5001.34223959448.00E+021.26E+00

7001.39999999259.00E+021.21E+00

9001.36981698371.00E+031.17E+00

11001.31097198811.10E+031.13E+00

13001.24881161911.20E+031.09E+00

15001.19196543821.30E+031.06E+00

17001.14220535751.40E+031.03E+00

19001.09899783071.50E+031.01E+00

21001.06128365971.60E+039.86E-01

23001.02805669351.70E+039.67E-01

25000.99849640231.80E+039.44E-01

27000.97196171031.90E+039.31E-01

29000.9479543361

31000.926083577

33000.9060390377

35000.8875707399

37000.8704747729

39000.8545828648

41000.8397546999

43000.8258721737

45000.8128350328

49000.7889657766

53000.7675916445

57000.7482911236

61000.7307374255

sey-curve

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0

impact energy (eV)

delta

Nb SEY Curve

slice-rerun

0

0

0

0

0

0

0

0

0

0

0

0

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0

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0

impact energy (eV)

delta

Copper SEY Curve

24061

slice-rerun

2.50E+05100

5.00E+05100

7.50E+05100

1.00E+06100

1.25E+0661.47818067671.4783551885

1.50E+0661.38181143281.47982238961.25E+0671.43439504011.3029531429

1.75E+0661.47980607691.47977763571.25E+0681.37423355291.3100230271

2.00E+0641.43917833221.44329137771.25E+0691.18209158781.3402197887

2.25E+0641.43190503381.4451342517

2.50E+06100

2.75E+061002.00E+0641.4391584391.4482451136

3.00E+06100

4.00E+06100

5.00E+06100

6.00E+06100

7.00E+06100

8.00E+06100

9.00E+06100

1.00E+07100

1.10E+07100

1.20E+07100

1.30E+07100

1.40E+07100

1.50E+07100

1.60E+07100

1.70E+07100

1.80E+07100

1.90E+07100

2.00E+07100

2.10E+07100

2.20E+07100

2.30E+07100

2.40E+07100

2.50E+07100

2.60E+07100

2.70E+07100

2.80E+07100

2.90E+07100

3.00E+07100

24061

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0

Nb beam pipe

Eacc (V/M)

delta

MP in coaxial coupling region

240617-0.001168110.02697520.0461025514.86915.75531

240618-0.001687670.03896330.0460744757.21517.26481

240619-0.001167770.02697530.0460161527.7519.74411

2406110-0.001687460.03896310.0459875772.76521.25361

2406111-0.001168270.02697490.0459262543.33523.73291

2406112-0.001689770.03896310.0458979786.14825.24241

2406113-0.001170030.02697470.0458341556.41327.71171

2406114-0.00168910.03896320.0458034788.53829.24121

2406115-0.001169230.02697470.0457363557.69331.71051

2406116-0.001686720.03896330.0457039786.81533.241

2406117-0.001164990.0269750.0456325556.82735.70931

2406118-0.001679490.03896350.0455981792.34337.22881

2406119-0.001159940.02697510.0455226558.80139.70811

2406120-0.001672590.0389640.0454866783.13641.23761

2406121-0.001154330.02697550.0454068554.76743.70691

2406122-0.001663330.0389640.0453684790.51445.22641

2406123-0.001150140.02697610.0452853557.45147.70571

2406124-0.001658090.03896450.0452454787.69149.22521

2406125-0.001147350.02697570.0451584555.65851.70451

2406126-0.001653910.03896450.0451163787.19453.2241

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Documents

Update on LHC 800MHz Crab Cavity Conceptual Design