SSCL-N-690

DISTORTION AND ATTENUATION OF SSC MAIN RING BEAMPOSITION MONITOR SIGNALS

R. B. Shafer, Los AlamosNationalLaboratoryJanuary26, 1990

1. INTRODUCTIONThepurposeof thisNote is to estimatethe signalamplitudefrom the proposedSSC

Main Ring beampositionmonitors,andto calculatethedistortionandattenuationcausedbycoaxialcablesup to 270 m long. Becausethechoiceof the signalprocessingmethodwilldependentin parton the signalcharacteristics,it is importantto havea goodunderstandingof theseeffects.

In Section2 thefrequency-domainsignalpowerfor the expectedbeampositionmonitor responseto a varietyof beambunchlengthsis calculated,andthe effectof longlossycoaxialcablesis estimated.In Section3 the time-domainsignalis calculatedtakinginto accountthe dispersionof the cables,which distortsthe phaserelationshipof thevariouscomponentfrequencies.

In Section4, someof the issueswhichneedto be consideredin selectingone or moresignalprocessingmethodswill be reviewed.Includedis a discussionof the costadvantageto placingthe nichesclosertogetherandeliminatingthe longcableruns.Anotherconsiderationis the choiceof thecharacteristicimpedanceofthe cables,which haveminimumattenuationanddistortionwhen theircharacteristicimpedanceis in the70Qto75 range.

2. FREQUENCY DOMAMN ANALYSISThe signalpowerin the variousharmonicsof the beambunchingfrequencyis

calculatedusing the following expressionfor a sthplinebeamposition monitor1

£t -yeNCcAtOt4ui1, S221 1

Here f0 = wJ2it is the beambunchingfrequencyand o = rn®0 wherern is theharmonicnumber, N is the numberof protonsperbunch,and Amw0 is the amplitudefactor for aGaussianbunchof mis width a given by

J 2

SSC MAIN RING BPM SIGNAL DISTORTION SHAFER PAGE 2

Thespecificbeamcharacteristicsusedfor thesecalculationsareN = protonsper bunch= 1 x 1010

= beambunchingfrequency=60MHza = mis bunchlength =7 cm nominalto 30 cm maximum

Thebeampositionmonitorandcablecharacteristicsusedin thesecalculationsareX = electrodelength= 10cm

* = electrodeangularwidth =45degreesZ = electrodeimpedance=50ohmsz = cablelength= 270 meterscableattenuation= 1.27 dB per 100 mat 100 MHz 7/8" Heliax

3.44 dB per 100 mat 100 MHz 3/8" Heliaxassumedto scaleas [frequency]1/2

Figure 1 presentstheexpectedpoweroutputin decibelsfor the variousharmonicsofthe bunchingfrequencyat the pickupoutputfor a rangeof bunchlengthsusing N = 1010

protonsperbunch.For the expectedbunchlengthof 7 cm, the signalpowerrangesfrom -

6.5 dBm at 60 MHz to +7 dBm at 360 MHz. As canbe seen,the signalpowerin allharmonicsdecreasesasthe bunchlengthbecomeslonger.For theexpectedbunchlengthof7 cm, the higherharmonicshavemoresignalpowerthanthe lowerharmonics.However,the higherhannonicsaremoresensitiveto bunchlengthvariationsthan arethe lowerharmonics.

Figure2 presentsthe samesignalafterpassingthrough270 metersof 7/8" Heliaxcable Figure3 presentssimilardatafor 270 metersof 3/8" Heliax cable.In bothcases,thesignalpowerin the lowerharmonicshasincreasedrelativeto the higherharmonics.

Theassumptionin the abovecalculationsis that the beamis bunchedwith a bunchingfrequencyof 60 MHz, andthatthe requiredmeasurementscanbe madein the frequencydomainat oneor moreharmonicsof thebunchingfrequency.Thisapproachis notadequatefor measuringthe positionof a singlebunch,however. In orderto resolvea singlebunchin a periodicbunchtrain, time-domainprocessingi.e., gatingwill benecessary.Thussomeunderstandingof the temporalsignalprofile of abeambunchsignalis required.

3. TIME DOMAIN ANALYSISIn timedomainanalysis,theentirepowerspectrumof the signalis measuredfor a

SSC MAIN RING BPM SIGNAL DISTORTION SHAFER PAGE 3

specifiedtime interval.Thepresenceof dispersionin coaxialcablescandistortthephase

relationshipandmakethemeasurementdifficult.Dispersionin cables,i.e. the dependenceof signal velocity on frequency,is adirect

result of the skin effectlosses.2Theresultof this is that the variousharmoniccomponentsof abeamposition monitorsignaldo notmaintaintheir properphaserelationshipafterpropagatingdown a lossytransmissionline. Specifically,if a signalat the inputto a lossy

meaningskin effectlossescoaxialcablecanbe expressedas

V@i V0* 2V0 3

thenthe signalat the outputmay be written as

Vfi V0 2L/0’Ze 4cos[w0T+&-o&i] 4

whereamz is the attenuationin nepersat frequencymw0 of acableof lengthz andinsertiondelay t = z/c’Jec is the speedof light ande is the relativepermittivity of thedielectric.The attenuationanddispersionfor 100 m of 7/8" Heliax is shownin Table I..Figure4 is a plotof the calculatedattenuationofa 7/8" 50 Cl coaxwith signalvelocity =

0.916that agreeswell with the measuredattenuationof 7/8" Heliax.Phaseshift is thedeviationin thephasedelayfrom theexpectedphasedelay= m®0t. Note in Table 1 thatthephaseshift in radiansdue todispersionis numericallyequalto the attenuationin nepers.

The bipolarsignaloutputof a 10 cmlong, 45°, 50Q striplinepickup may be writtenin the form

eu ¶Awo&ikJ sk 5

Cablelossesandphasedistortioncanbe includedby addingbothan attenuationfactoranda phaseshift:

MJ6

Figures5 and 6 showthe distortionin a bipolarbeamposition monitorsignalat theoutputof a 270 m sectionof 3/8" Heliax cable.Figures7 and8 showthe samecalculation

SSC MAIN RING BPM SIGNAL DISTORTION SHAFER PAGE 4

for 7/8" Heliax. In both cases,the bipolardoubletsymmetryof the inputpulseis lost dueto the dispersion.Nevertheless,the signal still haszero net area.Thepeakamplitudeof thefir st positive lobe is reducedby a factorof about8 in the3/8" heliaxand2 in the7/8"heliax.

The peakamplitudeof the first lobe is a strongfunctionofthe bunchlength.Figure 9showsthepeakamplitudeat the outputof the 7/8"Heliax asa function of the rms bunchlength Gaussianbunchprofile. At longerbunchlengths,the peakamplitudevariesinverselyasthe squareof the bunchlength.3 For shortbunches,the peakoutputamplitudeof the beampositionmonitorshouldscaleinverselywith the rms bunchlength.Thecableattenuationanddispersionwill flatten outthis responseby removingthe high frequencycomponents.This is seenin Fig. 9.

4. CONCLUSIONSThebeampositionmonitoring systemin the SSCMainRingshasfour important

functions:

1. Commissioningfirst turn, beamstorage,if andmagnetramping, etc.;2. Normal operationtuning, steering,dispersionmeasurements,etc.;3. Detectionof andrecoveryfrom off-normalconditionsbeamabort,cusphunting

etc.;and4. Advancedacceleratordevelopmentandexperiments.

In designingthe beampositionsystems,somethoughtneedsto be put into how theplannedsystemwill performunderthe four activitiesoutlinedabove.Eachactivity imposesdifferentrequirementson the system.In addition,thereare diagnosticmeasurementswhichneedto be measuredonly a few times perring, perhapsin warmregions,andsomemeasurementswhich needto be measuredglobally i.e. atevery half-cell.

In the commissioningprocess,the beampositionmonitorsystemin the SSCwillprobablybe usedfor bothpositionmeasurementandintensitymeasurement.For thisreasonit would be an advantageto havea sumsignalfrom the electrodeswhich isproportionalto the totalnumberof protonsperbunchandminimally sensitiveto the beambunchlength.In lookingat Figs. 1-3 it is apparentthat frequency-domainprocessingof thelowestharmonicsignalswould providethe bestintensitysignal.However,thereis moresignalpowerin the higherharmonicsignals,evenwhenattenuationby the coaxialcablesis

SSC MAIN RING BPM SIGNAL DISTORTION SHAFER PAGE 5

included.Theassumptionin Section2 wasthat the beamis a seriesof equalintensity,periodicallyspacedbunches.Thereappearsto be sufficientsignalpowerin anybunchingharmonicsuchthatcommissioningcould be carriedoutwith a seriesof about10 bunchesof lO protonsat60 MHz spacing.Optionally, commissioningcouldbe carriedoutwith asinglebunchof 1 x 1010 protons.

Thereis a relatedissuewhich mayprecludecertaintypesof frequency-domainprocessing.To performthe i-f partof the signalprocessingin amplitude-modulation-to-phase-modulationAM/PM procesingfor example,the if signalsarriving at theelectronicsneedto be in phasewithin about± 5 degreesat the processingfrequency.Thisrequiresphasematchingthe cables,which may turn out to bean expensivei.e.,a laborintensiveprocess.If theif signalamplitudeswereenvelope-detectedprior to otherprocessing,thencablephasematchingwould not berequired.ThisprecludesAM/PMprocessing.

In the normalacceleratoroperationit is of interestto measurethe characteristicsof asingle beam bunch,eitherisolatedorcontainedwithin a longperiodicbunchtrain, whilethe beamcirculates.It is apparentthat frequency-domainprocessingcannotresolvesinglebunches,so if the beampositionof a singlebunchneedsto be measuredglobally,peaksensingtechniquesmustbe used.As hasbeenshown,the peakamplitudeis dependentonthe type andlength of cableused,andalsoon the beambunchlength.Thiswill notaffectthe actualpositionmeasurement,however,sincethe positionis derivedfrom the signalratio.

Therealissuehereis whetherthe capabilityfor singlebunchpositionmeasurementmustbe global i.e.,ateveryhalf cell or at onlya fractionof the position measurementstations.All buncheswill on the avengehavethe sameorbit circumference,becausetheifsystemrequiresit. Buncheswill oscillateaboutthe closedorbit with a combinationofbetatronandsyschrotronfrequencies.Theonly areawherethe beampositionof eachbunchneedsto be controlledat the fewmicron level is at IPsintersectionpoints.Henceit is notobviousthata global beampositionmeasurementsystemwith single-bunchresolutionisrequired.

It hasbeensuggestedthata fraction of the beamposition monitorsperhapsaquarterora third would be sufficientfor the earlycommissioningprocess,andthat the remainderbe usedprimarily for the otheractivitieslistedabove.If thereare4 electrodesperbeampositionmonitorin everyhalfcell, thenthereareenoughtocarryoutcommissioningandtheneededmeasurementsfor normaloperation.If therearetwo electrodespermonitor,

SSC MAIN RING BPM SIGNAL DISTORTION SHAFER PAGE 6

thensomemonitorsmayneedto perform in bothroles.If peakdetectionis requiredfrom the position monitorson the 270 m cables,then the

7/8" Heliax is probablyrequired.If thereareabout140 niches,eachwith sixteen270m7/8" Heliax 4 cablesper monitor, onemonitorperhalf cell in eachring, this representsabout 600km of Heliax ata costof $14 perm, or $14M worthof cable.If the numberofnichesis increasedfrom 140 to about190, theselongcablescouldbe eliminated.If thecostpernich includingthe associatedcostsof the overheadelectronicswhich mustbeaddedisless thanabout$280K, thenplacingthe nichesat a 360m spacingratherthana 540 mspacingmightbe financially preferable.

Cablelossesfor agiven outerdiametercablecanbe reducedby usinga characteristicimpedanceof about763U ratherthan5012, where is the signalvelocity A 75 12beampositionelectrodewill havea 50%higherpoweroutputatall frequenciesthan a5012electrode.Thiswill alsoincreasethe longitudinaland transversecouplingimpedancesasimilaramount,however.Theeffectcould be reducedby adjustingthe pickupelectrodelengthor width, if necessary.5

5. REFERENCES1. R. E. Shafer,"BeamPositionMonitoring,"Los AlamosNationalLaboratoryinternalreport# LA-UR 89-34721989.SeeEq. 13.2.

2. R. E. Shafer,"DispersionandAttenuationin CoaxialCables,"Los AlainosNationalLaboratoryinternalreport# AT-3 :TN 90-21990.

3. Reference1, Eq. 8.3.

4. Reference2, Eq. 6.

5. The signalpowerscalesasthe squareof the electrodelength,and thecouplingimpedancesscalelinearly.

TABLE 1. PROPERTIES OF COAX WITH SKIN EFFECT LOSSES EQUIVALENT TO 7/8" HELIAXIMPEDANCE, ATTENUATION, PHESE DELAY, PHASE VELOCITY, AND PHASE SHIFT VS FREQUENCY.

OUTER RADIUS = 1.110 CMINNER RADIUS = 0.447 CMRELATIVE DIELECTRIC CONSTANT 1.192NOMINAL CHARACTERISTIC IMPEDANCE = 50.00 OHMSNOMINAL PHASE VELOCITY BETA = 0.9160LENGTH 100.0 METERSRESISTIVITY 2.20E-08 OHM METERS

F ---ATTENUATION---- --PHASE DELAY-- PHASE SHIFT

MHz OHMS DEGREES NEPERS dB RADIANS NSEC =v/c RADIANS

1.0 50.32 -0.364 0.01463 0.127 2.303 366.497 0.91014 0.014731.5 50.26 -0.298 0.01794 0.156 3.450 366.067 0.91121 0.018042.0 50.23 -0.258 0.02073 0.180 4.597 365.810 0.91185 0.020833.0 50.19 -0.211 0.02541 0.221 6.890 365.506 0.91261 0.025515.0 50.14 -0.164 0.03284 0.285 11.473 365.201 0.91337 0.032937.0 50.12 -0.139 0.03887 0.338 16.055 365.039 0.91378 0.03896

10.0 50.10 -0.116 0.04648 0.404 22.927 364.894 0.91414 0.0465715.0 50.08 -0.095 0.05694 0.495 34.378 364.758 0.91448 0.0570420.0 50.07 -0.082 0.06577 0.571 45.827 364.677 0.91468 0.0658630.0 50.06 -0.067 0.08057 0.700 68.722 364.581 0.91492 0.0806750.0 50.05 -0.052 0.10404 0.904 114.506 364.484 0.91517 0.1041470.0 50.04 -0.044 0.12312 1.069 160.286 364.433 0.91530 0.12322

100.0 50.03 -0.037 0.14717 1.278 228.951 364.387 0.91541 0.14727150.0 50.03 -0.030 0.18026 1.566 343.387 364.344 0.91552 0.18037200.0 50.02 -0.026 0.20816 1.808 457.816 364.319 0.91558 0.20828300.0 50.02 -0.021 0.25496 2.215 686.667 364.288 0.91566 0.25509500.0 50.01 -0.016 0.32917 2.859 1144.350 364.258 0.91574 0.32931700.0 50.01 -0.014 0.38948 3.383 1602.018 364.242 0.91578, 0.38965

1000.0 50.01 -0.012 0.46553 4.044 2288.507 364.227 0.91581 0.465721500.0 50.01 -0.010 0.57014 4.952 3432.632 364.214 0.91585 0.570392000.0 50.01 -0.008 0.65833 5.718 4576.740 364.205 0.91587 0.658633000.0 50.01 -0.007 0.80626 7.003 6864.929 364.196 0.91589 0.806655000.0 50.00 -0.005 1.04079 9.040 11441.246 364.186 0.91592 1.041387000.0 50.00 -0.004 1.23139 10.696 16017.518 364.181 0.91593 1.23218

10000.0 50.00 -0.004 1.47164 12.783 22881.882 364.176 0.91594 1.47274

Figure 1. Signalpowerin decibelsvs.rms bunchlengthat variousharmonicsof the 60MHz bunchingfrequency,with N = 1 x 1010 protonsper bunch.Thepickupelectrodeis a10 cm, 45°, 500electrode.

-30

0 10 20 30 40 50

Figure2. Similar to Fig. 1, exceptthat the attenuationof 270 m of 7/8" Heliaxcableisincluded.

IC

C

-IC

-20

-40

5gna1 power dBm SIGNJL POWER VS BUNCH LNGTHI

AND HARMONIC OF BUNCHING FREQUENCY

.

Includes 270 m of 7/8" Heflax cable

120 MHz

*______

F = 60 MHz

N a 1EIO protons / bunch

60 MHz bunch freiuency cwI

10cm electrodes,

45 degree wide electrodesI

50 ohm impedanceI

270 m of 7/8 Hehax -

- I

F=33ooMHrN

Rms bunch length cm*

0 10 20 30 40I -

50

20

50 ohm impedance

270 m of 3/8 Heliax

Figure3. Similar to Fig. 1, exceptthat the attenuationof 270 m of 3/8" Heliax cableisincluded.

10

0

-10

-20

-30

-40

N= lElOprotons/bunch

60 MHz bunch frequency cw

10 cm electrodes

45 degree wide electrodes

0 10 20 30 40 50

Figure4. Plot of the calculatedattenuationfrom Table1 andthe measurementsof theattenuationin 7/8" AndrewsHeliax coaxialcable.

1 10 100 1000 10000

Figure5. Voltagewaveformoutputof a beamposition monitorelectrodebeforeand after

270m of 3/8" Heliax cable.Thebeamis 1010 protonsin a 7 cm rms lengthbunch.The

10000

8000

6000

4000

2000

0

-2000

-4000

-6000

-8000

-10000-1.0

1OUTPUT millivolts

.

Pickup output

. .

270 m of3/& Heliax ]

ii2J Q. $ itt,,

cable outputes.

__:___

gwwa4wa VirCTU?? flWWW’TWV

TIME ns

-05 0.0 0.5 1.0 1.5 2.0 2.5 3.0

. . . I

electrodeis a 10cm,45°, 50 0 pickup.

1000

750

500

250

0

-250

-500

-750

-1000-1.0

Figure6. SameasFig, 5 exceptthatthe verticalaxis is expanded.Note the asymmetricpulseshapeandthe temporalphaseshift of the zerocrossingcausedby the dispersion.

-0S 0.0 0.5 1.0 1.5 2.0 2.5 3.0

10000

6000

6000

4000

2000

0

-2000

-4000

-6000

-8000

-10000-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Figure7. SameasFig. 5, exceptfor 270 m of 7/8" Heliax cable.

4000

3000

2000

1000

1000

-2000

3000

-40003.0

0

-1.0 0.0 0.5 1.0 1.5 2.0 2.5

Figure8. SameasFig. 7, exceptthat the verticalaxis is expanded.

10000

1000

100100

Figure9. Plotof peakoutputvoltageat the endof 270 m of 7/8" Heliax vs.beambunch

length.Sameconditionsasshownin Figs. 7 and 8, exceptthat the bunchlength is a

variable.

1 10