Padamsee, H

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SRF for Muon Colliders*H. Padamsee,Laboratory of Nuclear Studies, CornellUniversity, Ithaca, NY 14853AbstractInterest in the Muon Colliders is growing [1].  Electron-positron colliders beyond 2 TeV CM energy are likely tolimited by background from beamstrahlung, and protoncolliders beyond 20 TeV CM are likely to be limited bythe sheer size of the multi-hundred km circumference.Being 200 times more massive than electrons, muons donot suffer from beamstrahlung limits. A 3 TeV muoncollider is likely to fit on a site such as Fermilab.  Butmuons are unstable.  Problems from  muon decay are theheat load, large detector background and a neutrinoradiation hazard.  The last adversity can be turned into thefortune of an intense neutrino source.1  INTRODUCTIONLike electrons and positrons, muons are point particles, sothat their energy is not shared among constituents, as inthe case of the quark and gluon components of protons.Being 200 times more massive than electrons, theradiative energy loss of muons is less by a factor of 1.6billion (200 raised to the fourth power).  Therefore muonscan be  accelerated to high energies by recirculation insmall arcs.  TeV energy muons can be stored and collidedin small storage rings.  The catch is that muons areunstable, with a rest frame life time of 2.2 microseconds.But the time dilated lifetime at one TeV is 21milliseconds, long enough for storing 1000 turns in a 6km circumference ring.  The trick is to produce, capture,cool and accelerate the low energy, short lived muons asfast as possible.  For rapid acceleration superconductingcavities are ideal.It is likely that the acceleration will be the mostexpensive part of the Muon Collider.  Fig. 1 reproducesthe lay out for a generic muon collider from [2].  We willaddress mainly the acceleration systems after the muoncooling section.  Since development of RF structures is along lead time item, it would be advisable to address thiswork early, or at least in parallel with the extremelychallenging muon production and muon cooling stages.2  MUON COLLIDER PARAMETERSTable 1 reproduces some of the relevant parameters for thefirst linac and subsequent recirculators[1].  We aim topresent scenarios for the use of SRF cavities for all theaccelerators listed, and from these scenarios, to draw* Work supported National Science Foundation.lessons about where development efforts are necessary.Although the original Table 1 calls for copper cavities inthe first linac (0.1 to 0.7 GeV) as well as for the first tworecirculators (0.7 to 7 GeV), we will discuss SRF linacsfor these columns also.3  SRF ACCELERATION STAGESAt the high energy end, from 200 to 1500 GeV theconcept is to use TESLA type cavities at 1300 MHz,although these cavities may have to be improved withrespect to their HOM properties.  For the high bunchcharge and 10 mm bunch length the beam induced HOMpower will be on the order of 200 W/m, demanding veryefficient extraction.  For our estimates we assume that10% of this power is dumped in liquid He.In vertical tests[3], TESLA cavities now routinely reachEacc = 25 - 30 MV/m at Q values above 5x109.  Thesuccess of TESLA cavities at 1300 MHz has lulled theMuon Collider Collaboration to adopt a complacentattitude toward acceleration development, especially whenfaced with the severe technical challenges of othersystems, such as muon cooling and the muon production.However, because of the longer bunch lengths at lowerenergies, the RF frequency desired decreases to 800 MHzbetween 50 and 200 GeV, and to a prodigious 200 MHz atlower energies.  At the longest bunch length it may evenbe necessary to go down to 100 MHz, but we hope thatthis will be only be needed for a very small fraction of theoverall acceleration.Although there is considerable SRF experience at 350MHz and 500 MHz, there is no experience at all in 200MHz systems - especially in pulsed operation - and verylittle experience at 800 MHz.   The advent of highintensity proton linacs for neutron sources is likely to fillthe 800 MHz gap over the next five years.  We will showthat the scope of the systems from 200 to 800 MHz isquite significant compared to the 1300 MHz RF, so that itwould be wise to address 200 MHz RF development early.Another key point is that a First Muon Collider (FMC) ismost likely to be targeted at a maximum energy of 50GeV, so calling exclusively for the low frequencysystems.  Therefore the fact that TESLA accelerationsystems exist at 1300 MHz is likely to be of little help inthe birth of the Muon Collider.In general, the higher the gradient the shorter the linac andthe less the muon losses from decay - a major designconsideration.  The  success of 500 MHz KEK-B Nbcavities and 400 MHz LHC Nb/Cu cavities in reachingaccelerating gradients of 15 MV/m at 4.2 K encourages usto pick 15 MV/m as the gradient for 100 - 200 MHzsystems, 20 MV/m for 800 MHz.  and 25 MV/m for1300 MHz.  At the lower frequency the attraction ofNb/Cu cavities becomes quite strong, especially since thecost of sheet Nb becomes a major component.  Further itmay be possible to use thicker sheet copper to obtain alower Lorentz force detuning coefficient for these 200MHz behemoths.For Q0 values, we chose 1x 1010 at the operatingtemperature of 4.5 K for 100 - 200 MHz and the same Q0at the operating temperature of 2.1 K for the 800 MHz to1300 MHz structures.  Our estimate is based on a residualresistance of 10 n W,  plus a BCS resistance  given byRBCS = 1.2x10-4 x 1T x ( Freq MHz1500 MHz)2x e(-17.67T)Here we take into account any gains in BCS Q that maybe obtained by baking at 140 C and reducing the RFsurface mean free path [4,5].  For 200 MHz and 4.5 K, theBCS resistance is also about 10 n W , resulting in anexpected Q of 1.3x1010.Our aim is to calculate the capital cost-intensive itemssuch as, RF power, linac length, refrigerator size as wellas the AC power for each of these acceleration stages.  Wewill then insert some very preliminary numbers for thecapital costs to determine in which billion dollar class thescope of a 3 TeV collider is likely to fall.  Since this is afirst cut we neglect reserves needed as for items, such asRF control or refrigeration.By discussing one system (7 - 50 GeV) in detail wepresent our strategies, assumptions and algorithms.Assuming the gradient of 15 MV/m, the active length ofthis linac is 260 m, and the total voltage to be installed inthis stage is 3.9 GV, comparable to the LEP-IIinstallation.  At 200 MHz the cell length = 0.75 m.  Thenumber of cells depends on the coupler power capabilityand ease of handling large lengths.  For both reasons weprobably do not wish to exceed two cell units.  It shouldbe possible to put several cavity units into one cryostat toimprove the filling factor.RF Power ConsiderationsTo find the size of the RF peak power installation, westart with the average beam power.Average Beam Power = Bunch charge x bunch frequency x (Final energy - Initial Energy)2x1012 x 1.6x10-19x (50 - 7)x109= 410 kWTo obtain the peak RF power we need the RF-on dutyfactor.RF on duty factor = RF on time x rep rate= 15 Hz x 64 m sec = 10-3The RF has to stay on for 11 beam recirculation passesthrough the arcs which are 1.74 km in length.  Thereforethe RF on time required for the beam on will beRF on time = Number of recirculations x circumferencec = 64 m secWe neglect the 10 ns time between the two muonbunches.  The peak RF power for this stage is then 430MW, which translates to a peak beam power of 1.65MW/m, or 1.2 MW per coupler for single cell units.Clearly high power coupler development will beimportant, especially if we wish to use 2-cell units.Couplers used for HPP in vertical test stands havesuccessfully been operated with one MW and 200 m sec.Before we can determine the klystron power we need toestimate the total pulse length, which includes the fillingtime, dominated by the Qext of the input coupler.Assume that we aim to match to the beam power.Qext =  Gradient2(RQ) x Peak Beam Power per meter= 8.2x105For R/Q ( W /m), we scale with frequency from the TESLAstructure. RQ (Wm) = 1080 x ( 200 MHz1300 MHz)T h e nRF fill time = 2 ln 2 x QLw = 0.9 msTherefore the total RF on time = 0.96 ms.  A survey(carried out in '92) of available klystrons showed that theavailable peak power capability of klystrons decreaseswith increasing pulse length according to Fig. 2.  At 1 mspulse length we can count on 4 MW klystrons, althoughthe impetus of TESLA has pushed this power capabilityup by a factor of 2.  We will continue to use graph ofFig. 2 to chose the lower klystron power.  The totalnumber of klystrons needed is 113.Table 1: Parameters for a 3 TeV Collider [1]At Qext = 8.2x105, the corresponding bandwidth is 244Hz.  This may be a challenge for pulsed operation in thepresence of Lorentz force detuning. On the other hand, aswe discussed earlier, the use of thick copper for the Nb/Cumay be an appropriate countermeasure.RefrigerationTo obtain the dynamic heat load, we first calculate the RFduty factor which depends on the fill time, the flat top anddecay time.RF on duty factor = Rep rate (RF on time + fill time + decay) = = 0.019The 2% duty factor is similar to TESLA.  The total RFdissipated power in 4.5 K helium is thenTotal Dynamic Heat Load = Gradient2x Active Length x RF Duty Factor(RQ) x Q0= 685 WFor the large diameter cryostat that will accompany the200 MHz cavity we assume a static heat leak of 5 watt/m.Using a filling factor of 0.5, the total static heat leak forthis stage will be 2.6 KW, far larger than the dynamicheat load.  Clearly, filling factor and static heat load areareas where improvements will be welcome.  Anothercomponent of the heat load is the fraction of beam inducedHOM power that will be dissipated in liquid helium.  Forthe HOM loss factor (k||) we scale from TESLA withfrequency and bunch length (equals 1 mm for TESLA and36 mm for this stage.).k|| = 6.6x1012 x ( 200 MHz1300 MHz)2x 1x10-336 x10-3= 2.6 x 1010 Volts/CoulombTotal HOM Power =  k|| x Length x (Bunch Charge)2 x Bunch Frequency x Number of Recirculations=230 WHOM power couplers have to be designed to extract 90%of this power, which is well within the range of presentHOM coupler technology.  Allowing for an averagedistribution system heat load of 0.5 W/m, the totalcryogenic heat load is thereforeTotal Cryo Heat Load = 685 (dynamic) + 2600 (static) + 23 (HOM fraction) + 265 (distribution)=3573WCapital and Operating Cost EstimatesWith economies of scale and cost dependence on frequencywe estimate that the unit cost for the cryomodules will begiven byCryomodule Cost per meter =133x103 x [0.8]Log (L) x 1300 MHzFrequency (MHz)For L = 260 m of 200 MHz structures, the result is of theorder of 200 k$/m.  The capital cost for the refrigerator isabout 1300 $/watt at 4.5 K.  For higher energy stages thatoperate at 2 K we have increased the capital costcoefficient by a factor of 2.A 1992 survey of klystron peak power cost showed thatthe cost increases with pulse length as shown in Fig.3.For 1 ms pulse we anticipate a unit cost of 0.06$/peakwatt. To this we add the cost of the High Voltage powersupply and modulator for each klystron at 0.5 M$,resulting in a unit RF cost of 0.73 M$ per klystronsystem.  In summary, the capital cost distribution for 7-50 GeV acceleration stage turns out as:Table 2Linac 51  M$RF 82  M$Refrigerator 4.3  M$Total Capital 138 M$Note that the RF cost dominates.With a klystron efficiency of 0.65 and an overallrefrigerator efficiency of 3x10-3, the total AC power is9.6 MW.  The beam power to AC wall power efficiencyis a not too impressive 4%.  This is because of the smallnumber (11) of recirculations for this stage.  For thehigher energy stages the efficiency rises.Table 3 shows the results of comparable calculationscarried out for the other acceleration stages.  Thealgorithms have been adjusted to take care of different RFfrequencies and different operating temperatures.  Note thatthe efficiency rises to 20% at the top energy.Table 3:Energy Span(GeV)RF Fre -quency (MHz)ActiveLength(m)Peak RFPower(MW)Heat Load(W)CapitalCostM$AC Power(MW)Efficiency(%)Linacs0.4 - 0.6 100 13 72 211 18 1.4 0.140.6-1.0 200 27 72 325 15 0.76 0.5Recirc.Linacs1-2 100 8 195 103 20 1.2 0.82-7 200 33 365 382 30 1.3 3.6*7-50 200 260 430 3575 138 10 3.850-200 800 500 412 4168 105 7.2 20200-1000 1300 1185 1223 31900 310 37 211000-1500 1300 1175 500 23640 220 27 18Totals 3200 3269 64. kW 856 86NeutrinoFactory0.6-1 200 27 163 311 20 1 0.231- 10 200 150 915 1600 109 5.8 0.9410-50 200 666 1148 8285 267 26 0.92Totals 842 2226 10.2 kW 396 334  MUON STORAGE RING FORNEUTRINOSThe path to a 3 TeV muon collider is filled with manychallenges.  A time scale shorter than 20 years seemsunlikely.  Recall that the TESLA effort was started around1987, and is still many years towards completion.  As afirst step, the collaboration is very interested in building aMuon Storage Ring based neutrino source.  Atmosphericneutrino, solar neutrino and short baseline acceleratorexperiments accumulate evidence to show that neutrinoshave a small but finite mass.  If this is confirmed, itcould be a big part of the solution to the "dark matter"problem: "Where is 90% of the mass of the universe?"  Ifneutrinos have mass, then according to the theory theyshould oscillate in flavor, which opens up exciting fieldsof neutrino flavor physics, such as the search for CPviolation in neutrino interactions.The goal of the neutrino factory would be to provide 3 x1020 muon decays per year.  The demands on muoncooling are much reduced over that for a collider.  Onescenario[6] calls for three acceleration stages: 1 GeV linacfollowed, by two recirculators.  Only four recirculationloops are envisioned, which results in a rather lowefficiency.  The last part of Table 3 shows the capital costitems.ACKNOWLEDGEMENTSI am grateful the members of the Muon ColliderCollaboration for an interesting education, in particular:Norbert Holtkamp and Scott Berg.REFERENCES[1] C.N. Ankenbrandt et al, BNL 65623[2] m + m - Collider, A Feasibility Study, BNL 52503(1996)[3] D. Trines, this conference.[4] F. Palmer, PhD Thesis, Cornell University (1988).[5] P. Kneisel and K. Saito, this conference.[6] N. Holtkamp, priv. comm.Fig. 1: Generic Layout for a 3 TeV collider [2].1000010001001 0110100Pulse length  (µsec)Peak Power/klystron ( MWatt)Fig. 2: Peak power of klystrons vs. pulse length.1000010001001 0.01.11Pulse Length (µsec)Klystron Cost ($/peak watt)Fig. 3: Unit cost of klystron peak power vs. pulse length.

SRF for Muon Colliders

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